Multiple Physics, Multiple Approaches

When adding the physics for a multiphysics model, there are a number of ways in which you can handle the physics setup. In COMSOL Multiphysics, there are three different approaches:

1. Fully automatic
2. Manual with predefined couplings
3. Manual with user-defined couplings

Each approach is advantageous for different modeling scenarios and varies in terms of ease of implementation and amount of effort required from the user. The manual approach involves selecting the individual physics interface and then adding the multiphysics couplings. This is typically done in a sequential order and by conducting multiple standalone analyses to incrementally build up to the multiphysics problem. The user-defined couplings involve including user-defined expressions, equations, or functions to combine the physics in your model when there are no predefined multiphysics couplings available. In this post, we will focus on the fully automatic approach and address the two others in subsequent blog posts.

The Automatic Approach for Defining a Multiphysics Model

The fully automatic approach is a highly recommended way to add physics for a multiphysics model. By automatic, we mean to use the predefined multiphysics interfaces that are built in and readily available in COMSOL Multiphysics, as well as automatically preconfigured for the multiphysics interaction being simulated. These interfaces are available for several disciplines of engineering and type of application area, including electromagnetics, structural mechanics, acoustics, fluid flow, heat transfer, and chemical engineering.

Multiphysics interfaces make the modeling process simple. Their use automatically adds all of the necessary physics and couplings to your model at once. Additionally, they automatically include the optimal element discretization settings for the combination of physics in a model. In these ways and more, the automatic approach lets you more quickly dive into defining the physics for a multiphysics model without having to get bogged down with the small details or do all of the work from scratch.

For a complete list of the multiphysics interfaces available to you for any COMSOL products you hold a license for, you can view the Specification Chart. There are a number of ways you can browse the chart, as noted in a previous blog post. Simply select the application area your module(s) fall under or the modules themselves (or both) and scroll down to the Predefined Multiphysics Interfaces section to see the list of built-in interfaces.

The Specification Chart with the Acoustics application area selected.

Below, we highlight one example of the numerous multiphysics interfaces included in the software, as well as what it can be used for.

Multiphysics Modeling: A Plasma Example

Perhaps you work in the plasma sciences and need to build a multiphysics model observing several effects, such as in plasma arc welding applications. Modeling this complex process requires including and coupling electricity, magnetism, heat transfer, and fluid flow. In COMSOL Multiphysics, you can use the Combined Inductive/DC Discharge multiphysics interface to automate the entire physics setup, thus enabling you to define the multiphysics phenomena present in plasmas in a significantly easier way.

The Combined Inductive/DC Discharge multiphysics interface selected and added under the Plasma branch of the Physics Wizard, with the branch containing the multiphysics couplings expanded.

Modeling Resistive Heating and Thermal Expansion Using the Automatic Approach

Let’s use the thermal-electrical-mechanical (“tem”) version of the thermal microactuator tutorial model found in the Application Gallery on the COMSOL website, to demonstrate the automatic approach for adding the physics for a multiphysics model.

Note: For the sake of brevity, assume that all steps in the modeling workflow, apart from defining the physics, are complete. Thus, the geometry, materials, mesh, and study are already set up. Additionally, we will narrow our focus to defining the multiphysics aspects of the model and not go into detail regarding how to add and define specific boundary conditions for the constituent physics interfaces.

First, we define the physics for Joule heating and thermal expansion. A voltage is supplied to the bottom of the anchor on the middle arm. The conducted current is resisted as it flows through the actuator, resulting in electric heating, which raises the temperature of the device and causes it to deform. The base of all of the anchors are fixed, but the dimples enable the arms to translate in the xy-plane.

The thermal microactuator geometry with the parts labeled. The device is made of polysilicon.

To study the electrical-thermal-structural interaction that occurs, we can use the predefined Joule Heating and Thermal Expansion multiphysics interface. To include this interface in the simulation:

1. Open the Add Physics window
2. Expand the Structural Mechanics branch
3. Select and add the Joule Heating and Thermal Expansion interface to the model component

The Joule Heating and Thermal Expansion multiphysics interface being added to a model component.

Upon adding Joule heating and thermal expansion to a model, notice that several physics nodes have also been added to the model tree. These include the Electric Currents interface; Heat Transfer in Solids interface; Solid Mechanics interface; and a multiphysics node containing the couplings for electromagnetic heating, the temperature field, and thermal expansion.

A screenshot of the physics setup that is automatically added when using the automatic approach.

The electromagnetic heating multiphysics coupling passes the resistive heating induced from the electrical problem (the current conducted through the actuator) to the heat transfer problem. The temperature multiphysics coupling passes the temperature field from the thermal problem (the heating of the actuator) to the structural problem. Depending on the materials assigned to the geometry, it also passes the temperature back to the electrical problem so as to modify any material properties that are temperature dependent, such as the electrical conductivity. Lastly, the thermal expansion multiphysics coupling combines the thermal problem with the structural problem (the structural stresses and strains induced due to thermal changes) by including the temperature field as a thermal load.

This is why we always recommend using the automatic approach whenever possible. By adding the multiphysics effect you want to analyze, it instantly adds all of the appropriate individual physics interfaces, automatically couples them, and includes the modified settings that are optimal for computing the combination of physics included in your simulation. You don’t have to worry about recalling if you’ve included the correct multiphysics nodes or applied the appropriate settings from one physics interface to another, since it is all automated.

From this point forward, we can focus on defining the physics for each individual physics interface, such as adding any necessary boundary conditions or constraints and editing the settings.

To see how to build the complete model using this approach, see the thermal microactuator tutorial model in the Application Gallery.

Speed Up the Model Building Process

Take advantage of the multiphysics interfaces and options available for different physics disciplines that are available in the COMSOL® software, which, in tandem with the multiple setting modifications performed automatically, provide several distinct benefits.

Watch the related tutorial video to see a demonstration of the fully automatic approach. The video uses the Bracket – Thermal Analysis tutorial model as an example, so between this blog post and the video, you get to see two different multiphysics examples!

Stay tuned for future blog posts that will discuss the other two manual approaches, using predefined couplings or user-defined couplings, for setting up a multiphysics model…

Tutorial Video: Performing a Parameter Estimation Study in COMSOL Multiphysics®

Using the Parameter Estimation Study Step for Inverse Modeling

Suppose that you have a set of external data (either from experimental measurements or a collection of reference data) that you want to model your simulation after. In this situation, you can use inverse modeling. As the name implies, inverse modeling is when you take a reverse modeling approach to your problem: Instead of solving for the outcome, you solve for the inputs.

To get the desired simulation results, there are several model inputs that you might want to investigate or experiment with, such as material properties. When solving for the values of these inputs, you are looking for the optimal values that provide you with the closest match between a set of external data and the simulation results. A natural approach is to minimize the sum of the squares of the differences between the data sets. As such, an efficient modeling strategy is to formulate the problem as a least-squares optimization problem. To streamline the process of setting up and solving the problem, you can use the Parameter Estimation study step in the COMSOL Multiphysics® software.

To use the Parameter Estimation study step, the study must be time dependent and a license for the Optimization Module is required. In addition, a set of reference data needs to be included through either an interpolation function or user-defined reference expression. Note that the reference data must either be time dependent or a function of a single argument.

The Settings window for the Parameter Estimation study step.

The Parameter Estimation study step is useful for a variety of inverse modeling problems — mainly parameter estimation. The objective is to estimate values for the desired model inputs (i.e., parameters), which provides insight into the ways that the values (and hence the properties themselves) affect the objective function.

