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.

from wrap import * 
import numpy as np
metafor = None
 
class PythonHyperMaterial:
    def __init__(self, _no):
        self._no = _no
 
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