## Structural Mechanics Module Updates

For users of the Structural Mechanics Module, COMSOL Multiphysics^{®} version 5.5 brings contact modeling to shells and membranes, plasticity, creep, viscoplasticity and viscoelasticity availability for shells, and a physics interface for the mechanical analysis of pipes. Browse these structural mechanics features and more below.

### Contact Modeling Extensions

The contact modeling functionality has been extended to more physics interfaces, now available in: *Solid Mechanics*, *Multibody Dynamics, Shell* (new), *Layered Shell* (new), and *Membrane* (new). Additionally, you can analyze contact between boundaries modeled with any two of these interfaces. Similarly, contact can be modeled between a boundary on which any of these interfaces is active, and an arbitrary meshed part, even if the latter does not have physics assigned to it.

You can see this new functionality in the following models:

- block_on_arch (new model)
- instability_two_contacting_arches (new model)
- contacting_rings
- snap_hook
- snap_hook_penalty
- transient_rolling_contact
- hyperelastic_seal

### Plasticity, Creep, Viscoplasticity, and Viscoelasticity Extensions

The *Plasticity*, *Creep*, *Viscoplasticity*, and *Viscoelasticity* features, intended for modeling inelastic deformations in metals and alloys, are now available in the *Shell* interface. This is important for reducing computational time when modeling thin-walled structures. You can control the balance between accuracy and computation time by selecting the number of integration points in the through-thickness direction. You can see this new feature in the Twisting and Bending of a Metal Frame and Pressurized Orthotropic Container - Shell Version models.

*Metal frame*The von Mises stress in a thin-walled frame modeled with the

*Shell*interface after twisting and bending at a load level cause yielding.

### Decohesion Enhancements

There are now two fundamental families of decohesion models: *Displacement based damage* and the new *Energy based damage*. Additionally, you can set up models with a new traction separation law, *Exponential separation*. Decohesion models are inherently unstable, due to the loss of material stiffness, and to improve the numerical behavior, you can include a *Delayed damage* regularization method.

*Using the Displacement based damage decohesion model*Debonding of a laminated composite using the

*Displacement based damage*decohesion model.

### Multiphysics Interface for FSI with Heat Transfer

In some fluid-structure interaction (FSI) problems, heat transfer between the fluid and the solid is important. Usually, this is also accompanied by thermally induced deformations or stresses in the solid. A new multiphysics interface, *Fluid-Solid Interaction, Conjugate Heat Transfer* has been added to make it convenient to set up models combining these effects. It combines the three physics interfaces *Heat Transfer in Solids and Fluids*, *Solid Mechanics*, and *Laminar Flow* together with a moving mesh and appropriate multiphysics couplings. As with all other FSI interfaces, the flow can easily be changed from laminar to be turbulent. You can see this new feature in the Bimetallic Strip in Airflow model.

*Bimetallic strip in airflow*Flow around a bimetallic strip that bends when subjected to heating from the fluid.

### Fluid-Structure Interaction for Two-Phase Flows

The suite of multiphysics interfaces for fluid-structure interaction has two new entries for two-phase flows: *Fluid-Solid Interaction, Two-Phase Flow, Phase Field* and Fluid-Solid Interaction, Two-Phase Flow, Phase Field, Fixed Geometry_. When you select the *Fluid-Solid Interaction, Two-Phase Flow, Phase Field* option from the Model Wizard, the *Laminar Flow*, *Solid Mechanics*, and *Phase Field* interfaces are added, along with the *Fluid-Structure Interaction* and *Two-Phase Flow* multiphysics couplings and a *Deforming Domain* feature. The fixed geometry option includes the same, minus the *Deforming Domain* feature. You can see this new functionality in the Two-Phase Flow with Fluid-Structure Interaction model.

*Two-phase flow simulation*Simulation of two-phase flow (water and air) interacting with a thin shell. The blue surface is the free water boundary. The displacements in the shell and flow streamlines are also shown.

### Mechanical Analysis of Pipes

The new *Pipe Mechanics* interface provides functionality for performing stress analysis of pipe systems. In addition to external mechanical loads, you can account for internal pressure, axial drag forces, and temperature gradients through the pipe wall. The fluid loads can be taken directly from the *Pipe Flow* interface, and the temperatures can be taken from the *Heat Transfer in Pipes* interface. You can see this new interface in the Coupled Analysis of Flow and Stress in a Pipe model.

*Coupling flow, heat transfer, and mechanical analysis in a piping system*Results from a coupled flow, heat transfer, and mechanical analysis in a piping system: pressure and velocity (left,) temperature (middle), and stress with exaggerated deformation (right).