Perhaps one of the most typical uses of this functionality is curve fitting or similar data-fitting applications. This process involves fitting a function to a series of data points. The fitting of the function is done by estimating the values for the coefficients used in the function, essentially fitting a parameterized analytic function to a collection of data. By fitting a curve to a set of data points, we can interpolate values from the function to areas where data isn’t explicitly available.

In the tutorial video at the top of this blog post, we demonstrate a parameter estimation via a modified version of the elbow bracket tutorial model. Before computing this study, we need to properly define the problem…

Performing a Parameter Estimation Study in COMSOL Multiphysics®

Performing a parameter estimation study generally involves three major steps:

1. Prestudy: preparing the definitions, such as the parameters, variables, and functions
2. Study setup: customizing various aspects of the study and computing it
3. Poststudy: postprocessing to visualize and compare the simulation and experimental results, as well as extracting the optimal values for the estimated model inputs

Let’s look at how to complete these steps and the important factors to consider when setting up the Parameter Estimation study step in a model.

Step 1: Preparing Definitions for a Parameter Estimation

Before we perform a parameter estimation study, we must create the definitions needed to formulate the problem. This typically involves creating a combination of parameters, functions, and variables. First, we define the parameters of the model inputs for which we want an estimated value. Next, we include the external data by defining either a reference function or expression. Lastly, we define a variable that pulls and evaluates the output quantity from the simulation results, which are compared to the measured output data.

In the video above, we perform a time-dependent heat transfer analysis on the elbow bracket. The model data from the heat transfer simulation is then compared to the experimental data, which is used to estimate the value for the thermal conductivity of the material.

In the Heat Transfer in Solids node, the thermal conductivity is represented by k. Hence, we create a parameter named k, enter a rough estimate of its value, and use it in the appropriate node to define the thermal conductivity.

Left: The parameters used in the parameter estimation study, including the parameter k for estimating the thermal conductivity. Right: The node (named Solid 1) in which we use the parameter k to define the material property to be estimated.

Next, we create a definition so that we can implement the data from our external file into the COMSOL® software. In this case, the reference data is a collection of time-dependent temperature measurements contained in a comma-separated values (CSV) file. This data can be quickly and easily entered into COMSOL Multiphysics by adding an Interpolation function to our model component and then using the Load from File button. The data is automatically imported in a tabular format, with the first column containing the times and the second column containing the temperature measurements.

The Interpolation function incorporates the reference data into the simulation. The Load from File button is used to import the external file into the function.

Under the Units section, we simply enter the respective units for the argument (time) and function (temperature). We do not need to be concerned with the options selected for the Interpolation and Extrapolation settings of the function, since the study only computes the differences at the times explicitly stated in the argument or t column of the function. Thus, the smoothing between data points and the behavior of the function outside of the range of the data is not relevant.

We now need to define an expression to extract the temperature quantity from the simulation results. (This quantity is later compared to the temperature measurements in the interpolation function.) The quantity we want to extract and use for comparison is the average temperature of the surface on the top-right end of the bracket.

Since we want to obtain the average of a quantity (temperature), we first add an Average component coupling under the Definitions node. We then select the geometry we want to obtain the average temperature for (i.e., the boundary on the top-right end of the elbow bracket). Note the tag in parentheses to the right of the Average component coupling, aveop1, as this will be used in the expression for defining our variable.

The Average component coupling (highlighted in blue) helps us obtain the average value of a quantity on the selected geometry.

To compare the computational and experimental results, we must define a variable to extract the quantity, and thus its value when computed, from the simulation results. Since we are looking at a specific part of the geometry, we define a local variable under the Definitions node or the Definitions ribbon tab. (A global variable is not suitable for our study, as the Global Definitions node is global in scope and defines, applies, or evaluates an expression over the entire model geometry.)

When defining the variable, we name it Tave, since we are looking to obtain the average (ave) temperature (T). For the expression, we can call out to the Average component coupling created earlier by entering aveop1. We then specify the quantity that we want the average of by entering the variable T (for temperature) in parentheses.

The defined variable, which is later used in the Parameter Estimation study step.

Step 2: Setting Up and Computing the Study

Now we can add and set up the Parameter Estimation study step, for which several settings have already been handled. The reference data and study step selections are automatically linked to the interpolation function that contains the external data and the time-dependent study.

The expression entered in the Model expression field is evaluated and then compared to the external data at each time step specified in the reference function; i.e., each time in the argument column of the interpolation function. As such, this field is where we enter our local variable, Tave.

Notice that in the syntax of the Model expression field in the images below, we specify the location of our local variable, component 1, by including it before the variable name. The reason is that the scope of the Parameter Estimation study step is global. As a result, the study step does not “see” variables defined locally within a component unless we indicate their scope in the expression. For a global variable, we simply enter its name in the Model expression field. To enter the variable with its scope specified automatically, you can use the Auto Completion feature to select and enter the variable from the list of definitions.

Left: Using the Auto Completion feature to select the local variable defined earlier. Right: A screenshot of the completed setup for the Parameter Estimation study step.

Now we just need to identify the parameters we want to estimate and select the optimization method. We provide a rough estimate for the parameter under the Initial value column, add an upper and lower bound for the values that the parameter can take, and set the Scale value. Applying the appropriate scale is important, as it can significantly slow down the convergence of the optimization solver or stop it from converging altogether. Using the default value works for the elbow bracket example, but it might not always be suitable. (For more information, read the chapter on parameter estimation in the Optimization Module User’s Guide.)

Next, we want to select the appropriate optimization algorithm and compute it. The different methods apply to certain use cases, which are discussed in further detail in the video. Since the parameter we want to estimate controls the value of a material property — and we want to impose an upper and lower bound on the value — we use the SNOPT method.

Step 3: Comparing Results and Extracting Input Values

Once the model finishes solving, we need to perform some additional postprocessing. We can visualize and compare the two sets of data by plotting the results, and then we can extract the optimal values for the estimated model inputs. To see and compare both sets of data on a single plot, we add a new 1D Plot Group and include two Global plots under it. One Global plot displays the simulation results, while the other displays the reference data.

Since our interpolation function is a collection of data points, we want it to appear as a point graph. To do so, we change the time selection of the data points so that they are only plotted at the times specified by the argument column of the function. Additionally, we adjust several of the settings in the Coloring and Style section to further distinguish the two sets of data.

Comparison of the simulation and experimental results. The highlighted sections in the Settings window need to be adjusted to display the experimental data as a point graph.

This plot shows that the model results closely match the experimental data. We can now extract the optimal value for the thermal conductivity of the elbow bracket material. To do so, we add a Global Evaluation node under the Results tab (or under the Derived Values node). In the Settings window, all we need to do is update the Time selection option to Last so that we can evaluate the value in the last time step, since the thermal conductivity is independent of time.

The Settings window for the Global Evaluation node.

After entering the parameter k in the Expression field, we click Evaluate and are provided with the optimal value for that parameter.

The optimal value for the thermal conductivity.

As shown above, a thermal conductivity of ~0.27 W/(m*K) provides the simulation temperature results that best match measurements from experimental data.

Modeling in Reverse via the Parameter Estimation Study Step

In COMSOL Multiphysics, the Parameter Estimation study step helps estimate the optimal values for the inputs of a simulation. By estimating the values that define various aspects of a model, you can investigate the parts of the problem that either hinder or help in best matching the computed results with a data set from an external file.

This functionality also enables you to solve other types of inverse modeling problems by streamlining and expediting the process of defining, setting up, and solving a least-squares optimization problem. For more details about this useful study step, watch the tutorial video at the top of this post, which provides guidance on how to use this functionality with a simple example.

