## MEMS Module Updates

For users of the MEMS Module, COMSOL Multiphysics^{®} version 6.0 brings new interfaces to couple magnetic and mechanical effects, component mode synthesis, and several viscoelasticity improvements. Read about these and more updates below.

### Magnetomechanics Multiphysics Interfaces

Two new physics interfaces for analysis of coupled magnetic and mechanical effects have been added: *Magnetomechanics* and *Magnetomechanics, No Currents*. When you add such an interface, two physics interfaces are added to the model: *Solid Mechanics* and either *Magnetic Fields* or *Magnetic Fields, No Currents*. The new *Magnetomechanical Forces* multiphysics coupling is also added. These interfaces can be found under the *Electromagnetics and Mechanics* branch in the *Add Physics* tree. Note that in addition to the MEMS Module, these interfaces require either the AC/DC Module, Structural Mechanics Module, or Acoustics Module.

*The dynamic behavior of an AC contactor. An AC contactor is a particular kind of switch that is activated by a coil carrying an AC current.*

### Piezoelectric Waves, Time Explicit Multiphysics Interface

With the *Piezoelectric Waves, Time Explicit* multiphysics interface, you get access to new capabilities for modeling piezoelectric phenomena in the time domain for wave propagation. Both the direct and inverse piezoelectric effects can be modeled and the piezoelectric coupling can be formulated using the strain-charge or stress-charge forms. The new interface couples the *Elastic Waves, Time Explicit* interface with the *Electrostatics* interface using the new *Piezoelectric Effect, Time Explicit* multiphysics coupling.

The interface is based on the discontinuous Galerkin (dG or dG-FEM) method and uses a time-explicit solver. The electrostatics part of the equation system is solved at every time step through an algebraic system of equations solved with the classical finite element method (FEM). This ensures a very computationally efficient hybrid method that can solve very large models with many millions of degrees of freedom (DOFs). The method is well suited for distributed computing on cluster architectures.

*Piezoelectric Waves, Time Explicit*multiphysics interface in an angle beam nondestructive testing (NDT) setup.

### Component Mode Synthesis

Linear components built using the *Solid Mechanics* and *Multibody Dynamics* interfaces can be reduced to computationally efficient reduced-order models using the Craig–Bampton method. Such components can then be used in dynamic or stationary analyses, either in a model consisting entirely of reduced components or together with nonreduced elastic finite element models. The latter can then be nonlinear. The approach, which is called component mode synthesis (CMS) or dynamic substructuring, can give large improvements in terms of computing time and memory usage. The results, such as stresses and strains, in a reduced component can be presented in the same way as for any other part of the model.

### Axial Symmetry with Twist

In the *Solid Mechanics* interface, in 2D axisymmetry, it is now possible to include circumferential deformations. This can be enabled by selecting the *Include circumferential displacement* check box in the *Axial Symmetry Approximation* section in the physics interface. With this option, it is possible to model, for example, torsion of axisymmetric structures in a computationally efficient manner.

### Point Loads at Arbitrary Locations

With the new *Point Load, Free* and *Ring Load, Free* features, point loads can be applied at arbitrary locations that do not coincide with a geometrical point or mesh node. This is particularly useful in the following cases:

- Imported meshes, where there may not be suitable points for load application
- Moving loads
- Models with many point loads, in which case it may be impractical to create geometry points at all load locations

This functionality is available in the *Solid Mechanics*, *Shell*, *Plate*, *Membrane*, *Beam*, *Truss*, and *Multibody Dynamics* interfaces.

### Significantly Easier Modeling of Mechanical Contact

Structural analysis of assemblies, including mechanical contact, is now significantly easier to set up. This is due to built-in automation of pairs, contact, and continuity features. If there is at least one contact pair in the model, then a default *Contact* node will automatically be created in the relevant structural mechanics interfaces. Similarly, if there is at least one identity pair, a default *Continuity* node is automatically created. Thus, if parts in your geometry are placed adjacent to each other, they will also be connected from the physics point of view, assuming that you are using automatic pair creation in the *Form Assembly* node in the geometry sequence.

As a result of the general reformulation of the pair functionality, the *Source external to current physics* check box in *Contact* is no longer needed and has been removed. That is, contact between different physics interfaces is also automatically handled.

All models containing *Contact* or *Continuity* have been updated accordingly.

*Contact*nodes are automatically generated in both the

*Solid Mechanics*and

*Shell*interfaces. However, it is only on the shell side that there is a full set of controls, since the solid acts as the source side of the pair.

