def get_yield_function(self,stress):
if material_type=='druckerprager': #yf=J_2**0.5+alpha*tr(stress)-k
from mesh import Point
poi=Point()
m=poi.get_mean_stress(stress)
J2=poi.get_second_invariant_of_deviatoric_stress(stress)
yf=J2**0.5+3*alpha*m-k
return yf
def Rmatrix(ipoint):
from mesh import Point
from math import sin, cos
poi = Point()
R = np.zeros([3, 3], dtype=float)
angle = poi.get_angle(ipoint)
# angle=0.
R[0, 0] = cos(angle)
R[0, 1] = sin(angle)
R[1, 0] = -sin(angle)
R[1, 1] = cos(angle)
R[2, 2] = 1.
return R
def get_derivative_of_yield_function(self,stress):
import numpy as np
if material_type=='druckerprager':
from mesh import Point
poi=Point()
J2=poi.get_second_invariant_of_deviatoric_stress(stress)
J2+=1.e-10
dJ2=np.empty(3,dtype=float)
for i in range(3):
j=(i+1)%3
k=(i+2)%3
dJ2[i]=(2*stress[i]-stress[j]-stress[k])/3
dyf=np.empty(6,dtype=float)
dyf[0]=0.5*dJ2[0]*J2**(-0.5)+alpha
dyf[1]=0.5*dJ2[1]*J2**(-0.5)+alpha
dyf[2]=0.5*dJ2[2]*J2**(-0.5)+alpha
dyf[3]=stress[3]*J2**(-0.5)
dyf[4]=stress[4]*J2**(-0.5)
dyf[5]=stress[5]*J2**(-0.5)
return dyf
