# Structural Mechanics Module Glossary

This glossary contains finite element modeling terms in a structural mechanics context. For mathematical terms as well as geometry and CAD terms specific to the COMSOL Multiphysics software, please see the Multiphysics Glossary.

The glossary content is copyright © COMSOL, Inc. For permission to reproduce content, contact .

### anisotropy

Variation of material properties with direction. Both global and local user defined coordinate systems can be used to define anisotropic material properties.

### axial symmetry

Symmetry in both load and geometry, solves for the radial (r) and axial (z) displacement.

### bar

A line element that only has translational degrees of freedom, capable of sustaining axial forces, with no bending moments, torsional moments, or shear forces. Can be used on lines in 2D and 3D.

### beam

A line element having both translational and rotational degrees of freedom. Capable of sustaining axial forces, bending moments, torsional moments, and shear forces. Can be used on curves in 2D and 3D.

### benchmark

Standard test designed to evaluate the accuracy or efficiency of a finite element system or model.

### body forces

Forces distributed through the volume of a body.

### buckling

The sudden collapse or reduction in stiffness of a structure under a critical combination of applied loads.

### cable

A tension-only truss member used to model large deformation including sag.

### Cauchy stress

The most fundamental stress measure defined as force/deformed area in fixed directions not following the body.

### compliance matrix

The inverse of the elasticity matrix. See elasticity matrix.

### constitutive equations

The equations formulating the stress-strain relationship of a material.

### constraint

Constrains the displacement or rotations to zero or a specified value.

### contact model

The mathematical method to model bodies that come into contact with each other.

### contact pair

A pair that consists of some source boundaries and destination boundaries and is used for contact modeling.

### coordinate system

Global Cartesian, local geometrical, application specific, and user-defined coordinate systems. Loads, constraints, material properties, and postprocessing variables are defined in a specific coordinate system.

### creep

Time-dependent material nonlinearity that usually occurs in metals at high temperatures in which the effect of the variation of stress and strain with time is of interest.

### damping

Dissipation of energy in a vibrating structure. A common assumption is viscous damping where the damping is proportional to the velocity. See also Rayleigh damping.

### destination boundary

One side of a contact pair; the destination boundary is prohibited to penetrate the source boundary.

### eigenfrequency study

Solving for the undamped natural frequencies and vibration modes of a structure.

### elasticity matrix

The matrix D relating strain to stresses:

### elastoplastic material

A material model where the material exhibits both elastic and plastic behavior. See also plasticity.

### equilibrium equation

The equation expressing the equilibrium formulated in the stress components.

### first Piola-Kirchhoff stress

A rather mathematical stress measure used in the hyperelastic material model, its conjugate strain is the displacement gradient.

### flexibility matrix

The inverse of the elasticity matrix. See elasticity matrix.

### free vibration

The undamped vibration of a structure after it is displaced from the equilibrium position and released. See also eigenfrequency analysis.

### frequency response

A harmonic analysis solving for the steady-state response from a harmonic excitation. Typically a frequency sweep is performed, solving for many excitation frequencies at one time.

### geometric nonlinearity

See large deformation.

### Green-Lagrange strain

Nonlinear strain measure used in large-deformation analysis. In a small strain, large rotation analysis, the Green-Lagrange strain corresponds to the engineering strain, with the strain values interpreted in the original directions. The Green-Lagrange strain is a natural choice when formulating a problem in the undeformed state. The conjugate stress is the second Piola-Kirchhoff stress.

### hyperelastic material

Material where the stresses are computed from a strain energy density function. Often used to model rubber, but also used in acoustoelasticity.

### initial strain

The strain in a stress-free structure before it is loaded.

### initial stress

The stress in a non-deformed structure before it is loaded.

### isotropic material

A material where the material properties are independent of direction.

### isotropic hardening

A hardening model for an elasto-plastic material where the yield surface increases in size but maintains its original shape.

### kinematic hardening

A hardening model for an elasto-plastic material where the yield surface is translated to a new position in the stress space as the plastic strain is increased, with no change in size or shape.

