Glossary of Terms
anisotropy
Variation of material properties with direction. Both global and local user-defined coordinate systems can be used to define anisotropic material properties.
arbitrary Lagrangian–Eulerian (ALE) method
A technique to formulate equations in a mixed kinematic description. An ALE referential coordinate system is typically a mix between the material (Lagrangian) and spatial (Eulerian) coordinate systems.
augmented Lagrangian method
A method for solving contact problems. Augmentation components are introduced for the contact pressure and the components of the friction traction vector. Additional iteration levels are added where the displacement, contact pressure and traction variables are solved separately. The algorithm repeats this procedure until it fulfills a convergence criterion.
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. Also called spar or truss element. In COMSOL Multiphysics the term truss element is used.
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 lines in 2D and 3D.
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 variables are defined in a specific coordinate system.
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.
deformation gradient
Tensor containing the complete information about the local straining and rotation of the material. It is a positive definite second rank tensor.
destination boundary
One side of a contact pair; the destination boundary is prohibited to penetrate the source boundary.
double dogleg solver
The default nonlinear solver for mechanical contact. This solver is also useful for highly nonlinear simulations such as large plastic deformation or hyperelastic materials.
eigenfrequency study
Solving for the damped or undamped natural frequencies and vibration modes of a structure.
elasticity matrix
The matrix D relating strain to stresses:
equilibrium equation
The equation expressing the equilibrium formulated in the stress components.
Eulerian
Model described and solved in a coordinate system that is fixed (spatial frame). See also Lagrangian and arbitrary Lagrangian-Eulerian method.
first Piola–Kirchhoff stress
A stress measure used when geometric nonlinearities arise. All forces in COMSOL Multiphysics in case of geometric nonlinearity are of this type.
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
In solid mechanics, the deformation state characterized by finite (or large displacements) but small to moderate strains. Not all material models are suitable for large strain analysis, even though the displacement and rotation can be large.
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.
initial strain
The strain in a stress-free structure before it is loaded.
initial stress
The stress in a nondeformed structure before it is loaded.
isotropic material
A material where the material properties are independent of direction.
Lagrangian
Model described and solved in a coordinate system that moves with the material. See also Eulerian and arbitrary Lagrangian–Eulerian method.
large deformation
The deformations are so large so the nonlinear effect of the change in geometry or stress stiffening need to be accounted for. See also geometric nonlinearity.
linear buckling analysis
Solves for the linear buckling load using the eigenvalue solver.
linear viscoelasticity
See viscoelastic material.
load multiplier
A load used in linearized buckling analysis for estimating the critical load at which a structure becomes unstable.
mass damping parameter
Rayleigh damping parameter, the coefficient in front of the mass matrix.
mass participation factors
A measure of the sensitivity of a certain eigenmode to a uniform acceleration.
mixed formulation
A formulation used for nearly incompressible materials, where the mean stress have been added as a dependent variable to avoid numerical problems.
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 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 beam 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.
plate
Thin plane structure loaded in the normal direction.
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.
rate of strain tensor
The rate at which the strain tensor changes with respect to time in time-dependent studies.
quasistatic transient study
The loads vary slow enough for the inertia terms to be negligible. 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, rigid connectors, rigid domains, and shells have rotational degrees of freedom.
second Piola–Kirchhoff stress
Conjugate stress to Green–Lagrange strain used in large deformation analysis. The orientations of the stress components follow the material directions.
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.
spar
see bar.
spin tensor
The skew-symmetric part of the velocity gradient tensor.
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.
stress stiffening
The geometrically nonlinear effect which supplies the out-of-plane stiffness for membranes, for example.
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. Also called elastic energy.
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 equivalent 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.