Additional Resources

To learn more about parameter estimation in COMSOL Multiphysics, its use cases, and the various study step settings, read the chapters on parameter estimation in both the Introduction to the Optimization Module and Optimization Module User’s Guide documentation.

An archived webinar on parameter estimation is also available. (Note that the archived webinar uses the Optimization interface instead of the Parameter Estimation study step.)

Geometry Creation in COMSOL Multiphysics®

There are four main ways you can generate the geometry for your simulation in COMSOL Multiphysics:

1. Draw the geometry within the COMSOL® software
2. Import an external CAD file
3. Use one of the LiveLink™ products
4. Import mesh data from an external file

Each of these means of geometry creation provides different opportunities and advantages. The first method enables you to generate your geometry using only the COMSOL Multiphysics modeling environment. This method is the focus of today’s blog post, as we will discuss its associated workflow.

The general steps for creating a geometry include:

1. Building geometry primitives corresponding to the model’s spatial dimension
2. Using geometry operations (such as Boolean, partition, and transformation operations) to manipulate existing geometries to a new one
3. Indicating how the software should deal with overlapping objects using Form Union or Form Assembly

Sometimes, it can be more efficient to create geometry primitives in lower dimensions using work planes and then extend them into the dimension that was not initially considered. Work planes can also be used to define cross sections from a higher dimensional entity to a lower dimensional workspace.

Let’s now dive further into the details of using geometry primitives, geometry operations, and work plane operations. Note that these operations can be used for geometries native to COMSOL Multiphysics as well as those created through another CAD program.

Using Geometric Primitives

COMSOL Multiphysics contains a number of ways in which you can generate the objects for your geometry. One option is to choose an object from the selection of built-in geometric shapes in the software, select and add the primitive object to your geometry sequence, and then edit the template provided through the Settings window. This enables you to specify the exact position, angle, and dimensions of the object as well as to quickly make changes to any of those settings, if needed. Once in the sequence, the object can then be combined and manipulated with other primitive objects to form your final geometry.

Creating and modifying a rectangle using the Settings window in COMSOL Multiphysics.

The types of objects available for you to choose from depend on the spatial dimension of your component. This includes geometric primitives for conventional shapes as well as other less traditional shapes. For 3D models, you can add objects like blocks or spheres as well as torus or helix objects. Similarly, for 2D models, primitives such as rectangles, circles, Bézier polygons, and parametric curves are available.

Another option for generating objects in your geometry sequence, available for 2D and 1D models, is to sketch geometric primitive objects with the mouse.

This is done by:

1. Clicking on the respective button for the object you want to build
2. Using the mouse in the Graphics window to click and define the center or corner of the object
3. Dragging the mouse to generate the desired size and then clicking again

Immediately afterward, the object you have outlined appears and is added to your geometry sequence.

Creating and modifying a rectangle using the geometry drawing tools.

For 3D models, although you cannot sketch a geometry primitive with the mouse, you can draw a cross section of it in a work plane, which can then be expanded into a 3D object. We demonstrate both options mentioned above in dedicated chapters within the building 2D geometries part of the video series. Additionally, we discuss the advantages of using parameters during this process and demonstrate how they aid in streamlining your geometry setup.

Boolean, Transformation, and Partition Operations

After generating a few objects in your geometry sequence, you can start to combine them in meaningful ways using geometry operations. In the video chapters on building 2D geometries and 3D geometries in our series, we build a rectangular plate containing slots and a grille, respectively. This was done by using a combination of several Boolean and transformation operations.

The rectangular plate with slots (left) and with a grille (right).

The Boolean operations used to create the geometries pictured above include the Union, Intersection, and Difference operations, which enable you to combine objects, create a new object from the intersection of other objects, and subtract objects from one another, respectively. Likewise, the transformation operations used include the Move, Copy, Mirror, and Array operations, which enable you to change the position of objects; create duplicate objects; reflect objects over a plane, line, or point; and create an arrangement of duplicates of another object.

Aside from some of the more conventional geometry features used above, there are also specialized geometry tools used to help create certain types of geometries. Partition operations enable you to split geometric entities such as objects, domains, boundaries, and edges so that you can separate, remove, or simplify the geometry in your model. When we discuss using partition operations for geometries in the video, we demonstrate how to perform this on a helix object as well as the geometry for the shell and tube heat exchanger tutorial model.

A helix geometry split down the middle, from our video chapter on partitioning geometries.

As you continue to build upon your geometry (adding more of these operations and other primitives to your sequence), you’ll notice that your sequence can become quite complex and that making any changes thereafter can become cumbersome. Changing the size of one object in the geometry may require other objects to be resized to accommodate that change. For these and other reasons, we encourage the use of parameters in the geometry operations you use in your sequence. We discuss the reasons for this and demonstrate how with a few of the example geometries built throughout the video series.

Work Plane Operations

COMSOL Multiphysics contains several tools known as work plane operations, which can be used to convert a 2D geometry in a work plane into a 3D object. In the video series, we show and demonstrate the Extrude, Revolve, and Sweep operations.

The Extrude operation enables you to extrude objects from a work plane or planar face to create 3D objects.

The Extrude operation, converting a rectangular plate with holes into a 3D block containing slots. The blue arrow in the center represents the direction in which the shape is extended, which is perpendicular to the work plane.

With the Revolve operation, you can revolve objects from a work plane or planar face about an axis to create 3D objects.

The Revolve operation, converting a circle into a torus. The blue arrows represent the axis about which the shape is revolved.

Finally, there’s the Sweep operation, which enables you to sweep objects from a work plane or planar face along a path to create a 3D object.

The Sweep operation, converting a circle and 2D line path into a pipeline. Two work planes that are perpendicular to each other are used to define the shape and line path separately.

Using these work plane operations (starting from a 2D model and then expanding it into 3D) can be a significantly quicker alternative for building your 3D geometry, as opposed to building it entirely of 3D objects.

Cross Section Geometry Operation

The COMSOL Multiphysics software also contains a tool for converting a 3D geometry into a 2D geometry. This is done through using a work plane along with the Cross Section geometry operation. The functionality can be used to simplify your model, among other things, which we discuss in the video series.

The axisymmetric cross section of a light bulb, built in the video chapter on creating 2D models from 3D geometries.

The geometry generated through the Cross Section operation is based on the intersection of your 3D geometry with a work plane. Thus, the 2D geometry you obtain is the result of wherever the work plane cuts through the 3D solids in your model. Within the operation, you can choose for the work plane to intersect (and thus include) all objects or a selection of objects that you specify.

To obtain the appropriate cross section for your analysis, using this functionality may require performing some additional preparation on the original 3D geometry. Sometimes, this means separating and then removing certain parts of your geometry, wherein partition operations can be helpful. We elaborate on this further and demonstrate it in a dedicated chapter within the video series.

Next Step: Watch the Introductory Video Series on Using Geometry Tools

Whether you are building a geometry entirely within COMSOL Multiphysics or working off of an external file, you can use the geometry functionality discussed in this blog post to completely customize the composition of your geometry objects. If you are interested in seeing these tools in action, watch our introductory geometry video series:

Tutorial Video: Using the Find and Auto Completion Tools in COMSOL Multiphysics®

Searching Within a Model Using the Find Tool

With the Find tool, we can search within a model for a parameter, variable, or even general text. To open this tool, we either click the respective Find button on the Quick Access Toolbar (or the Main Toolbar for the Linux® operating system and macOS) or use the Ctrl+F keys.

The Find button in the Windows® operating system version of the COMSOL Desktop®.

