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 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 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
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 += 1.0e-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
