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# -*- coding: utf-8 -*-
"""
Created on Thu Apr 3 10:42:13 2025
@author: nroisin
"""
import numpy as np
def stress_from_strain(strain_tensor,c11= 165.77,c12= 63.93,c44 = 79.62):
strain_voigt=np.zeros((1,6))
strain_shape=np.shape(strain_tensor)
if len(strain_shape)==2:
if strain_shape[0]==3 and strain_shape[1]==3:
strain_voigt[0]=strain_tensor[0,0]
strain_voigt[1]=strain_tensor[1,1]
strain_voigt[2]=strain_tensor[2,2]
strain_voigt[3]=strain_tensor[1,2]
strain_voigt[4]=strain_tensor[0,2]
strain_voigt[5]=strain_tensor[0,1]
if strain_shape[0]==1 and strain_shape[1]==6:
strain_voigt=strain_tensor
else:
strain_voigt=np.array([strain_tensor])
compliance_tensor=np.array([[c11,c12,c12,0,0,0],
[c12,c11,c12,0,0,0],
[c12,c12,c11,0,0,0],
[0,0,0,c44,0,0],
[0,0,0,0,c44,0],
[0,0,0,0,0,c44]])
return compliance_tensor @ strain_tensor
def strain_from_stress(stress_tensor,c11= 165.77,c12= 63.93,c44 = 79.62):
stress_voigt=np.zeros((1,6))
stress_shape=np.shape(stress_tensor)
if len(stress_shape)==2:
if stress_shape[0]==3 and stress_shape[1]==3:
stress_voigt[0]=stress_tensor[0,0]
stress_voigt[1]=stress_tensor[1,1]
stress_voigt[2]=stress_tensor[2,2]
stress_voigt[3]=stress_tensor[1,2]
stress_voigt[4]=stress_tensor[0,2]
stress_voigt[5]=stress_tensor[0,1]
if stress_shape[0]==1 and stress_shape[1]==6:
stress_voigt=stress_tensor
else:
stress_voigt=np.array([stress_tensor])
compliance_tensor=np.array([[c11,c12,c12,0,0,0],
[c12,c11,c12,0,0,0],
[c12,c12,c11,0,0,0],
[0,0,0,c44,0,0],
[0,0,0,0,c44,0],
[0,0,0,0,0,c44]])
return np.linalg.inv(compliance_tensor) @ stress_tensor
def straintensor(direction,cristal_plane,N=11,emin=-0.05,emax=0.05,C11=165.77,C12=63.93,C44=79.62, poisson=True) :
# Constants
retour=np.zeros((3,3,N))
eps=np.linspace(emin,emax,N)
# Initiation
uniepsilon001=np.zeros((3,3,N))
uniepsilon110=np.zeros((3,3,N))
uniepsilon111=np.zeros((3,3,N))
biepsilon001=np.zeros((3,3,N))
biepsilon110=np.zeros((3,3,N))
biepsilon111=np.zeros((3,3,N))
shear001=np.zeros((3,3,N))
shear110=np.zeros((3,3,N))
shear111=np.zeros((3,3,N))
hydro=np.zeros((3,3,N))
# Matrix computation
# Uniaxial
if poisson:
uniepar001=-C12/(C11+C12)*eps
else:
uniepar001=0
uniepsilon001[0][0]=uniepar001
uniepsilon001[0][1]=np.zeros(N)
uniepsilon001[0][2]=np.zeros(N)
uniepsilon001[1][0]=np.zeros(N)
uniepsilon001[1][1]=uniepar001
uniepsilon001[1][2]=np.zeros(N)
uniepsilon001[2][0]=np.zeros(N)
uniepsilon001[2][1]=np.zeros(N)
uniepsilon001[2][2]=eps
if poisson:
uniepar110=- ( 4*C12*C44 ) / ( 2*C11*C44+(C11+2*C12)*(C11-C12) )*eps
else:
uniepar110=0
uniepsilon110[0][0]=0.5*(eps+uniepar110)
uniepsilon110[0][1]=0.5*(eps-uniepar110)
uniepsilon110[0][2]=np.zeros(N)
uniepsilon110[1][0]=0.5*(eps-uniepar110)
uniepsilon110[1][1]=0.5*(eps+uniepar110)
uniepsilon110[1][2]=np.zeros(N)
uniepsilon110[2][0]=np.zeros(N)
uniepsilon110[2][1]=np.zeros(N)
uniepsilon110[2][2]=uniepar110
if poisson:
uniepar111 = - (C11 + 2*C12 - 2*C44) / (C11 + 2*C12 + 2*C44)*eps
else:
uniepar111 = 0
uniepsilon111[0][0] = (eps + 2*uniepar111) / 3
uniepsilon111[0][1] = (eps - uniepar111) / 3
