## Structural Mechanics Module Updates

For users of the Structural Mechanics Module, COMSOL Multiphysics^{®} version 6.0 brings a new *Magnetomechanics* multiphysics interface, component mode synthesis (CMS), and wrinkling of membranes. Read about these updates and more below.

### Magnetomechanics Multiphysics Interface

Under the *Electromagnetics-Structure Interaction* branch, in the *Add Physics* tree, two new physics interfaces for analysis of coupled magnetic and mechanical effects have been added: *Magnetomechanics* and *Magnetomechanics, No Currents*. Typical applications are when a magnetic field induces deformations in a solid or, conversely, when a moving structure changes the magnetic field. This functionality is used in the new Deformation of an Iron Plate by Magnetic Force tutorial model. Note that this feature requires the AC/DC Module.

### 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.

### 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.

### Physics Interface for Poroelasticity with Large Deformations

The new *Poroelasticity, Large Deformation, Solid* multiphysics interface is used for modeling poroelasticity under finite structural deformations. With this interface, you can model situations where there are significant changes in the geometry of the poroelastic solid and resulting changes in the porosity. Note that this new interface requires the Porous Media Flow Module.

### 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. You can see this feature used in the new Axisymmetric Twist and Bending tutorial model.

### Enhancements to Beam Cross Section Data Evaluation and Visualization

The *Beam Cross Section* interface is now available in 3D. In the 3D version, you have the possibility to extrude the cross section and then show a full 3D representation of the stresses in a beam. The 2D version of the interface has also been significantly updated. One major change is that the interface can now handle more than one cross section. In addition, there are new multiphysics couplings, *Beam Cross Section - Beam Coupling* and *Beam-Beam Cross Section Coupling*, for transfer of data between a *Beam Cross Section* interface on one side and a *Beam* or *Pipe Mechanics* interface on the other side.

*Beam Cross Section*interface (below).

### 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 and can be viewed in the updated Pratt Truss Bridge tutorial model.

### Improved Visualization of Shells

When using the *Shell* dataset, it is now possible to plot results in shell models with a full solid representation. The through-thickness distribution of a result quantity can also be visualized as if the shell were represented by a solid object.

*Shell*dataset. The transparent parts of the model consist of solid elements.

### Couplings Between Disjoint Shells

In the *Shell* interface, three new boundary and edge conditions have been added to facilitate easier coupling between parts of shells that are located so that there are gaps in the geometry. These are: *Edge to Edge*, *Edge to Boundary*, and *Boundary to Boundary*. The couplings can be rigid or elastic. Some applications are:

- Imported geometries where there are gaps between parts and the new couplings can be used to join those parts.
- Midsurface generation having residual gaps between parts and the new couplings can be used to join those parts.
- Avoiding the artificial flexibility caused by using a common edge in, for example, a T-joint. The shell thickness can now be taken into account in a more accurate way.
- Weld modeling, in which case you can use the flexible version of the coupling, and evaluate the forces in the weld.

*Edge to Edge*coupling. Foreground: Midsurface representation together with the connected edges. Background: The same results using true 3D thickness in a

*Shell*dataset.

### Loads on Top or Bottom Surface of Shells

It is now possible to apply loads in the *Shell* and *Plate* interfaces not only on the midsurface but also on the top and bottom surfaces. Using the actual location in the thickness direction can be important for shells with significant thickness, in particular when curved. The reason is that the corresponding torque contributions will otherwise not be accounted for. You can see this new feature in the updated Connecting Shells and Solids tutorial model.

### 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. View this new feature in the Component Mode Synthesis Tutorial tutorial model.

### 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.

### 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.

### Enhancements in Bolt Modeling

Several enhancements have been introduced to improve the productivity when modeling bolted structures:

- The
*Bolt Pretension*feature is now also available in the*Beam*interface, thus facilitating simplified modeling of bolts using beam elements. - The
*Solid-Beam Connection*multiphysics coupling has been extended with an option to connect a point on a beam to an edge on a solid. This enhancement is in no way limited to bolt modeling, but it is particularly useful for a simplified representation of the bolt head when beam elements are used to model bolts. - It is now possible to tighten a set of bolts in a user-defined sequence by using a single
*Bolt Pretension*study step. This makes it much more convenient to model cases where the order in which the bolts are tightened is important. - The bolt preload can now also be prescribed in terms of a tightening torque.
- When bolts are present in a model, an evaluation group containing bolt forces will be automatically created.
- The identifying bolt labels can be automatically generated.

View these improvements in the new Modeling of Pretensioned Bolts tutorial model.

### 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. You can see these improvements in the updated Eigenmodes of a Viscoelastic Structural Damper and Viscoelastic Structural Damper — Transient Analysis tutorial models.