The Find tool searches the entire model for every instance that a search entry is used throughout the nodes of the model tree. We can search for all components and their sequence of operations, node names, identifiers, tags, and labels by using the Find tool.

After opening the Find tool, we have several options with which we can conduct our search. Using the All tab enables us to search the model itself, while using the Methods tab lets us search within the Method Editor of the built-in Application Builder tool. There are also check boxes that we can use to obtain specific results, including:

• Exact matches
• A text string within a model, using the regular expression syntax
• Case-sensitive searches

In the tutorial video at the beginning of this blog post, you can get a detailed demonstration of how to search with the All tab. For more information on the other option for the Find tool — in the Methods section of the Application Builder — see the “Find and Replace” section of the Introduction to Application Builder documentation.

The Find tool.

After performing a search, a new tab appears in the Messages/Progress/Log window. This new Find Results tab is where we can find our search results in table form. The table lists every instance that the term or terms that we searched are used throughout the model. We can double-click any row within the table to automatically be redirected to the node and section in which the parameter or variable is being used.

In the tutorial video, we show how the Settings window and node selected in the Model Builder update as we toggle between several of the rows in the search results table. Additionally, each column within the table lists properties such as the node it is being used under, the context of how it is being used within the node, and the text with which it appears through the Node, Type, and Text columns, respectively. In the Text column, if we search some terms used in an expression, for example, the software provides the other text and characters that are a part of that same expression. If we search text that appears in the description for a parameter, the remaining text part of that description column also appears.

Every time we complete a new search, a new Find Results tab opens. This means that we can always refer back to previous search results in the designated tabs. Additionally, as we continue to work on and adjust a model, we can refresh the table to repopulate the search results.

How to Use the Auto Completion Tool

When you want to quickly recall and use parameters, variables, functions, and other definitions that you have created in your simulation, you can do so by using the Auto Completion tool.

To open this tool, we hold down the Control key and press the space bar while in the Expression field of any window.

The Auto Completion tool, used to define a Heat Flux boundary condition.

When using a second input language, an alternative shortcut is to hold down the Control key and press the Forward Slash key.

When we create a model and progress through each step of the modeling workflow, it can become cumbersome to have to return to the node and window section where a definition such as a parameter, variable, or function is originally defined. This is especially the case when working with large or complex models that use numerous definitions.

The Auto Completion tool enables us to quickly and easily formulate expressions and fill in the settings for almost any node in the model tree, such as when defining a physics boundary condition. Almost anywhere we enter an expression in the software, we are able to use this functionality.

In the tutorial video, we demonstrate how to use the Auto Completion tool to define a parameter, review several categories of definitions and operators available when defining a variable, and show how to define a boundary condition in a model.

After prompting the Auto Completion window to open, we can access not only the parameters, variables, and functions that we’ve defined, but also several other categories — including math operators, physical constants, and other operators. Keep in mind that the categories available for selection will vary depending on the node under which we work. Different options will be available when we enter an expression within a geometry node versus a mesh or physics node. For example, if we use the Auto Completion tool to define a parameter, we can use other parameters defined previously in the Parameters table. If we used the Auto Completion tool to define a variable, we are able to implement other variables as well as parameters in our expression.

Streamline Your Modeling Workflow with the Find and Auto Completion Tools

No matter the simplicity or complexity of your simulation, the Find and Auto Completion tools are useful for your modeling workflow. Whether you are dealing with 5 or 50 parameters, being able to quickly and easily locate where a definition is used and access it to define other aspects of your simulation makes the process of setting up your model more efficient. To learn how to take further advantage of these features in COMSOL Multiphysics, watch the video at the top of this post.

Additional Resources

• Learn about other modeling tools and resources on the COMSOL Blog:
  • How and When to Open Recovery Files in COMSOL Multiphysics®
  • Using the Help Tools in COMSOL Multiphysics® for Modeling Guidance
  • Using the COMSOL Website Resources for Modeling and Software Help
• Browse more tutorials on the core functionality and tools available in COMSOL Multiphysics in the Video Gallery

The COMSOL Blog

If you are reading this post, you most likely already know how useful of a resource the COMSOL Blog can be. If this happens to be your first visit and you are a new reader, welcome to the blog! Whether you are a new user of COMSOL Multiphysics, are familiar with the software, or are looking for more information on multiphysics modeling and simulation, the COMSOL Blog contains a plethora of content that caters to your needs.

The COMSOL Blog (how meta!)

We publish new blog posts here multiple times per week. These posts cover a wide variety of topics, from the COMSOL® software to interesting news in the science and engineering community. We have covered frequently asked questions from COMSOL Multiphysics users, modeling strategies for different types of physics, how industry leaders use multiphysics simulation for innovative product development, and even the science and physics behind effects observed in the real world.

On the top-right corner of this (and any other) blog post, you can click on the Get New Posts by Email button to subscribe to the blog. This enables you to stay up to date with every new post.

We encourage you to discuss the information you find on the blog with colleagues and peers by using the Comment section found at the bottom of every post. Note that you will need a COMSOL Access account to post a comment.

Post a comment sharing your thoughts about the blog post.

The COMSOL Video Gallery

Another valuable resource on our website is the COMSOL Video Gallery, which includes over 200 videos. Similar to the blog, this space is also updated with new content on a regular basis. These videos are especially helpful if you happen to be a visual learner.

Many of the videos in the Video Gallery can also be viewed on the COMSOL YouTube channel.

There are several types of videos in the Video Gallery that serve different purposes, the most prominent being instruction. These videos include tutorials, model demonstrations, and archived webinars. Our tutorials, both individual videos and tutorial series, cover core functionality topics and modeling processes — many of which are applicable regardless of your field.

Each tutorial video includes:

• An introduction to the topic
• An overview of what you will learn
• Applications and use cases
• A step-by-step, detailed demonstration of the topic
• A summary of the key facts and points to remember
• Next steps you can take

Model demonstration videos offer a broader overview of simulation for certain application areas and show how easy it is in the COMSOL® software. Archived webinar videos feature recordings of previously aired online seminars conducted by COMSOL staff and include a software demonstration.

A small portion of the Video Gallery, featuring some of our postprocessing tutorial videos.

Product overview videos, also available to watch in the Video Gallery, teach you about the products we offer and special features of the add-on modules. While product overview videos inform you of the potential of what you can do in the software, the user perspective videos show you how other people use it. These videos highlight the breadth and depth with which COMSOL® software users combine their knowledge and expertise with the power of multiphysics simulation to further innovate technology and product development.

The Application Gallery

Just as the COMSOL Blog is a great place to learn by reading and the Video Gallery is a great place to learn by watching, the Application Gallery enables you to learn through practice. This part of the website contains over 800 models, spanning every engineering discipline and industry. Whether you are developing an electrical, mechanical, fluid flow, heat transfer, or chemical application, you can search the gallery and find relevant tutorial models.

Examples of tutorial models included in the Application Gallery.

Besides downloading these models, you can also access accompanying documentation that provides detailed background context and insight. By logging into your COMSOL Access account, you can download model files and documentation from the Application Gallery.

Many of the tutorials and demo apps in the Application Gallery can also be found directly in the product via the Application Library.

The Discussion Forum

As a follow-up to how the Application Gallery fosters learning through practice, the Discussion Forum provides a space where you can connect with other COMSOL Multiphysics users and get their insight on various topics. The forum is a place to communicate with other software users in the multiphysics simulation community regarding topics of interest, formulating problems, new and alternative modeling approaches, modeling challenges, and other modeling and simulation topics.

