User defined materials

This section explains how any user can define its own constitutive equation in Metafor (usermat or user-defined feature).

The idea is to create a Python class (e.g., in the input file) that derives from the C++ class `PythonHyperMaterial` and overwrites the following functions:

def PythonHyperMaterial.__init__(self, _no): with _no being the material number chosen.
def computeStressPython(self, FTotal):
- Input: The total deformation gradient FTotal, sent from C++ to Python through a std::vector [F11, F12, F13, F21, F22, F23, F31, F32, F33], hence FTotal[0] = F11, etc.
- Output: The Cauchy stress, in the current configuration, returned from Python to C++ through a Python list [Sig11, Sig22, Sig33, Sig12, Sig13, Sig23]

The relation between stress and strain is defined by the user.

Selective integration with pressure report SRIPR for the integration will not work.

The material tangent moduli is automatically approximated using finite central difference.

Example: A NeoHookean Model

from wrap import * 
import numpy as np
metafor = None
 
class UserMat(PythonHyperMaterial):
    def __init__(self, _no):
        PythonHyperMaterial.__init__(self, _no)
 
    def computeStressPython(self, FTotal):
        C1 = 0.5
        K = 1000
 
        F = np.array(FTotal).reshape(3, 3)
        J = np.linalg.det(FTotal)
 
        Fbar = J**(-1/3) * F
        Bbar = np.dot(Fbar.T, Fbar)
 
        cauchyStress = C1/J * Bbar + (-1/3 * np.trace(Bbar) + K*(J-1)) * np.identity(3)
        return [cauchyStress[0, 0], cauchyStress[1, 1], cauchyStress[2, 2], cauchyStress[0, 1], cauchyStress[0, 2], cauchyStress[1, 2]]
 
def getMetafor(_p):
    # ... some code ... #
 
    myNeoHookean = UserMat(1)
    domain.getMaterialSet().add(myNeoHookean)
 
    # ... some code ... #
 
    elementsProps = ElementProperties(Volume2DElement)
    elementsProps.put(MATERIAL, 1)
 
    # ... some code ... #
 
    return metafor