"""
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, flow_stress):
self.flow_stress2 = float(flow_stress*flow_stress)
self.factor = sqrt( 2.0/3.0 )*flow_stress
super(VonMisesPlasticity2D,self).__init__(dest, sources)
[docs] def loop(self, d_idx, d_s00, d_s01, d_s02, d_s11, d_s12, d_s22):
s00a = d_s00[d_idx]
s01a = d_s01[d_idx]
s02a = d_s02[d_idx]
s10a = d_s01[d_idx]
s11a = d_s11[d_idx]
s12a = d_s12[d_idx]
s20a = d_s02[d_idx]
s21a = d_s12[d_idx]
s22a = d_s22[d_idx]
J = s00a* s00a + 2.0 * s01a*s10a + s11a*s11a
scale = 1.0
if (J > 2.0/3.0 * self.flow_stress2):
scale = self.factor/sqrt(J)
# store the stresses
d_s00[d_idx] = scale * s00a
d_s01[d_idx] = scale * s01a
d_s02[d_idx] = scale * s02a
d_s11[d_idx] = scale * s11a
d_s12[d_idx] = scale * s12a
d_s22[d_idx] = scale * s22a
[docs]class StiffenedGasEOS(Equation):
"""Stiffened-gas EOS from "A Free Lagrange Augmented Godunov Method for the
Simulation of Elastic-Plastic Solids", B. P. Howell and G. J. Ball, JCP
(2002). http://dx.doi.org/10.1006/jcph.2001.6931
"""
def __init__(self, dest, sources, gamma, r0, c0):
self.gamma = float(gamma) # Gruneisen gamma
self.c0 = float(c0) # unshocked sound speed
self.r0 = float(r0) # reference density
super(StiffenedGasEOS,self).__init__(dest, sources)
[docs] def loop(self, d_idx, d_e, d_rho, d_p, d_cs):
# Eq. (17)
d_p[d_idx] = self.c0*self.c0 * (d_rho[d_idx] - self.r0) + \
(self.gamma - 1.0)*d_rho[d_idx]*d_e[d_idx]
# Eq. (21)
d_cs[d_idx] = sqrt(
self.c0*self.c0 + (self.gamma - 1.0) *
(d_e[d_idx] + d_p[d_idx]/d_rho[d_idx])
)
[docs]class MieGruneisenEOS(Equation):
def __init__(self, dest, sources, gamma,r0, c0, S):
self.gamma = float(gamma)
self.r0 = float(r0)
self.c0 = float(c0)
self.S = float(S)
self.a0 = a0 = float(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