Whatever the case or question may be, this platform serves as a great place for you to discuss ideas with peers. Although you are free to view and read through forum threads and posts, in order to take part in the conversation, you need to log into your COMSOL Access account.

The Model Exchange

The Model Exchange is another community-oriented outlet where COMSOL Multiphysics users can share and exchange ideas. Through this platform, you can share models and papers as well as access those created by other users. Similar to the blog, each entry can be discussed through the Comment section on the page. Again, if you are logged into your COMSOL Access account, you can download entries or post comments.

The Support Knowledge Base

Another resource available online through the COMSOL website is the Support Knowledge Base. This space contains solutions, background information, and examples for FAQs about the software. These topics include, for instance, issues when installing a COMSOL® product, how to reference the simulation software in research papers and publications, and error messages while working in the software.

Next Step: Watch a Video on Using the COMSOL Website Resources

Whatever your preferred learning style — whether it’s reading, watching, practicing, or discussing — we try to provide you with resources that cater to your needs. Next, watch a tutorial video to see how to access each resource on the COMSOL website and learn how they can be useful to you.

As we mentioned earlier, although you are free to search and view all of the above resources, we encourage you to create a COMSOL Access account. This will enable you to take full advantage of all that they have to offer. To create an account, you can go to the COMSOL Access page. Then, join the discussion below! What is your favorite COMSOL resource to use?

The Help Window

When setting up a simulation in COMSOL Multiphysics, you may want to seek out more information on the software as you go. Whether it’s learning about a node in the model tree, the settings for an operation you’re currently working in, or the differences between a set of options you are choosing from and what they will mean for your model, it’s helpful to have guidance available at your fingertips. This is the convenience that the Help window in COMSOL Multiphysics provides.

The Help window, displaying topic-based content for the Electric Potential boundary condition.

The Help window, accessed by clicking the Help button in the top right-hand corner of the software (the blue question mark) or the F1 key on your keyboard, enables you to promptly access information pertaining to the model tree node or window in which you are currently working. The text that displays updates automatically as you select items in the software or add settings to your model. This enables you to instantly get help right when you need it.

Since this window appears in the COMSOL Desktop® when opened, you can access the information you need without having to compete for screen space with your simulation. Instead of having to fit multiple windows on your monitor, you are able to view the help content and Model Builder together.

Additionally, you can search and navigate the text in the Help window using the respective buttons.

The Documentation Window

In addition to receiving topic-based help, there may be times when you want to more easily access, navigate, and search all of the comprehensive COMSOL Multiphysics documentation. This includes the user guides and manuals for any modules for which you have a license. You can find this documentation in the Documentation window, which you can access either from within COMSOL Multiphysics, by going to File > Help, or externally from your computer in your COMSOL Multiphysics installation folder.

The Documentation window, with the AC/DC Module User’s Guide opened.

The Documentation window enables you to quickly and easily access your entire library of COMSOL Multiphysics documentation, all within a single window. When open, you can choose between the PDF or HTML version of any guide, manual, or handbook. Additionally, the sections of each individual document are hyperlinked and bookmarked. The sections are displayed on the left side of the window, as shown above. This enables you to quickly jump between different chapters and documents.

This resource also provides more options when it comes to searching through the software documentation. This includes the ability to search through the entire library, only within a specified set of documents you have preselected, or exclusively through the Application Library Manual for all licensed products. Searching the Application Library Manual, in particular, enables you to find models and applications that demonstrate use of some specific physics, software features, and functionality.

Whereas the Help window provides quick access to documentation while modeling, the Documentation window serves as a more comprehensive resource when you need further clarification and more powerful search tools.

The Application Libraries Window

Now you know that you can access information about what you are working on. The ability to access modeling examples relevant to your work is equally as important. These examples enable you to learn how to use the software, examine COMSOL Multiphysics models, and access guidance that you can apply to your own simulations. In the COMSOL® software, the modeling examples can be found in another valuable resource, the Application Libraries window.

The Application Libraries window, with the Thermal Actuator tutorial model selected and displayed.

The Application Libraries window, accessed by going to File > Application Libraries, contains hundreds of models and simulation applications, spanning every module and engineering discipline. Using the Search field, you can find applications and models that cover some specific physics or feature that you want to see how you can use. Each entry includes a brief summary of the model; the COMSOL Multiphysics model file; and a PDF document that provides a comprehensive introduction and detailed, step-by-step overview of the model-building process. This provides you with the logic behind how the model is built, why and how boundary conditions are applied, and other useful information that you can use as insight into the models you create.

By following along with any of the tutorial models available, you can experience building a model firsthand. In addition, relevant examples from the Application Libraries can be experimented with and expanded upon, serving as a starting point for your own designs.

Tip: The tutorial models and demo applications featured in the Application Libraries are also available online in the Application Gallery.

Next Step: Watch a Video on Using the Resources and Help Tools in COMSOL Multiphysics®

Now that we’ve introduced the help tools available in the COMSOL® software and the advantages they provide, watch our video tutorial covering it all. In the video, we demonstrate how to access and use each of the resources discussed above.

After you’ve finished watching the video, you’ll be ready to use all of the help tools and resources available to you in COMSOL Multiphysics.

Conduct Material Sweeps to Automate Comparing Materials

When assigning materials to your model geometry, you may want to experiment with a few options and see how different materials affect your simulation results. In COMSOL Multiphysics, you can automate this process via the Material Sweep parametric study and Material Switch feature. As such, you do not need to add several materials one at a time and compute for the corresponding solution. In addition to saving you time during model set up, this facilitates the comparison of results during postprocessing.

Screenshot from the material sweeps video, showcasing the ability to switch between different results based on the material.

The Material Switch node houses the materials that you want to sweep over and provides functionality to automatically switch materials while your model is solving.

In the five-minute tutorial video below, we outline the procedure for performing a material sweep in your model and then walk you through the steps for doing so. This includes adding a Material Switch node; specifying parts of the geometry that the material sweep will be applied to; selecting the materials to switch between; adding the Material Sweep parametric study; and finally postprocessing the sweep’s results. We also briefly discuss how you can customize the materials being swept over as well as how to easily toggle between different sets of results obtained from your material sweep.

Video Tutorial: How to Sweep and Compare Materials in COMSOL Multiphysics

Easily Define Material Properties Using Material Functions

As mentioned earlier, COMSOL Multiphysics features a large collection of built-in materials that are available regardless of which modules you hold a license for. Upon adding any of these materials to your model, you will notice that the material properties are provided with certain default values.

In some cases, material properties are constant. In other cases, they may vary in space or be dependent on a physics variable such as temperature. If you want to make a constant material property variable, or if the built-in variation is not what you want to use, you can define your own function. In COMSOL Multiphysics, there are three types of functions that you can use to define a material property: Interpolation, Analytic, and Piecewise functions.

Data table and plot for an Interpolation function.

Interpolation functions are used to define a material property through reading in data from a table or file that contains values of the function at discrete points. You can enter this data manually or import it from an external file. This is useful when you have material properties that are obtained from experiments. COMSOL Multiphysics will automatically evaluate and then generate a function that fits the data you provide. Then, you can also choose how the function interpolates between the measured values or extrapolates outside of your specified range of data.

Input fields and plot for an Analytic function.

Analytic functions are used to define a function using built-in mathematical functions or other user-defined functions. You can enter an expression, specify the input arguments, and define the value range for each of the arguments in your equation.

Settings for a Piecewise function.

Piecewise functions are used to define a material property using different expressions over different intervals. The start and end point for each set of values, as well as the function applicable to that interval, can be entered manually or imported from an external file. The intervals that you define cannot overlap and there cannot be any holes between the intervals. That way, you have a continuous function uniquely defined in terms of the independent variable.

