Linear geometry mechanical laws

This section documents the mechanical laws that assume the linear geometry (small strain, small rotation) approximation.

A mechanical law is the constitutive part of a solids4foam case: the solid model assembles and solves the momentum equation, and the mechanical law answers the single question given the current displacement field, what is the stress? Linear geometry laws answer that question in terms of the small-strain tensor

epsilon = symm(grad(D))

or, for an incremental solid model, in terms of the increment symm(grad(DD)) accumulated onto the old-time strain. There is no distinction between the reference and deformed configurations, no deformation gradient F, and no distinction between Cauchy and Piola-Kirchhoff stress. Laws in this directory are registered under the linGeomMechLaw run-time selection table and are intended for use with the linear geometry solid models, for example linearGeometryTotalDisplacement, unsLinearGeometry and poroLinearGeometry.

Note

The nonlinear geometry counterparts live in nonLinearGeometryLaws and areregistered under a separate nonLinGeomMechLaw table. A law from one tablecannot be selected by a solid model that uses the other.

Catalogue

For every law in this subsection the run-time selection name registered by addToRunTimeSelectionTable is identical to the C++ class name, so the class name is what you type in constant/mechanicalProperties.

Runtime type	Purpose
`linearElastic`	Isotropic Hooke's law
`orthotropicLinearElastic`	Nine-parameter orthotropic Hooke's law
`linearElasticMisesPlastic`	Hooke's law with J2 (von Mises) plasticity
`linearElasticMohrCoulombPlastic`	Hooke's law with Mohr-Coulomb plasticity
`poroMechanicalLaw`	Wrapper adding a pore-pressure term
`thermoMechanicalLaw`	Wrapper adding a thermal expansion term
`viscousHookeanElastic`	Generalised Maxwell (Prony series) viscoelasticity
`anisotropicBiotElastic`	Orthotropic elasticity for soil skeletons
`diffusionElastic`	Hooke's law scaled by a mesh motion diffusivity
`linearElasticCt`	`E` from CT data; not currently built
`linearElasticFromFile`	Hooke's law with `E` read as a field from disk

Three of these are wrappers rather than stand-alone constitutive models: poroMechanicalLaw and thermoMechanicalLaw each own a nested, run-time selectable law and add a spherical stress contribution to whatever it returns. They can therefore be combined with most of the other entries in the table.

diffusionElastic is not a physical material model; it exists so that a solid model can be used as a mesh motion solver.

Selecting a law

Mechanical laws are selected in constant/mechanicalProperties. The mechanical entry is a list of sub-dictionaries, one per material, so multi-material cases are expressed by adding further entries:

planeStress     no;

mechanical
(
    steel
    {
        type            linearElastic;
        rho             rho [1 -3 0 0 0 0 0] 7854;
        E               E [1 -1 -2 0 0 0 0] 200e9;
        nu              nu [0 0 0 0 0 0 0] 0.3;
    }
);
  

The name of each sub-dictionary (steel above) is arbitrary; for multi-material cases it must match the corresponding cellZone.

Entries every law understands

These are read by the mechanicalLaw base class, so they are valid inside any of the sub-dictionaries above:

Entry	Default	Description
`rho`	required	Density, `[1 -3 0 0 0 0 0]`
`solvePressureEqn`	`no`	Solve a Laplacian for hydrostatic pressure
`pressureSmoothingScaleFactor`	`100`	Scale factor for that equation
`regionName`	auto	Object registry holding the solid mesh

rho is looked up on demand rather than at construction, so a missing rho is reported the first time the solid model asks for the density. solvePressureEqn is intended for nearly incompressible materials; not every law honours it, and the individual pages say which do.

The top-level planeStress switch sits outside the mechanical list and is read by the base class through the mechanicalProperties dictionary itself. Several laws in this subsection abort if planeStress is yes — see the individual pages.