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 to a large number of physics areas. There is a wide variety of material models available for accurately describing your solid mechanics problem, and it is easy to extend these features via equation-based modeling. Define material properties yourself 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. You can prescribe an offset in the direction normal to a selected surface, which simplifies modeling where you work with 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 is dedicated to transient linear elastic waves propagation problems 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, but you can also access a wide range of nonlinear material models, including hyperelastic and elastoplastic, by adding the Nonlinear Structural Materials Module or Geomechanics Module.

In addition, there are many possibilities to extend the existing material models or create your own. Enter expressions that depend on stress, strain, spatial coordinates, time, or fields coming from another physics interface directly in the input field for a material property. In frequency-domain analyses, you can enter complex-valued expressions. You can, for example, add custom differential equations to provide inelastic strain contributions.

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

Loads and Constraints

The Structural Mechanics Module provides you with a multitude of different loads and constraints options, which facilitates high-fidelity modeling. Define distributed loads on domains, boundaries, and edges, follower loads, and moving loads. Specify a total force, include gravity or added mass, and include rotating frames with centrifugal, Coriolis, and Euler forces.

For constraining the 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 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 the 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 the capability of 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, 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 to 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.

J-integrals and stress intensity factors can be computed in 2D and 3D. You can also prescribe a load on the crack faces.

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

Engineering Features

In the Structural Mechanics Module, you will find several structural engineering features that help you create 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
• Safety factor expressions
• Computation of section forces in a cut through a solid
• Load cases
• Superposition of load cases
• Computation of effective material properties
  • Uses representative volume elements (RVE)