### Solid Mechanics on Rotating Domains

When modeling multiphysics problems in systems where there is a mixture of rotating and stationary domains, you can use the *Solid Mechanics* interface in a corotating configuration, such that only the deformations relative to the rotation are modeled. This is far more efficient than solving for the total displacements that include large global rotations. In many cases, it is even possible to use a linear formulation for the mechanical problem. To this end, the *Rotating Frame* feature provides a superposition of the rigid body rotation, and the relative displacements, for controlling the spatial frame on which the other physics interfaces are operating.

*Electric generator rotor: Magnetic field and stresses*Electric generator where the rotor is modeled using the

*Solid Mechanics*interface. Results show the magnetic field (left) and stresses (right).

### Nonrigid Joints Between Beams

In the *Beam* interface, you can specify that two (or more) edges that meet at a point have disconnected degrees of freedom. Using the new *Beam End Release* feature, you select the point where there is a discontinuity and in what direction (displacement and/or rotation) to release the beam end. This can be used for modeling internal hinges or other mechanisms in a frame, as demonstrated in the new Stress Analysis of a Portal Crane model.

*Using the Beam End Release feature*Introducing a hinge (that rotates in the y direction) in a model of a portal crane using the new

*Beam End Release*feature.

### Magnetostrictive Material with Hysteresis

The nonlinear *Magnetostrictive Material* has been extended to include the Jiles–Atherton model of magnetic hysteresis. The model is suitable for investigating the hysteretic loss effects in applications such as power transformers and rotating electric machines. The model parameters are related to microscopic physical effects in magnetic materials and they can also be estimated based on experimental data.

*Investigating hysteretic loss effects*Settings for the hysteretic magnetostrictive model, together with hysteresis loops generated from simulation.

### Random Vibration Analysis

When loads are random in nature, such as turbulent wind gusts or road-induced vibrations on a vehicle, it is not possible to describe them in a deterministic way. Using the new functionality for random response analysis, you can study the response to loads that are represented by their power spectral density (PSD). The loads can be fully correlated, uncorrelated, or have a specific user-defined cross-correlation. Examples of computed results include PSDs of displacements or stresses, as well as the root mean square (RMS) value or higher moments of the spectral distributions.

This new functionality is demonstrated in the following models:

- Random Response Analysis of a Deep Beam (new model)
- Bracket — Random Vibration Analysis (new model)

*Motherboard subjected to random vibration*RMS vertical acceleration in a motherboard subjected to vibration testing with a given acceleration spectral density.

### Visualization of Loads

Applied mechanical loads are now available as default plots in all structural mechanics physics interfaces. The loads plots are solution dependent, so both arrow directions and colors are updated when a dataset is updated with a new solution. Even abstract loads, such as forces and moments applied to rigid connectors and rigid domains are plotted at their true point of application. A new arrow type, used for plotting applied moments, has been introduced for this functionality. More than 100 models are updated with this new functionality.

### User-Defined Material for Membranes

The *External Stress-Strain Relation* material model has been added to the *Membrane* interface. With this material model, you can add your own material models, coded in C or other programming languages.

*Adding a user-defined external material*Adding an external material in the

*Membrane*interface (left) and sample C code (right).

### Point Selections in Rigid Connector for Shell

You can now select points and edges for the selection in a *Rigid Connector* feature in the *Shell* interface. With this, you can add a rigid connector that is only connected to a set of points, by adding it at the point level. This makes it easier to create simplified bolted or riveted connections, for example.

*Pipe connected to a set of points*Pipe connected to eight points on a plate through a rigid connector.

### Direct Stiffness Input for Shells and Plates

In the *Shell* and *Plate* interfaces, it is now possible to describe the elastic stiffness of a cross section in terms of membrane and bending stiffness, rather than by material data and thickness. This new *Section Stiffness* material model facilitates the modeling of homogenized complex structures, such as corrugated sheets. As an alternative, you can provide the input on a flexibility form.

In a general case, it is difficult to compute stresses directly in homogenized materials, since the local details are removed. This type of material model is thus most useful when only the stiffness is important. However, you do have the option of entering expressions for how to compute stresses from section forces for cases when such an operation is well defined.

### Multiphysics Coupling for Heat Transfer in Thin Structures

Effects of thermal expansion can be important in solids as well as thin structures like shells and membranes. Multiphysics couplings have been added so that temperatures computed in a heat transfer analysis of a thin structure can be automatically transferred to corresponding structural mechanics interfaces.

To this end, three new multiphysics interfaces have been added:

*Thermal Stress, Shell*, combining the*Heat Transfer in Shells*and*Shell*interfaces*Thermal Stress, Layered Shell*, combining the*Heat Transfer in Shells*and*Layered Shell*interfaces*Thermal Stress, Membrane*, combining the*Heat Transfer in Shells*and*Membrane*interfaces

You can also connect to the structural mechanics interfaces from the *Thin Layer* feature within the *Heat Transfer in Solids* interface.

View this functionality in the updated Heating Circuit model.