### Wrinkling in Membranes

Membranes are only stable as long as all in-plane stresses are tensile. When a principal stress in a membrane falls below zero, the stiffness matrix becomes singular. Physically, this means that wrinkling will occur. This situation can now be handled by adding the new *Wrinkling* subnode under the *Linear Elastic Material* node in the *Membrane* interface. You can see this new feature in the following models:

- inflation_of_a_square_airbag
- torsion_of_a_circular_membrane
- uniaxial_stretching_of_a_rectangular_membrane

### 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 the 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*, 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*.

### Crack Modeling Enhancements

When modeling cracks using the *Crack* feature, there are several enhancements:

- You can now inhibit overclosure of the crack by adding a
*Crack Closure*subnode. This will add a contact condition, in which friction in the crack can also be taken into account. - When using a
*Face Load*subnode, you can now assign a load group in order to limit and scale the load for certain load cases. - The stress intensity factors K
_{I}, K_{II}, and K_{III}are now computed with a sign. It is thus possible to determine the range of, for example, K_{II}for a set of load cases. A negative value of K_{I}would indicate that the crack surfaces are overlapping (assuming that*Crack Closure*is not used). To control the definition of the signs of the stress intensity factors in 3D, a new subnode,*Reverse Crack Front*, has been added. - Using a new option in the
*J-integral*subnode, you can get detailed control over how the stress intensity factors K_{I}, K_{II}, and K_{III}are determined from the J-integral.

*Crack Closure*feature.

### 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.

### Stress Linearization Enhancements

The *Stress Linearization* functionality in the *Solid Mechanics* interface has two enhancements that make it much easier to use:

- It is no longer necessary to use a geometrical line to define a stress classification line through the thickness. You can now use a line between two arbitrary points. The points can either be geometrical points or just locations specified by coordinates.
- Stress linearization values can be presented as a field over a boundary. In this case, the evaluation is performed using a large number of automatically generated lines, extending orthogonal to the boundary. By using this method, you can find the worst location for placing a stress classification line.

You can see these enhancements in the updated Temperature-Dependent Plasticity in Pressure Vessel tutorial model.

### Fiber-Reinforced Linear Elastic Material

By adding one or more *Fiber* subnodes under a *Linear elastic material*, you can augment the stiffness by the effect of distributed fibers. The fiber content is assumed to be a small fraction of the total material volume. The fibers can optionally be active only in tension, in order to simulate fiber buckling. You can also model thermal expansion of the fibers by adding a *Thermal expansion* subnode under the *Fiber* node.

### Computation of Section Forces in Solids

By adding the new *Section Forces* node in *Solid Mechanics*, you can compute section forces (axial force, shear forces, bending moments, and twisting moment) on a cross section in a solid structure. You can see this new feature in the updated Prestressed Bolts in a Tube Connection tutorial model.

### Initial Imperfection in Buckling Analysis

You can now use a linear combination of buckling modes from a linear buckling analysis as initial imperfections to the geometry when performing a full nonlinear buckling analysis. This functionality is controlled from the new *Buckling Imperfection* node. The updated Linear Buckling Analysis of a Truss Tower tutorial model demonstrates this new feature.

### Input of Residual Stress

In the *External Stress* subnode settings, there is now an option called *Residual Stress*. A residual stress contribution will not directly affect the displacements. That is, if you just enter a residual stress, and no other loads, there will be no displacements. The stress is, however, added to the stress tensor in the sense that it will be part of the stress state that is used in various material models. This can, for example, be used to prescribe residual stresses that exist in a material after welding.

### New Tutorial Models

COMSOL Multiphysics^{®} version 6.0 brings several new tutorial models to the Structural Mechanics Module.

#### Inflation of a Square Airbag

Application Library Title:

*inflation_of_a_square_airbag*

Download from the Application Gallery

#### Torsion of a Circular Membrane

Application Library Title:

*torsion_of_a_circular_membrane*

Download from the Application Gallery

#### Uniaxial Stretching of a Rectangular Membrane

Application Library Title:

*uniaxial_stretching_of_a_rectangular_membrane*

Download from the Application Gallery

#### Deformation of an Iron Plate by Magnetic Force

Application Library Title:

*deformation_of_an_iron_plate_by_magnetic_force*

Download from the Application Gallery

#### Stress in Cooling Pipeline Network

Application Library Title:

*stress_in_cooling_pipeline_network*

Download from the Application Gallery

#### Hanging Cable

Application Library Title:

*hanging_cable*

Download from the Application Gallery

#### Axisymmetric Twist and Bending

Application Library Title:

*axisymmetric_twist_and_bending*

Download from the Application Gallery

#### Modeling of Pretensioned Bolts

Application Library Title:

*modeling_of_pretensioned_bolts*

Download from Application Gallery

#### Component Mode Synthesis Tutorial

Application Library Title:

*cms_tutorial*

Download from the Application Gallery