Material models

This page helps you choose a material model based on your requirements. Each linked model page (see Stable models) provides the equations, constructor, state behavior, implementation notes, provenance, acknowledgements, and references.

Which model should I use?

The table below is a non-exhaustive overview of frequent problem classes and suitable material formulations; applicability should still be checked for each case.

See the Stable models table below for the full list and related variants.

Stable models

The dt column indicates whether the material is rate-dependent and actively uses the time step size dt for material state updates.

Using MaterialModelsBase.jl models

FerriteSolidMechanics.jl focuses on established material models provided as a whole, but also supports modularly composed materials from the following packages by Knut Andreas Meyer (which also offer extended tooling for them, such as parameter differentiation for calibration and stress-state-driven point simulations): MaterialModelsBase.jl specifies an interface for constitutive models, and MechanicalMaterialModels.jl provides an existing library of material models (such as elasto-(visco)plasticity and viscoelasticity).

Any material implementing this interface can be used directly through the FromMaterialModelsBase wrapper. FerriteSolidMechanics' own constitutive interface deliberately follows similar conventions. Trial/commit state management, threaded/MPI assembly, stress output, and try_stiffness_matrix-based adaptive stepping (local convergence failures surface as MaterialModelsBaseConvergenceError) therefore all work as for bundled material models.

The bridge targets MaterialModelsBase.jl 0.4; a different version may require an update. The extension activates when MaterialModelsBase is loaded:

using Pkg
Pkg.add(url="https://github.com/KnutAM/Newton.jl") # dependency of MechanicalMaterialModels
Pkg.add(url="https://github.com/KnutAM/MaterialModelsBase.jl")
Pkg.add(url="https://github.com/KnutAM/MechanicalMaterialModels.jl")

using FerriteSolidMechanics
import MaterialModelsBase   # activates the extension; prefer `import` over `using` (both packages export `material_response`)
using MechanicalMaterialModels: Plastic, LinearElastic, Voce, ArmstrongFrederick, NortonOverstress

mmmMaterial = Plastic(;
    elastic    = LinearElastic(E=210.0e3, ν=0.3),
    yield      = 100.0,
    isotropic  = Voce(Hiso=50.0e3, κ∞=100.0),
    kinematic  = ArmstrongFrederick(Hkin=200.0e3, β∞=200.0),
    overstress = NortonOverstress(tstar=1.0, nexp=2.0)
)

mat = FromMaterialModelsBase(mmmMaterial)  # kinematics=SmallStrain() is the default
fem = create_assembler(mat, dh, ch)        # then solve exactly as with bundled models

For finite-strain MaterialModelsBase materials pass FromMaterialModelsBase(mmmMaterial; kinematics=FiniteStrain()), which uses the deformation gradient F and expects the material to return (P, ∂P∂F, new_state) (first Piola–Kirchhoff stress, its tangent, and updated state). Note that FerriteSolidMechanics' PlaneStrain/PlaneStress material wrappers are unrelated to MaterialModelsBase's stress-state types of the same names. Whether a material model used through FromMaterialModelsBase can be combined with these 2D wrappers is currently untested. Hooking into the wrappers states the requirements for a wrappable material model.

Related pages

• Material model API lists the constructor docstrings of all bundled models, the PlaneStrain / PlaneStress wrappers, and the wrapper extension points.
• Wrappers explains how 3D material models are embedded into 2D plane strain and plane stress analyses.
• Experimental models lists comparison variants under FerriteSolidMechanics.Experimental.
• Developer guide explains the material interface (material_response + kinematics, trial/commit state handling, and the optional element-level assembly hook) needed to support these features in custom materials.