*Multiphysics model of a heating circuit*Temperature distribution (left) and stress (right) in a heating circuit. The thin conducting layer is modeled using a

*Membrane*interface and the substrate is modeled using the

*Solid Mechanics*interface. Both interfaces receive the temperature from the heat transfer analysis through multiphysics couplings.

### Thin Elastic Layers with Mass

The *Thin Elastic Layer* feature, intended for abstract modeling of layers that are thin compared to the rest of the geometry, has been augmented by a possibility to add a mass distribution. This can be important for high-fidelity structural dynamics simulations.

### New Elastic Waves, Time Explicit Physics Interface

The new *Elastic Waves, Time Explicit* physics interface is based on the discontinuous Galerkin time explicit method and enables efficient multicore computations of elastic wave propagation in solids. Features are included to provide realistic material data including anisotropy and damping. The interface is suited for modeling ultrasound propagation in solids, such as with transducers and sensors, and for nondestructive testing (NDT) applications, and is applicable to any acoustically large system that involves transient propagation over many wavelengths, which includes seismic wave propagation in soil and rock.

You can see the new interface used in the following models:

- Ground Motion After Seismic Event: Scattering off a Small Mountain (new model)
- Isotropic-Anisotropic Sample: Elastic Wave Propagation (new model)
- Angle Beam Nondestructive Testing (new model)
- Immersion Ultrasonic Testing Setup (new model)

### Multiphysics for Acoustic-Structure Interaction with the Time Explicit Interfaces

For large transient acoustic-structure interaction simulations, a new *Acoustic-Structure Interaction, Time Explicit* multiphysics coupling is available. This coupling connects the *Pressure Acoustics, Time Explicit* and new *Elastic Waves, Time Explicit* physics interfaces. To take full advantage of the time explicit formulation, the use of nonconforming meshes is essential when coupling domains with different properties. This is achieved through the new *Pair Acoustic-Structure Boundary, Time Explicit* multiphysics coupling that handles geometric assemblies. The use of nonconforming meshes is a natural extension and use of the properties of the discontinuous elements. You can see this functionality used in the Immersion Ultrasonic Testing Setup model.

### New Tutorial Models

Version 5.5 brings several new tutorial models.

##### Stress Analysis of a Portal Crane

*Portal crane with an internal hinge*This tutorial shows how to model an internal hinge in a frame. The results show the deflection and stress in a portal crane with an internal hinge.

**Application Library Title:**

*portal_crane*

##### Bimetallic Strip in Airflow

*Bimetallic strip in airflow*Flow around a bimetallic strip that bends when subjected to heating from the fluid.

**Application Library Title:**

*bimetallic_strip_fsi*

##### Block Pressing on Arch

**Application Library Title:**

*block_on_arch*

##### Coupled Analysis of Flow and Stress in a Pipe

*Flow and stress in a pipe*Analysis of stresses in a pipe subjected to fluid loads and gravity. Results show the pressure and fluid velocity (lower) and von Mises stress and deformation (upper)

**Application Library Title:**

*pipe_flow_stress*

##### Instability of Two Contacting Arches

*Deformation evolution for two contacting arches*Evolution of deformation and stress as the upper arch forces the lower arch downwards. The contact problem is computed using the

*Shell*interface, and the snap-through path is traced.

**Application Library Title:**

*two_arches*

##### Random Vibration Analysis of a Deep Beam

**Application Library Title:**

*random_vibration_deep_beam*

##### Bracket — Random Vibration Analysis

*Bracket subjected to random vibration*RMS stresses in a bracket subjected to a random vibration load.

**Application Library Title:**

*bracket_random_vibration*

##### Random Vibration of a Motherboard

*Motherboard subjected to random vibration*RMS vertical acceleration in a motherboard subjected to vibration testing with a given acceleration spectral density.

**Application Library Title:**

*motherboard_random_vibration*

##### Eigenmodes of a Viscoelastic Structural Damper

*Damper*Second eigenmode in a model of a damper where the frequency-dependent viscoelastic material makes it necessary to solve a nonlinear eigenvalue problem for each natural frequency.

**Application Library Title:**

*viscoelastic_damper_eigenmodes*

##### Pressurized Orthotropic Container — Shell Version

**Application Library Title:**

*orthotropic_container_shell*

##### Bracket — Topology Optimization

*Two bracket designs*Original design space and optimized structure with deformation from one of eight load cases.

**Application Library Title:**

*bracket_topology_optimization_stl*

##### Isotropic-Anisotropic Sample: Elastic Wave Propagation

*Isotropic and anisotropic materials*In this 2D tutorial, a test sample consists of an isotropic material on one side and an anisotropic material (a transverse anisotropic zinc crystal) on the other. Elastic waves in the sample are excited by a point-like force modulated at 0.17 MHz.

**Application Library Title:**

*isotropic_anisotropic_sample*