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, like
A complete list of all available model formulations is available in the hyperelasticity section of the API reference.