### large deformation

The deformations are so large so the nonlinear effect of the change in geometry or stress stiffening need to be accounted for.

### linear buckling analysis

Solves for the linear buckling load using the eigenvalue solver.

### mass damping parameter

Rayleigh damping parameter, the coefficient in front of the mass matrix.

### mixed formulation

A formulation where the pressure have been added as a dependent variable, used for nearly incompressible materials to avoid numerical problems.

### Mooney-Rivlin material model

A hyperelastic material model with three model parameters. The model is based on modified strain invariants.

### Murnaghan material model

A hyperelastic material model with five model parameters. The model is based on modified strain invariants and is typically used in acoustoelasticity.

### Neo-Hookean material model

A hyperelastic material model with two model parameters. The model is based on modified strain invariants.

### nonlinear geometry

See large deformations.

### orthotropic material

An orthotropic material has at least two orthogonal planes of symmetry, where material properties are independent of direction within each plane. Such materials require nine independent variables (that is, elastic constants) in the constitutive equations.

### parametric study

A study that finds the solution dependence due to the variation of a specific parameter.

### pinned

A constraint condition where the displacement degrees of freedom are fixed but the rotational degrees of freedom are free, typically used for frames modeled using beams and truss elements.

### plane strain

An assumption on the strain field where all out-of-plane strain components are assumed to be zero.

### plane stress

An assumption on the stress field, all out-of-plane stress components are assumed to be zero.

### plasticity

A time-independent material nonlinearity. Three classes of plastic behavior are considered: perfectly plastic, isotropic hardening, kinematic hardening.

### plate

Thin structure loaded in the normal direction.

### primary creep

The initial creep stage where the strain rate is decreasing with time.

### principle of virtual work

States that the variation in internal strain energy is equal to the work done by external forces.

### principal stresses/strains

Normal stresses/strains with no shear components that act on the principal planes. The magnitude of the principal stresses/strains are independent of the coordinate system used.

### quasi-static transient study

The loads vary slowly so inertia terms can be neglected. A transient thermal study coupled with a structural analysis can often be treated as quasi-static.

### Rayleigh damping

A viscous damping model where the damping is proportional to the mass and stiffness through the mass and stiffness damping parameters.

### rotational degrees of freedom

Degrees of freedom associated with a rotation around an axis. Beams, Mindlin plates, and shells have rotational degrees of freedom.

### secondary creep

A creep regime where the strain rate is almost constant.

### second Piola-Kirchhoff stress

Conjugate stress to Green-Lagrange strain used in large deformation analysis.

### shell elements

A thin element where both bending and membrane effects are included.

### source boundary

One side of a contact pair; the destination boundary is prohibited to penetrate the source boundary.

### stationary study

A study where the loads and constraints are constant in time. Also called static.

### strain

Relative change in length, a fundamental concept in structural mechanics.

### stress

Internal forces in the material, normal stresses are defined as forces/area normal to a plane, and shear stresses are defined as forces/area in the plane. A fundamental concept in structural mechanics.

### stiffness damping parameter

Rayleigh damping parameter, the coefficient in front of the stiffness matrix.

### strain energy

The energy stored by a structure as it deforms under load.

### tertiary creep

The creep stage where the strain rate increases very rapidly, followed by eventual failure.

### time-dependent study

A time-dependent or transient study shows how the solution varies over time, taking into account mass, mass moment of inertia, and damping.

### Tresca stress

An effective stress measure that is equal to the maximum shear stress.

See bar.

### viscoelastic material

Viscoelastic materials have a time-dependent response, even if the loading is constant. Many polymers and biological tissues exhibit such a behavior. Linear viscoelasticity is a commonly used approximation where the stress depends linearly on the strain and its time derivatives.

### viscoelastic transient initialization

A stationary study with viscoelasticity included. Used to precompute initial states for time-dependent studies when the viscoelastic material model is used. It is a regime of instantaneous deformation and/or loading.