uniepsilon111[0][2] = (eps - uniepar111) / 3
uniepsilon111[1][0] = (eps - uniepar111) / 3
uniepsilon111[1][1] = (eps + 2*uniepar111) / 3
uniepsilon111[1][2] = (eps - uniepar111) / 3
uniepsilon111[2][0] = (eps - uniepar111) / 3
uniepsilon111[2][1] = (eps - uniepar111) / 3
uniepsilon111[2][2] = (eps + 2*uniepar111) / 3
# Biaxial
if poisson:
bieper001 = -2 * C12 / C11 * eps
else:
bieper001=0
biepsilon001[0][0] = eps
biepsilon001[0][1] = np.zeros(N)
biepsilon001[0][2] = np.zeros(N)
biepsilon001[1][0] = np.zeros(N)
biepsilon001[1][1] = eps
biepsilon001[1][2] = np.zeros(N)
biepsilon001[2][0] = np.zeros(N)
biepsilon001[2][1] = np.zeros(N)
biepsilon001[2][2] = bieper001
if poisson:
bieper110 = -(C11+3*C12-2*C44)/(C11+C12+2*C44)*eps
else:
bieper110 = 0
biepsilon110[0][0] = 0.5*(bieper110+eps)
biepsilon110[0][1] = 0.5*(bieper110-eps)
biepsilon110[0][2] = np.zeros(N)
biepsilon110[1][2] = np.zeros(N)
biepsilon110[1][1] = 0.5*(bieper110+eps)
biepsilon110[1][0] = 0.5*(bieper110-eps)
biepsilon110[2][0] = np.zeros(N)
biepsilon110[2][1] = np.zeros(N)
biepsilon110[2][2] = eps
if poisson:
bieper111 = -2*(C11+2*C12-2*C44)/(C11+2*C12+4*C44)* eps
else:
bieper111=0
biepsilon111[0][0] = (bieper111+2*eps)/3
biepsilon111[0][1] = (bieper111-eps)/3
biepsilon111[0][2] = (bieper111-eps)/3
biepsilon111[1][0] = (bieper111-eps)/3
biepsilon111[1][1] = (bieper111+2*eps)/3
biepsilon111[1][2] = (bieper111-eps)/3
biepsilon111[2][0] = (bieper111-eps)/3
biepsilon111[2][1] = (bieper111-eps)/3
biepsilon111[2][2] = (bieper111+2*eps)/3
# Shear
shear001[0][2] = eps
shear001[2][0] = eps
shear110[0][2] = eps/np.sqrt(2)
shear110[2][0] = eps/np.sqrt(2)
shear110[1][2] = eps/np.sqrt(2)
shear110[2][2] = eps/np.sqrt(2)
shear111[0][1] = eps/np.sqrt(3)
shear111[0][2] = eps/np.sqrt(3)
shear111[1][0] = eps/np.sqrt(3)
shear111[1][2] = eps/np.sqrt(3)
shear111[2][0] = eps/np.sqrt(3)
shear111[2][1] = eps/np.sqrt(3)
# hydro
hydro[0][0] = eps/3
hydro[1][1] = eps/3
hydro[2][2] = eps/3
if direction == "uniaxial":
if cristal_plane == "001":
retour=uniepsilon001
elif cristal_plane == "110":
retour=uniepsilon110
elif cristal_plane == "111":
retour=uniepsilon111
elif direction == "biaxial":
if cristal_plane == "001":
retour=biepsilon001
elif cristal_plane == "110":
retour=biepsilon110
elif cristal_plane == "111":
retour=biepsilon111
elif direction == "shear":
if cristal_plane == "001":
retour=shear001
elif cristal_plane == "110":
retour=shear110
elif cristal_plane == "111":
retour=shear111
elif direction =="hydro" :
retour = hydro
return retour
def straintensor_scalar(direction,cristal_plane,eps=0,C11=16.577,C12=6.393,C44=7.962,poisson=True) :
# Constants
retour=np.zeros((3,3))
# Initiation
uniepsilon001=np.zeros((3,3))
uniepsilon110=np.zeros((3,3))
uniepsilon111=np.zeros((3,3))
biepsilon001=np.zeros((3,3))
biepsilon110=np.zeros((3,3))
biepsilon111=np.zeros((3,3))
shear001=np.zeros((3,3))
shear110=np.zeros((3,3))
shear111=np.zeros((3,3))
hydro=np.zeros((3,3))
# Matrix computation
# Uniaxial
if poisson:
uniepar001=-C12/(C11+C12)*eps
else:
uniepar001=0
uniepsilon001[0][0]=uniepar001
uniepsilon001[0][1]=0
uniepsilon001[0][2]=0
uniepsilon001[1][0]=0