In the following seven-minute tutorial video, we discuss how to create and define Interpolation, Analytic, and Piecewise functions for any material property in your model, the advantages of using each type, and best practices to keep in mind when creating them. We also go over the settings for each function type, demonstrate how the selection of options such as Extrapolation will change your data plot, and show how you can call out your function in the Material Contents table.

Video Tutorial: Use Functions to Define a Material Property

Utilize Global Materials and Material Links for Multiple Components

While creating a model in COMSOL Multiphysics, you will at some point need to identify the materials that your objects are made of. Normally, this requires completing a series of steps in which you open the Add Material or Material Browser windows; choose the material; select and add it to your component; and then go into the material node’s settings to select the parts of the geometry to which the material applies. You would then need to repeat this procedure for each unique material that you want to include in your simulation. In COMSOL Multiphysics, you can expedite the above process using global materials and material links.

Screenshot displaying use of the global materials and material links functionality.

When a material is added under the Global Materials node, it is available to use anywhere throughout the model. Further, global materials can be used for any geometric entity level, whether you assign them to domains, boundaries, edges, or points.

Material links are used locally under a component’s material node to refer to a global material. This is advantageous when you have a COMSOL Multiphysics file that contains multiple components that are made up of similar materials, as you only need to specify the material once under the Global Materials node and can then link to it under each individual component. It is also beneficial for models in which the same material is assigned to different geometric entity levels such as domains and boundaries. In this case, you would again only need to add the material once and could also add a separate Material Link node for each geometric entity type.

In the six-minute tutorial video below, we show you how to use the global materials and material links functionality. We begin by demonstrating how to add global materials to your model and discuss the differences between adding materials globally and locally. Then, we walk through the steps of how to add material links to your model components and assign them to the geometry. After watching this video, we encourage you to try out this functionality yourself and see firsthand the ease with which you can assign materials in a model that contains multiple components or when you want to use the same materials on multiple parts.

Video Tutorial: Use the Same Material for Multiple Components in COMSOL Multiphysics

Efficiently Define the Materials Used in Your Simulation Studies

You can significantly expedite the process of assigning materials to your model geometry using the features and functionality discussed here. To complement these tools, we’ve created instructional videos to help you learn how to utilize them in your own simulations. Whether you have a model file that involves multiple components, need to define a complicated material property, or have to test different materials in your simulation, COMSOL Multiphysics features built-in tools that make this process simpler and more efficient for you.

Browse Additional Tutorial Videos Relating to Materials

• To learn more about specifying and defining materials in your COMSOL Multiphysics models, watch this introductory video series: How to Use Materials in Your COMSOL Multiphysics Models
• Head over to our Video Gallery to check out other videos on the topic of material-based features and functionality

Expedite Your Model Setup with Explicit Selections

At virtually every step of the model creation process, you need to select and apply materials, physics boundary conditions, and other settings to your model geometry. As mentioned above, overseeing the administration of these settings can be challenging, whether you are working with a simple or complicated geometry. In COMSOL Multiphysics, one tool that you can use to organize your model geometry and thus alleviate such issues are Explicit selections.

Utilizing Explicit selections to organize a model geometry.

With Explicit selections, you have the ability to create selections of individual geometric entities. Each selection can contain one or more geometric entities, with the option to rename the selection using a label that reflects the geometry it contains.

There are many advantages to this approach. Instead of referring to different parts of your model geometry by their geometric entity numbers, you can simply refer to them using the selection that displays your customized label and includes the geometric entities you assigned to it. The labeled selections are available for all physics interfaces added to the geometry. This makes it faster and easier for you to apply settings to your model. By preparing Explicit selections in advance, for any applicable node that is open in the Model Builder window, you can choose a particular selection simply by selecting its respective label from the geometry selection drop-down menu.

The geometry selection drop-down menu, with several different Explicit selections shown.

As an added bonus, the above approach ensures that you never accidentally omit or include any geometric entities in a selection where they do not belong. Only those entities that are included in the selections when they are originally prepared will have the settings applied to them.

Taking into account the many conveniences that correlate with using Explicit selections, we have created an eight-minute tutorial video that explains how to create and use this selection tool in your own simulation workflow. We also demonstrate how to quickly include multiple geometric entities in a selection via the Select Box and Group by continuous tangent features. The video concludes with a discussion on how Explicit selections can sometimes retain your model setup depending on how the geometry is changed, while highlighting cases where they can be utilized and their overall benefits.

Video Tutorial: How to Use Explicit Selections to Organize Your Model Setup

Coordinate-Based Selections: Modify Your Geometry Without Changing Model Settings

Besides being used to represent different parts of your model geometry, there are other selection tools available in COMSOL Multiphysics that provide additional functionality. Let’s say, for instance, that you want to run your simulation on several different versions of a geometry, with parts of the geometry removed and new parts added, while keeping all of your model settings the same. Rather than having to go back into the settings for each node in the model tree and reselect any applicable parts of the geometry, you can utilize coordinate-based selections.

Cylinder, Ball, and Box selections are just some types of coordinate-based selections that are available. Cylinder selections, for example, are used to create selections of geometric entities that are partially or completely enclosed by a cylinder.

Screenshot of a cylinder selection.

Similarly, Ball and Box selections are used to create selections of geometric entities that are partially or completely enclosed by a ball or box, respectively. Unlike Explicit selections, each of these tools automatically updates if the geometry in your model changes, regardless of the means by which it changes. Whether modifications are made in the geometry sequence with the addition or removal of geometric entities or whether you’re importing a new CAD file with a significantly different design, coordinate-based selections will enable you to maintain your model setup.

In our seven-minute tutorial video on coordinate-based selections, we use two components — one containing a 3D geometry and the other a 2D cross section of that 3D geometry — to illustrate how to create each selection type. While defining these selections, we provide further details as to why we strongly encourage the use of parameters. The video also discusses the advantages of using coordinate-based selections in your model and how you can change the criteria by which geometric entities are included in your selections. To conclude, we change the geometry of the tutorial by importing a new file that exhibits a slightly different design, allowing us to see if our model assignments and definitions are maintained in spite of the introduced entity.

Video Tutorial: How to Use Coordinate-Based Selections in Your Model Setup

Create Customized Selections of Geometric Entities Using Boolean and Adjacent Selections

As mentioned earlier, each selection tool in COMSOL Multiphysics boasts different capabilities and functionalities for selecting geometric entities in your model. After learning about Explicit and coordinate-based selections, you may have already started creating a few named selections in your own simulation. But what if you are looking for a way to uniquely combine the selections you’ve already defined to create additional, even more useful selections of your model’s geometry? Boolean and adjacent selections are the ideal tools for doing so.

Boolean selections consist of Complement, Difference, Union, and Intersection selections. Each of these tools uses other previously defined selections as the input. With Complement selections, for instance, you can create selections that are the inverse of one or more selections.

A Complement selection, with the color red representing the inverted selections.

Difference selections, meanwhile, give you the ability to create selections of entities that are included in one selection, but not another.

A screenshot of a Difference selection, which displays the geometric entities added and removed in the Input Entities sections.

Say you want to unite two or more selections into a single selection. With a Union selection, you can do exactly that.

A screenshot showing a Union selection. Note that the input entities are identical to that of the Intersection selection.

Lastly, Intersection selections give you the option to create selections of any entities that are included in all of the input selections.

A screenshot depicting an Intersection selection. Note that the input entities are identical to that of the Union selection.

