Metafor

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====== 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.<nowiki>__init__</nowiki>(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.
    
<WRAP center round important 60%>
Selective integration with pressure report ''SRIPR'' for the integration will not work.
</WRAP>
<WRAP center round info 60%>
The material tangent moduli is automatically approximated using finite central difference.
</WRAP>


===== Example: A NeoHookean Model =====
<code python>
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
</code>