### New Damping Models

New damping models have been added for the mechanical material models:

- The
*Wave attenuation*model is essentially a viscous model, but with parameters given by measured data for the attenuation of elastic waves in the material. It is available in the*Linear Elastic Material*in*Solid Mechanics*. - The
*Maximum loss factor*model is mainly intended for time-domain analysis of materials for which a loss factor representation provides a good description in frequency domain. This damping model is available for all material models that support viscous damping. - In the
*Piezoelectric Material*feature, there is, in addition to the mechanical damping*Maximum loss factor*, also a new frequency-domain damping model for dielectric loss:*Complex Permittivity*. - For
*Charge-Conservation, Piezoelectric*, you can now add two new dispersion models:*Debye*and*Multipole Debye*.

### Debye Dispersion Models for Dielectrics

New damping models have been added for dielectric materials. Under *Charge Conservation*, when the material type is set to *Solid*, you can now use the *Dispersion* dielectric material model. In the *Dispersion* subnode, you can choose between the *Debye* and *Multipole Debye* dispersion models. This functionality is available for frequency-domain and time-dependent analysis. Note that this material model requires the AC/DC Module or the MEMS Module.

### Reduced Integration

In the *Solid Mechanics* and *Membrane* interfaces, a new framework has been added for a numerical technique known as reduced integration. Reduced integration is particularly useful when the computational cost per integration point is high, which is true for many advanced material models. It can also be used for relieving locking problems with some material models.

For elements with linear shape functions, reduced integration can cause singularities in the stiffness matrix. This is counteracted by the addition of hourglass stabilization.

Reduced integration is controlled from the *Quadrature Settings* section in various material models. It is available in top-level material models like *Linear Elastic Material*. The selected integration rule will then be inherited by any subnodes that may be added.

### Symmetry Plane for Electrostatics and Electric Currents

A new *Symmetry Plane* feature is available for the *Electrostatics* and *Electric Currents* interfaces. It provides symmetry and antisymmetry conditions for the electric field. For the antisymmetric case, a reference potential can be set to specify around what electric potential the field is antisymmetric (the default is ground).

### Compute Displacement Postprocessing Feature in Elastic Waves, Time Explicit

A new postprocessing feature called *Compute Displacement* has been added to the *Elastic Waves, Time Explicit* physics interface. The feature allows for optimally computing the displacement at points, along edges, on boundaries, or in domains by solving a set of auxiliary ODEs. The new features are added as subfeatures to a material model such as the *Elastic Waves, Time Explicit* model or the *Piezoelectric Material* model. The feature does not affect the results but is solely used for postprocessing and generates field variables that can be used to visualize and postprocess displacements. Since the feature adds and solves additional equations, using it requires additional computational resources.

### Viscoelasticity Improvements

There are several important additions to the viscoelastic material models:

- For frequency-domain and time-dependent analyses, all of the viscoelasticity models have been augmented with the possibility to include viscoelasticity also in the volumetric deformation.
- The
*Generalized Maxwell*model now has the possibility to prune branches representing frequency ranges outside the bandwidth of prescribed loads, improving the performance in time-dependent analyses for models with dozens of viscoelastic branches. - For frequency-domain analyses, a new user-defined viscoelasticity model makes it possible to enter frequency-dependent expressions for the loss and storage moduli or compliances.
- Through a new formulation of the viscoelastic equations, it is now possible to solve for eigenfrequencies in a structure containing viscoelastic materials using a standard procedure for damped eigenfrequency problems. Previously, the eigenvalue problem was nonlinear in the frequency and only one eigenfrequency at a time could be found.

### Improved Mixed Formulation

In material models that have an option to select a mixed formulation, you can now modify the discretization for the extra dependent variable (pressure or volumetric strain). This makes it easier to avoid locking and instabilities in materials with low compressibility.

When a mixed formulation is selected under the *Linear Elastic Material* settings, a new *Discretization* section will automatically appear for the material model. In this section, you can choose between different types of shape functions for the extra dependent variable.

### New Tutorial Models

COMSOL Multiphysics^{®} version 6.0 brings three new tutorial models to the MEMS Module.

#### Solidly Mounted Resonator 2D

Application Library Title:

*solidly_mounted_resonator_2d*

Download from the Application Gallery

#### Solidly Mounted Resonator 3D

Application Library Title:

*solidly_mounted_resonator_3d*

Download from the Application Gallery

#### Component Mode Synthesis Tutorial

Application Library Title:

*cms_tutorial*

Download from the Application Gallery