Like Boolean selections, adjacent selections also use other predefined selections as the input. This selection tool enables you to create selections of geometric entities that are touching other selections. Additional functionality allows you to choose between selecting interior or exterior geometric entities adjacent to the geometry that are included in the input selections you specify.

An adjacent selection, with the capability to toggle on selecting external boundaries showcased.

By utilizing Boolean and adjacent selections in your model setup with any of the other selection tools mentioned above, the possible combinations of selections to create, including the geometric entities of your choice, are infinite. This enables you to quickly and easily create unique selections of your model geometry, applying the definition that you would like. Similar to coordinate-based selections, Boolean and adjacent selections also update automatically, regardless if the changes made to the design are minor or major.

In the ten-minute tutorial video shown below, we define Boolean and adjacent selections and specify the means by which they select geometric entities. We also show you how to create each selection type, discuss their advantages in terms of the flexibility they provide, and explain why we encourage you to change the label of the selections as you define them. Near the end of the video, after assigning some definitions to a few of the selections, we change the geometry by importing a different file and then proceed to examine the changes, if any, that need to be made in order to preserve the geometry included in each of the defined selections, as well as the settings assigned to them.

Video Tutorial: Using Boolean and Adjacent Selections in COMSOL Multiphysics®

Easily Navigate Your Modeling Sequence with Named Selections

In COMSOL Multiphysics, named selections can be instrumental in simplifying your modeling processes. Such tools allow you to track the model settings applied to your geometry, retain the model settings applied to your selections if the geometry changes, and easily recognize which geometric entities are included in a selection. This not only gives you the ability to more easily navigate your model setup, but it also empowers others, such as your colleagues, to do so as well.

In the three tutorial videos featured here, you will notice that we used the same shell and tube heat exchanger tutorial model. It is our hope that by demonstrating how to create each selection type on a single model, you will not limit yourself to only utilizing any one selection tool in your own modeling processes. By combining such tools, you can optimize the overall efficiency of your simulation, achieving fast and accurate results.

Browse Additional COMSOL Multiphysics Tutorial Videos

• Interested in learning how to utilize other features and functionality available in COMSOL Multiphysics? Our Video Gallery is home to a plethora of tutorial videos. Browse these resources by simply searching under Core Functionality.

Find the Tools You Need, When You Need Them, in the COMSOL Desktop®

Creating and solving a simulation requires access to a range of functionality. In COMSOL Multiphysics, the COMSOL Desktop® environment serves as the UI that encompasses all of these elements, with various menus, tools, and windows included in the mix.

The COMSOL Desktop® environment.

Not only does the COMSOL Desktop house all of these important components in one place, but it also organizes them in a way that complements the model creation process. The ribbon across the top of the desktop, as well as the nodes in the Model Builder window, provide you with a clear outline of all the steps that should be taken to build your model from start to finish. These steps include choosing your spatial dimension, creating definitions, building your geometry, assigning materials, defining the physics, creating the mesh, running the simulation, and postprocessing your results.

COMSOL Multiphysics, as we’ve noted, is a modeling environment that is designed to be both intuitive and user-friendly. In light of this, we have created a short video that provides a guided tour of the COMSOL Desktop to help you get started. Along with showing you how to navigate through the desktop, we also review all of the main windows and toolbars in the software, explaining how they relate to one another and update depending on the operation that is performed.

Video Tutorial: Using the COMSOL Desktop® Modeling Environment

Visualize Various Elements of Your Model with the Graphics Window

Within the COMSOL Desktop, you will notice the Graphics window. Serving as an integral part of the UI, this window allows you to visualize your simulation’s geometry, mesh, and results.

The Graphics window itself houses the visual results of your model. The Graphics window toolbar, meanwhile, offers functionality that lets you easily customize your view. You can do so via a row of buttons, each of which include a capability that is represented by a distinct icon. Together, they can be used to achieve different types of graphics, views, images, and perspectives.

Graphics window displaying the geometry for the busbar tutorial model.

In a short tutorial video on the Graphics window, we show you all of the mouse movements that you can use to move around and rotate your geometry, as well as zoom in and zoom out. Further, we review the Graphics window toolbar buttons that enable you to perform each of the aforementioned actions, among others, including changing the view of your model as well as hiding, showing, and selecting geometric entities. This video also highlights the dynamic nature of the toolbar and how it updates automatically depending on the spatial dimension of your model component, as well as the node you currently have open.

Video Tutorial: Using the Graphics Window to Customize Model Visualizations

Access and Choose Geometric Entities Using the Selection Tools

One of the predominant, and most important, ways to interact with the visuals in the Graphics window is by selecting geometric entities. This takes place in virtually every step of the simulation workflow. In COMSOL Multiphysics, you will find a plethora of tools that can help you select geometric entities, regardless of the simplicity or complexity of your model’s geometry.

Screenshot of the video showcasing the mouse scroll wheel functionality.

Being aware of each of the selections tools available in the software can be an asset to you while modeling, as each of them caters to specific modeling cases. The following tutorial video discusses each option for selecting geometric entities, noting the advantages of the different methods. Some examples include using the hover-and-click method in the Graphics window for simple geometries or individual geometric entities; the mouse scroll wheel button to reach interior geometric entities; and the Selection List window for complex geometries.

Video Tutorial: Selecting Geometric Entities in COMSOL Multiphysics®

COMSOL Multiphysics, an Environment Designed with Users in Mind

Helping users like you quickly get models up and running in COMSOL Multiphysics is one of our primary goals. Through watching the videos shown above, it is our hope that you can become more aware of and knowledgeable about the features and functionality available in the software — all of which are designed with the user in mind. By making the simulation environment in which you run your studies easy-to-use, we aim to help you focus on what’s most important: the simulation study at hand.

Browse Additional Video Resources

• To learn about additional features and functionality available in COMSOL Multiphysics, as well as how to use them, head over to the Video Gallery today and browse the Core Functionality topics.

Video: How to Model Structural Mechanics in COMSOL Multiphysics

Conducting the structural analysis of a model is an imperative step in the design process. The Structural Mechanics Module, an add-on to COMSOL Multiphysics, offers a virtually limitless amount of capabilities for you to do just that.

This video introduces you to the Structural Mechanics Module and walks you through the entire model-building process for setting up and solving a mechanical problem. This includes demonstrations on how to create parameters, named selections for different parts of your geometry, local variables to implement complicated expressions defined in the model, custom meshes, and tabulated results. To demonstrate the workflow for building and solving a structural mechanics problem, the COMSOL Multiphysics version 4.4 tutorial model of a static bracket assembly is used.

The smallest components, while often overlooked in design, can be the most instrumental ones. Brackets serve as a core component of support for many mechanical devices in numerous industries. In this model, a bracket assembly is fixed in place through eight mounting bolts. A load is applied on the two arms of the bracket, which is representative of a pin being placed between the holes in the bracket arms. As a result, the two bracket holes will experience a loading from this pin. After an initial analysis is complete, the direction of the pin load is varied through a parametric sweep to see the variations in force exertion, stress distribution, and deformation.

Model Download

• Shown in the video: Bracket — Static Analysis (version 4.4)

Video Transcription

Today, we will be learning how to model a structural mechanics problem, in COMSOL Multiphysics. We will conduct a static analysis of a bracket assembly, and in the end, perform a parametric sweep to analyze a bearing load at different angles. So let’s get started.

