Solid Mechanics

The options for modeling solid mechanics include full 3D; 2D (plane stress, plane strain, and generalized plane strain); 2D axial symmetry; 1D (plane stress or plane strain in transverse directions); and 1D axial symmetry, and provide the most general approach to analyzing solid structures with built-in multiphysics couplings. There is a wide variety of material models available for accurately describing solid mechanics problem, and it is easy to extend these features via equation-based modeling. Users can define material properties with constant, spatially varying, anisotropic, or nonlinear expressions; lookup tables; or combinations of these. Elements can be activated and deactivated based on user-defined expressions. It is also possible to assign material models to surfaces, internal or external. This can be used to model, for example, glue layers, gaskets, fracture zones, or claddings.

Shells and Membranes

For thin structures, using shell (3D, 2D axisymmetry) and plate (2D) elements can be very efficient. The formulations allow for the transverse shear deformations needed to model thick shells. It is also possible to prescribe an offset in the direction normal to a selected surface, which simplifies modeling projects involving a full 3D representation of the geometry. The results from shell element analyses can be presented as a full solid representation.

Very thin structures, such as thin films and fabric, require a formulation with no bending stiffness. This is possible in the Membrane interface, in which curved plane stress elements in 3D or 2D axisymmetry are used to compute in-plane and out-of-plane displacements, including the effects of wrinkling. When studying this type of structure, the ability to start from a prestressed state is used extensively.

Elastic Waves

Model the propagation of elastic waves in isotropic, orthotropic, anisotropic, and piezoelectric solids, for single-physics or multiphysics applications, such as vibration control, nondestructive testing (NDT), or mechanical feedback. Application areas range from micromechanical problems to seismic wave propagation.

The Solid Mechanics interface uses a full structural dynamics formulation that accounts for the effects of shear waves and pressure waves in solids and analyzes elastic waves. Mechanical port conditions can be used to excite and absorb propagating modes in waveguide structures and to compute a scattering matrix of a component. Absorbing boundary conditions and perfectly matched layers (PMLs) enable efficient modeling of unbounded domains.

The Elastic Waves, Time Explicit interface can be used to compute the transient propagation of linear elastic waves over large domains containing many wavelengths. The interface uses a higher-order dG-FEM time-explicit method. The interface is multiphysics enabled and can be seamlessly coupled to fluid domains.

Material Models

The Structural Mechanics Module provides linear elastic, viscoelastic, and piezoelectric material models, and a wide range of nonlinear material models, including hyperelastic and elastoplastic models, is accessible by adding the Nonlinear Structural Materials Module or Geomechanics Module.

In addition, there are many possibilities for extending the existing material models or for users to create their own. Expressions that depend on stress, strain, spatial coordinates, time, or fields coming from another physics interface can be entered directly in the input field for a material property. In frequency-domain analyses, complex-valued expressions can be entered. For example, custom differential equations can be added to provide inelastic strain contributions.

The material models can accommodate thermal expansion, hygroscopic swelling, initial stresses and strains, and several types of damping. Material properties can be isotropic, orthotropic, or fully anisotropic. Users can include their own material model by providing external functions coded in the C programming language.

Loads and Constraints

The Structural Mechanics Module offers a multitude of different load and constraint options, which facilitates high-fidelity modeling. There are capabilities for defining distributed loads on domains, boundaries, and edges, follower loads, and moving loads. There is also support for specifying a total force, including gravity or added mass, and including rotating frames with centrifugal, Coriolis, and Euler forces.

For constraining a model, there are springs and dampers, as well as prescribed displacement, velocity, and acceleration. Periodic boundary conditions, low-reflecting boundaries, perfectly matched layers (PMLs), and infinite elements aid in reducing model size for efficient modeling.

Dynamics and Vibration

The Structural Mechanics Module covers transient as well as frequency-response analysis. Frequency-response analysis includes eigenfrequency, damped eigenfrequency, and frequency sweep analyses. In addition, specialized study types are available for random vibration and response spectrum analysis. Random vibration analysis allows for inputs based on power spectral density (PSD) as a function of frequency, including uncorrelated as well as fully correlated loads. A typical example is the wind load on a tower. Response spectrum analysis is used as an efficient method for determining structural response to short nondeterministic events like earthquakes and shocks.

Component mode synthesis (CMS), also known as dynamic substructuring, reduces linear components to computationally efficient reduced-order models using the Craig–Bampton method. These components can then be used in dynamic or stationary analyses, improving computation time and memory usage.

Beams, Pipes, Trusses, and Wires

There are specialized element types for modeling beams, described by their cross section properties. Formulations for both slender beams (Euler–Bernoulli theory) and thick beams (Timoshenko theory) are available. Predefined couplings allow for mixing beams with other element types to study reinforcements for solid and shell structures. A library of common cross section types are available as well as functionality for modeling general cross sections.

Additionally, the Structural Mechanics Module enables the modeling of slender structures that can only sustain axial forces (trusses and wires). These elements can also be used for modeling reinforcements.

Structural analysis of pipes is similar to that of beams but with the addition of an internal pressure that usually contributes significantly to the stresses in a pipe. Also, in this type of analysis, temperature gradients usually occur through the pipe wall, rather than across the entire section. The loads from internal pressure and drag forces can be taken directly from the results of a pipe flow and thermal analysis using the Pipe Flow Module.

Contact and Friction

Situations where objects come into contact with each other occur frequently in mechanical simulations. Static and dynamic analyses can include contact modeling, and the objects in contact can have arbitrarily large relative displacements. Additionally, the effects of friction, both sticking and sliding, can be modeled.

The contact analysis functionality also includes the possibility to prescribe adhesion and decohesion between the contacting objects, and to model removal of material by wear when the objects are sliding relative to each other.

Fracture Mechanics

Several different approaches for crack modeling are supported. A crack can either be infinitely thin and represented by a single boundary or represented by disjoint surfaces in the geometry. A crack can have any number of branches and corresponding crack fronts. Effects of crack closure, as well as loads on the crack faces, can be included. Stress intensity factors and energy release rates can be computed in 2D and 3D using J-integral or virtual crack extension methods.

By adding the Nonlinear Structural Materials Module or Geomechanics Module, users can model damage and cracking in brittle materials according to various criteria.

Engineering Features

The Structural Mechanics Module, includes several structural engineering features that allow for creating real-world models more quickly. These features include boundary conditions such as rigid connectors for modeling rigid regions and kinematic constraints, bolts with pretension, stress linearization for analysis of pressure vessels, and more.

• Rigid connector
• Rigid domain
• Automatic handling of RBE2 elements from NASTRAN^® import
• Bolt pretension
• Bolt thread contact modeling
• Stress linearization
• Weld evaluation
• Evaluation of warpage
• Safety factor expressions
• Computation of section forces in a cut through a solid
• Superposition of load cases
• Computation of effective material properties
  • Uses representative volume elements (RVE)