uniepsilon001[1][1]=uniepar001
uniepsilon001[1][2]=0
uniepsilon001[2][0]=0
uniepsilon001[2][1]=0
uniepsilon001[2][2]=eps
if poisson:
uniepar110=- ( 4*C12*C44 ) / ( 2*C11*C44+(C11+2*C12)*(C11-C12) )*eps
else:
uniepar110=0
uniepsilon110[0][0]=0.5*(eps+uniepar110)
uniepsilon110[0][1]=0.5*(eps-uniepar110)
uniepsilon110[0][2]=0
uniepsilon110[1][0]=0.5*(eps-uniepar110)
uniepsilon110[1][1]=0.5*(eps+uniepar110)
uniepsilon110[1][2]=0
uniepsilon110[2][0]=0
uniepsilon110[2][1]=0
uniepsilon110[2][2]=uniepar110
if poisson:
uniepar111 = - (C11 + 2*C12 - 2*C44) / (C11 + 2*C12 + 2*C44)*eps
else:
uniepar111=0
uniepsilon111[0][0] = (eps + 2*uniepar111) / 3
uniepsilon111[0][1] = (eps - uniepar111) / 3
uniepsilon111[0][2] = (eps - uniepar111) / 3
uniepsilon111[1][0] = (eps - uniepar111) / 3
uniepsilon111[1][1] = (eps + 2*uniepar111) / 3
uniepsilon111[1][2] = (eps - uniepar111) / 3
uniepsilon111[2][0] = (eps - uniepar111) / 3
uniepsilon111[2][1] = (eps - uniepar111) / 3
uniepsilon111[2][2] = (eps + 2*uniepar111) / 3
# Biaxial
if poisson:
bieper001 = -2 * C12 / C11 * eps
else:
bieper001=0
biepsilon001[0][0] = eps
biepsilon001[0][1] = 0
biepsilon001[0][2] = 0
biepsilon001[1][0] = 0
biepsilon001[1][1] = eps
biepsilon001[1][2] = 0
biepsilon001[2][0] = 0
biepsilon001[2][1] = 0
biepsilon001[2][2] = bieper001
if poisson:
bieper110 = -(C11+3*C12-2*C44)/(C11+C12+2*C44)*eps
else:
bieper110=0
biepsilon110[0][0] = 0.5*(bieper110+eps)
biepsilon110[0][1] = 0.5*(bieper110-eps)
biepsilon110[0][2] = 0
biepsilon110[1][2] = 0
biepsilon110[1][1] = 0.5*(bieper110+eps)
biepsilon110[1][0] = 0.5*(bieper110-eps)
biepsilon110[2][0] = 0
biepsilon110[2][1] = 0
biepsilon110[2][2] = eps
if poisson:
bieper111 = -2*(C11+2*C12-2*C44)/(C11+2*C12+4*C44)* eps
else:
bieper111=0
biepsilon111[0][0] = (bieper111+2*eps)/3
biepsilon111[0][1] = (bieper111-eps)/3
biepsilon111[0][2] = (bieper111-eps)/3
biepsilon111[1][0] = (bieper111-eps)/3
biepsilon111[1][1] = (bieper111+2*eps)/3
biepsilon111[1][2] = (bieper111-eps)/3
biepsilon111[2][0] = (bieper111-eps)/3
biepsilon111[2][1] = (bieper111-eps)/3
biepsilon111[2][2] = (bieper111+2*eps)/3
# Shear
shear001[0][2] = eps
shear001[2][0] = eps
shear110[0][2] = eps/np.sqrt(2)
shear110[2][0] = eps/np.sqrt(2)
shear110[1][2] = eps/np.sqrt(2)
shear110[2][2] = eps/np.sqrt(2)
shear111[0][1] = eps/np.sqrt(3)
shear111[0][2] = eps/np.sqrt(3)
shear111[1][0] = eps/np.sqrt(3)
shear111[1][2] = eps/np.sqrt(3)
shear111[2][0] = eps/np.sqrt(3)
shear111[2][1] = eps/np.sqrt(3)
# hydro
hydro[0][0] = eps/3
hydro[1][1] = eps/3
hydro[2][2] = eps/3
if direction == "uni":
if cristal_plane == "001":
retour=uniepsilon001
elif cristal_plane == "110":
retour=uniepsilon110
elif cristal_plane == "111":
retour=uniepsilon111
elif direction == "bi":
if cristal_plane == "001":
retour=biepsilon001
elif cristal_plane == "110":
retour=biepsilon110
elif cristal_plane == "111":
retour=biepsilon111
elif direction == "shear":
if cristal_plane == "001":
retour=shear001
elif cristal_plane == "110":
retour=shear110
elif cristal_plane == "111":
retour=shear111
elif direction =="hydro" :
retour = hydro
return retour