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.
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anisotropy
Variation of material properties with direction. Both global and local user defined coordinate systems can be used to define anisotropic material properties.
augmented Lagrangian method
Segregated solution method, where the solver switches between solving for the contact pressure and the displacements, used when modeling contact.
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 1D, 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 contact pair consists of some slave and master boundaries and is used for contact modeling.
continuum application modes
The application modes that solve for the displacement field without involving rotations. Solid, Stress-Strain; Plane Stress; Plane Strain; and Axial Symmetry, Stress-Strain are the continuum application modes.
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.
eigenfrequency analysis
Solving for the undamped natural frequencies and vibration modes of a structure.
elasticity matrix
The matrix D relating strain to stresses:
elasto-plastic 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.
fatigue
A term describing the phenomena where a component fails after repeated loadings and unloadings.
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 analysis
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.
master boundary
One side of a contact pair, the slave boundary is prohibited to penetrate the master boundary.
Mindlin plate
A thick plate including shear deformation. See also plate.
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 analysis
An analysis which 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 analysis
The loads vary slowly so inertia terms can be neglected. A transient thermal analysis 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.
slave boundary
One side of a contact pair, the slave boundary is prohibited to penetrate the master boundary.
static analysis
An analysis where the loads and constraints are constant in time.
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.
transient analysis
A time-dependent analysis, taking into account mass, mass moment of inertia, and damping.
tertiary creep
The creep stage where the strain rate increases very rapidly, followed by eventual failure.
Tresca stress
An effective stress measure that is equal to the maximum shear stress.
truss
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 static analysis with viscoelasticity included. Used to precompute initial states for transient and quasi-static transient analyses when the viscoelastic material model is used. It is a regime of instantaneous deformation and/or loading.