Small-Strain based Materials

User materials (Umat) based on the incremental small-strain tensor, suitable for elastic-plastic material formulations, are to be created with felupe.MaterialStrain. A user-defined function must be created with the arguments

Arguments	Description
dε	strain increment
εn	old strain tensor
σn	old stress tensor
ζn	list of old state variables

and must return:

Returns	Description
dσdε	tangent modulus
σ	new stress tensor
ζ	list of new state variables

def material(dε, εn, σn, ζn, **kwargs):
    return dσdε, σ, ζ

This function is further added as the material argument of felupe.MaterialStrain. Optionally, the shapes of internal state variables may be passed.

import felupe as fem

umat = fem.MaterialStrain(material=material, statevars=(0,), **kwargs)

FElupe contains two reference user materials, one for linear elastic materials and another one for linear elastic-plastic materials with isotropic hardening:

• felupe.constitution.linear_elastic()

• felupe.constitution.linear_elastic_plastic_isotropic_hardening()