Isotropic Hyperelastic Materials

User materials (Umat) based on the right Cauchy-Green deformation tensor, suitable for Total-Lagrangian isotropic hyperelastic material formulations, are to be created with Hyperelastic. Only the strain energy function must be defined. Both gradient and hessian are evaluated by forward-mode automatic differentiation. Therefore, only math-functions from tensortrax.math are supported. A user-defined function must be created with the argument and return values:

Kind	Symbol	Description
Argument	C	right Cauchy-Green deformation tensor
Return	W	strain energy function

import tensortrax.math as tm

def strain_energy_function(C, **kwargs):
    return W

This function is further added as the fun argument of Hyperelastic.

import felupe as fem

umat = fem.Hyperelastic(fun=strain_energy_function, **kwargs)

FElupe contains several reference implementations of hyperelastic user material formulations

• saint_venant_kirchhoff()

• neo_hooke()

• mooney_rivlin()

• yeoh()

• third_order_deformation()

• ogden()

• arruda_boyce()

• extended_tube()

• van_der_waals()

as well as a function decorator for the multiplicative isochoric-volumetric split of the Deformation Gradient.

• isochoric_volumetric_split()