A pin is placed between the two holes in the bracket arms, and the inner surfaces of the two bracket holes will experience a loading from this pin. We will want to vary the direction of the pin load to see the variations in stress distribution and deformation. After an initial analysis is done with the pin load applied to the bracket holes along the negative y-axis at zero degrees, we will perform a parametric sweep of the pin load direction, starting at 0 degrees, and rotating 45 degrees, up to 180 degrees. “theta0” will be used to specify the main direction of the load, and will be the parameter used later in our parametric sweep. “P0” is the peak load intensity applied to the bracket holes. Lastly, “y0” and “z0” are the coordinates of the centers of the bracket holes. It’s good practice to use parameters instead of just the numerical values. When you change these global parameters, they will update throughout the entire model.

Now that we’ve added selections to our model, we can define expressions for adding the boundary load. Local Variables can be used to introduce short and descriptive names for the complicated expressions defined in the model. Go to the ribbon and under the Definitions tab click Local Variables. In the table to define the load, we need an expression for the angle and load intensity, so we enter the following. The angle variable is used to help define the load intensity. This expression evaluates the radial angle, based on its position along the global z-coordinate. Since our loading direction will change in only in the y and negative z directions; or equivalently the 3^rd and 4^th Cartesian quadrants, we can have COMSOL Multiphysics solve for the angle, by computing the four-quadrant inverse tangent. This enables calculating the arctangent in all four quadrants. The load that the bracket holes experience will be sinusoidal in nature, so the sine function is used. This last part of this expression is added to make sure that the load is only applied to the bottom half of each bracket hole.

COMSOL uses a global Cartesian coordinate system by default to specify material properties, loads, and constraints in all physics interfaces and on all geometric entity levels. For this model we want to define the orientation of the load applied to the bracket holes. Since the load direction will be rotating about the negative z-axis, we need to create a rotated coordinate system. In the Coordinate Systems section of the ribbon, choose Rotated System. This creates a rotated coordinate system, relative to the global system, that defines the orientation of the load applied to the bracket holes. Under the Euler angles subsection, in the beta field type “-theta0”.

Because the mounting bolts are fully constrained, use a volume integration over those domains to accurately calculate the reaction forces. On the Results tab, click More Derived Values and choose Integration, Volume Integration. In the Volume Integration settings window, locate the Selection section and from the Selection list, choose Box 1 to add the bolts. Click Replace Expression here in the upper-right corner of the Expression section, and from the menu choose Solid Mechanics, Reactions, Reaction Force, and the x component of the reaction force. Click the Evaluate button. Let’s do this again for the Y and Z components as well. To save time you can edit the expression, in this case, by changing the component letter.

Click Evaluate and the results are shown in Table 1 under the Graphics window. They match what we would expect them to be; the entire load is in the y direction while negligible in the x and z directions.

After performing a parametric sweep, you can create a table that lists the solutions for each parameter value. This way you can view the different solutions all at once. In the Volume Integration 1 node, click Evaluate and then New Table. The reaction forces at the different parameter values are computed. The reaction force in the x-direction is always zero, while the y and z directions share the load, depending on the angle.

Video: Modeling Electromechanics in COMSOL Multiphysics

A capacitive pressure sensor is achieved by engineering a circuit such that its capacitance is dependent on the ambient pressure in which it is operating. In this model, a vacuum cavity serves as the dielectric in a miniature parallel plate capacitor. The cavity is sandwiched between a silicon die and a thin silicon membrane, which is exposed to the ambient atmosphere. Changes in the ambient air pressure induce deflections in the membrane, which alter the distance between the capacitor plates. The capacitance of the device is thus dependent on the ambient pressure and, when connected to suitable circuitry, can be used as the basis for a pressure sensor.

The silicon capacitor is packaged onto a steel base plate using a thermal bonding technique that requires a temperature that is much higher than that at which the sensor is intended to operate. Since silicon and steel have different coefficients of thermal expansion, the capacitor and the base plate contract at different rates as the device cools back down to its operating temperature. This results in mechanical stresses at the interface between the two materials, which can cause additional temperature-dependent deflections of the membrane. In this example, we examine the performance of the pressure sensor both with and without the thermal stresses induced by the packaging. The video demonstrates the importance of considering multiphysics effects when designing electromechanical devices.

Model Download

• Shown in the video: Capacitive Pressure Sensor

Video Transcription

Today, we will be simulating a capacitive pressure sensor, both with and without stresses induced by the packaging. The geometry of the sensor is symmetric, so only a single quadrant is modeled. The sensor consists of a thin chamber, sealed under high vacuum, acting as the dielectric in a capacitor. It is separated from the ambient air by a thin membrane, which is electrically isolated from the grounded body of the sensor. We will investigate the deflections of the membrane due to both ambient pressure changes and thermal stresses resulting from a poor choice of package. In both cases, the deflections are detected by measuring a change in the capacitance between the membrane and ground.

To begin, we select the Model Wizard and then choose a 3D Space Dimension. Next, we add the Electromechanics physics interface. From the Preset Studies list, we choose a Stationary study.

We’ve also created a collection of boundaries, which make up the YZ-Symmetry Plane and a collection of boundaries, which make up the XZ-Symmetry Plane. These will be used when specifying the symmetry boundary conditions in the physics interface. All the domains, which make up the steel base, have been selected. This is useful when we assign materials to the model.

First, we add a Linear Elastic Material node to the Electromechanics physics interface. From the Physics ribbon, we select “Domains”, “Electromechanics”, and “Linear Elastic Material”. Here, we can use one of our selections created earlier. We can assign the Linear Elastic Material to the Linear Elastic selection, which encompasses all domains except for the vacuum cavity.

The reason we apply this boundary condition is to constrain the position of this geometry in the Z-axis. This will prevent COMSOL from searching for solutions in which the whole geometry is translated arbitrarily up or down the Z-axis. So, to do that, we click “Prescribed in z direction” and we leave the default “0″ here. So, now the structure is pinned in place in the Z-coordinates and although it can deflect, it can’t translate in its entirety.

Next, moving mesh boundary conditions must be applied on the boundaries adjacent to the cavity. This will allow for the mesh to move as the surrounding material deforms. From the Electromechanics interface, we select the Prescribed Mesh Displacement node. Here, we clear the “Prescribed z displacement”, which allows the mesh to move up and down in the Z-direction as the membrane deflects.

Then, the final step is to sweep this mesh up along the Z-axis through the structure. So, we add a swept mesh node, Build All, and there you have it! A nice structured mesh suitable for this geometry. Now that the parameters, geometry, physics, and mesh are all configured, we can prepare the study.

Select micrometers, a more appropriate unit, and we can use the point integration operator to allow us to plot the maximum displacement. Now, we can tidy up the plot a bit. You’ll see here I’ve renamed this 1D plot group to Membrane Displacement and this shows the displacement of the membrane, as a function of pressure. I’ve added a title for the plot and labeled the axes.

Now, we can plot the capacitance as a function of pressure. Once again, from the Home ribbon, we select “Add Plot Group”, choose a “1D Plot Group” and a “Global plot”. This time, we choose the capacitance variable, which is output automatically by the Electrostatics interface. Picofarads is a more appropriate unit. Now, we can tidy up this graph a bit. And here, we have created our plot for the capacitance as a function of pressure. I’ve added a title for the plot, labeled the axes, and moved the legend to the left side of the plot.

Now that the stress-free study has been completed, we can add the effects of thermal expansion to the model. In the Electromechanics interface, we right-click “Linear Elastic Material” and choose the “Thermal Expansion” sub node. We set the temperature of the device to the parameter “T0″ and we set the reference temperature, which is the temperature at which there is zero stress due to thermal expansion, to be “Tref”, which is the temperature of the device when it was packaged.

Learn more about this and similar models at comsol.com/models.