"""
Equations for the High Velocity Impact Problems
###############################################
"""
from math import sqrt
from pysph.sph.equation import Equation
[docs]class VonMisesPlasticity2D(Equation):
def __init__(self, dest, sources=None, flow_stress=-1):
self.flow_stress = flow_stress
self.factor = sqrt( 2.0 * flow_stress/3.0 )
super(VonMisesPlasticity2D,self).__init__(dest, sources)
[docs] def loop(self, d_idx, d_s00, d_s01, d_s11):
s00a = d_s00[d_idx]
s01a = d_s01[d_idx]
s10a = d_s01[d_idx]
s11a = d_s11[d_idx]
J = s00a* s00a + 2.0 * s01a*s10a + s11a*s11a
scale = 1.0
if (J > 2.0/3.0 * self.flow_stress):
scale = self.factor/sqrt(J)
# store the stresses
d_s00[d_idx] = scale * s00a
d_s01[d_idx] = scale * s01a
d_s11[d_idx] = scale * s11a
[docs]class MieGruneisenEOS(Equation):
def __init__(self, dest, sources=None,
gamma=1.4,r0=-1, c0=-1, S=-1):
self.gamma = gamma
self.r0 = r0
self.c0 = c0
self.S = S
self.a0 = a0 = r0 * c0 * c0
self.b0 = a0 * ( 1 + 2.0*(S - 1.0) )
self.c0 = a0 * ( 2*(S - 1.0) + 3*(S - 1.0)*(S - 1.0) )
super(MieGruneisenEOS, self).__init__(dest, sources)
[docs] def loop(self, d_idx, d_p, d_rho, d_e):
rhoa = d_rho[d_idx]
ea = d_e[d_idx]
gamma = self.gamma
ratio = rhoa/self.r0 - 1.0
ratio2 = ratio * ratio
PH = self.a0 * ratio
if ratio > 0:
PH = PH + ratio2 * (self.b0 + self.c0*ratio)
d_p[d_idx] = (1. - 0.5*gamma*ratio) * PH + rhoa * ea * gamma