Strain based Materials

A user material (umat), based on the incremental strain tensor, e.g. suitable for linear elastic-plastic material formulations, is provided by MaterialStrain. A user-defined function must be created with the arguments and must return:

Kind	Symbol	Description
Argument	dε	strain increment
Argument	εn	old strain tensor
Argument	σn	old stress tensor
Argument	ζn	list of old state variables
Return	dσdε	tangent modulus
Return	σ	new stress tensor
Return	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 MaterialStrain. If the material makes use of state variables, the shapes of these internal state variables must be provided. By default, the small-strain framework is used. Optionally, this may be changed to a Total-Lagrange or a co-rotational strain framework.

import felupe as fem

umat = fem.MaterialStrain(
    material=material,
    statevars=(0,),
    framework="small-strain",  # also "total-lagrange" or "co-rotational"
    **kwargs,
)

FElupe contains three reference small-strain user materials, one for linear elastic materials, one for linear elastic-plastic materials with isotropic hardening and one for linear viscoelastic materials:

• linear_elastic()

• linear_elastic_plastic_isotropic_hardening()

• linear_elastic_viscoelastic()