Material models

A material model describes how a material responds, as opposed to a solid model, which describes how the governing equations are discretised and solved. solids4foam splits this into two independent models:

• the mechanical model, the mechanicalConstitutiveLaw framework, which turns deformation into stress and provides the density and the implicit stiffness used by the momentum equation. It is read from constant/mechanicalProperties, and every solid model uses it.
• the thermal model (thermalModel), which provides the specific heat capacity and thermal conductivity used by the heat equation. It is read from constant/thermalProperties and is only created by the solid models that solve for temperature.

The two are deliberately separate. A thermal analysis therefore needs both dictionaries: the density that multiplies the specific heat capacity is taken from the mechanical model, not the thermal one.

The mechanical model's classes live in src/solids4FoamModels/mechanicalConstitutiveLaw, whose README describes the framework's design.

User Guide

The constant/mechanicalProperties dictionary

mechanicalProperties is read MUST_READ, so it must exist for every solid case. It has these top-level entries:

planeStress is given once, for all materials, and is passed to every law; giving it inside a law's sub-dictionary is an error.

Selecting a mechanical law

The mechanical entry is a list, not a dictionary. Each element is a named sub-dictionary, and the type keyword inside it selects the mechanical constitutive law at runtime:

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;
    }
);

For a single-material case the name (steel above) is arbitrary. It becomes significant as soon as there is more than one entry — see below.

A law implements a small-strain stress update, a finite-strain one, or both. A linear geometry solid model asks for the small-strain update and a nonlinear geometry solid model for the finite-strain one; a law that does not implement the one asked for stops the run with an error.

Available laws

Each law has a page describing its entries, its state and the tutorials that use it:

rho, the density, is read by every law. The optional solvePressureEqn and pressureSmoothingScaleFactor (default 100) entries of a law ask the solid model to smooth the hydrostatic stress; see the solid model pages for which solid models support it. It is supported for a single material only.

Multi-material cases

Give the mechanical list more than one entry to assign different laws to different parts of the mesh:

planeStress     yes;

mechanical
(
    outer
    {
        type            linearElastic;
        rho             rho [1 -3 0 0 0 0 0] 1000;
        E               E [1 -1 -2 0 0 0 0] 200e+9;
        nu              nu [0 0 0 0 0 0 0] 0.3;
    }
    inner
    {
        type            linearElastic;
        rho             rho [1 -3 0 0 0 0 0] 1000;
        E               E [1 -1 -2 0 0 0 0] 20e+9;
        nu              nu [0 0 0 0 0 0 0] 0.35;
    }
);

The rules are:

1. The name of each entry must be the name of a cellZone. The keyword of each mechanical entry (outer, inner above) is taken verbatim as a cellZone name, and construction aborts if no cellZone of that name exists.
2. Every cell must be in exactly one of those cellZones. A cell in none of them, or in more than one, is an error.
3. The displacement gradient scheme must be material-aware. The stress is evaluated on the whole mesh, each cell with its own law, from one displacement gradient. Across an interface between materials the displacement is continuous but its gradient jumps, so a cell's gradient stencil must stay within its own material: set grad(D) leastSquaresS4f; (or grad(DD) for the incremental solid models) in fvSchemes. The cell-centred solid models refuse a multi-material case with any other scheme.

Cell zones are normally created after meshing with setSet followed by setsToZones (or with topoSet). The layeredPipe tutorial does exactly this, with a batch.setSet file that makes an outer and an inner cellSet and subtracts one from the other so the two do not overlap.

Multi-material limitations

Some capabilities are single-material only, and fail with a clear error rather than silently giving a wrong answer:

The vertex-centred solid model supports more than one material: each dual mesh face takes the law of the primary cell it lies in.

Thermal properties

Solid models that solve a temperature equation additionally read constant/thermalProperties, which selects a thermalLaw giving the specific heat capacity and thermal conductivity. See the thermal model page in this section.

Tutorials

Cases with more than one entry in the mechanical list:

• solids/multiMaterial/layeredPipe: a bi-material thick-walled cylinder with cellZones built by setSet/setsToZones and an analytical solution to compare against.
• solids/linearElasticity/punch: two separately meshed parts merged into one mesh, then split into the punch_top and punch_bottom cellZones.
• solids/thermoelasticity/hotCylinder/hotCylinderPredefinedTFieldMultipleMaterials: steel and aluminium materials, each a thermoMechanicalLaw wrapping a linearElastic law.