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constit.py
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constit.py
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"""
A set of methods for describing all of the constitutive models.
Each model operates on an individual material point, updating its' properties. The relevant properties are also mapped to the grid for visualisation.
The models which currently work reliably are:
- Rigid
- Elastic
- Von mises
- Newtonian viscosity
"""
import sys
from numpy import linspace, sin, cos, pi, zeros, outer, array, dot
from numpy import trunc, arctan, eye, trace, nan_to_num, tensordot
from numpy import sqrt, abs, ones, minimum, maximum, exp, isfinite
from numpy import inf
from numpy.linalg import norm
def RK4(func,dstrain,stress):
dstress1 = func(dstrain,stress)
dstress2 = func(dstrain,stress + 0.5*dstress1)
dstress3 = func(dstrain,stress + 0.5*dstress2)
dstress4 = func(dstrain,stress + dstress3)
dstress = (dstress1 + 2.*dstress2 + 2.*dstress3 + dstress4)/6.
return dstress
def rigid(MP,P,G,p):
"""Perfectly rigid particles. No stresses are calculated.
This material model has been validated and is functional.
:param MP: A particle.Particle instance.
:param P: A param.Param instance.
:param G: A grid.Grid instance
:param p: The particle number.
:type p: int
"""
pass
def elastic(MP,P,G,p):
"""Linear elasticity.
This material model has been validated and is functional.
:param MP: A particle.Particle instance.
:param P: A param.Param instance.
:param G: A grid.Grid instance
:param p: The particle number.
:type p: int
"""
de_kk = trace(MP.dstrain)
de_ij = MP.dstrain - de_kk*eye(3)/3.
MP.dstress = P.S[p].K*de_kk*eye(3) + 2.*P.S[p].G*de_ij
# for visualisation
MP.gammadot = sqrt(sum(sum(de_ij**2)))
MP.pressure = trace(MP.stress)/3.
MP.sigmav = MP.stress[1,1]
MP.sigmah = MP.stress[0,0]
for r in range(4):
n = G.nearby_nodes(MP.n_star,r,P)
G.pressure[n] += MP.N[r]*MP.pressure*MP.m
G.gammadot[n] += MP.N[r]*MP.gammadot/P.dt*MP.m
G.sigmav[n] += MP.N[r]*MP.sigmav*MP.m
G.sigmah[n] += MP.N[r]*MP.sigmah*MP.m
def elastic_time(MP,P,G,p):
"""Linear elasticity that is time dependent.
This material model has been validated and is functional.
:param MP: A particle.Particle instance.
:param P: A param.Param instance.
:param G: A grid.Grid instance
:param p: The particle number.
:type p: int
"""
if (p == 0) and (P.t > P.S[p].t_0):
if MP.m > P.S[p].rho_f*MP.V:
MP.m *= 0.95
K_curr = P.S[p].E_0/(3*(1-2*P.S[p].nu))
G_curr = P.S[p].E_0/(2*(1+P.S[p].nu))
# if p == 0:
# if P.t < P.S[p].t_0: E = P.S[p].E_0
# else: E = P.S[p].E_f + (P.S[p].E_0-P.S[p].E_f)*exp(-3.*(P.t-P.S[p].t_0)**2/P.S[p].t_c**2)
# else: E = P.S[p].E_0
# K_curr = E/(3*(1-2*P.S[p].nu))
# G_curr = E/(2*(1+P.S[p].nu))
de_kk = trace(MP.dstrain)
de_ij = MP.dstrain - de_kk*eye(3)/3.
MP.dstress = K_curr*de_kk*eye(3) + 2.*G_curr*de_ij
# for visualisation
MP.gammadot = sqrt(sum(sum(de_ij**2)))
MP.pressure = -trace(MP.stress)/3.
MP.sigmav = -MP.stress[1,1]
MP.sigmah = -MP.stress[0,0]
for r in range(4):
n = G.nearby_nodes(MP.n_star,r,P)
G.pressure[n] += MP.N[r]*MP.pressure*MP.m
G.gammadot[n] += MP.N[r]*MP.gammadot/P.dt*MP.m
G.sigmav[n] += MP.N[r]*MP.sigmav*MP.m
G.sigmah[n] += MP.N[r]*MP.sigmah*MP.m
def von_mises(MP,P,G,p):
"""Von Mises :math:`H^2` yield criterion --- see http://dx.doi.org/10.1016/j.ijsolstr.2012.02.003 Eqs 7.11 - 7.15
This material model has been validated and is functional.
:param MP: A particle.Particle instance.
:param P: A param.Param instance.
:param G: A grid.Grid instance
:param p: The particle number.
:type p: int
"""
de_kk = trace(MP.dstrain) # scalar
de_ij = MP.dstrain - de_kk*eye(3)/3. # matrix
dsigma_kk = 3.*P.S[p].K*de_kk # scalar
dev_work_norm = abs(sum(sum(MP.dev_stress*de_ij))) # scalar
dev_stress_norm = sqrt(sum(sum(MP.dev_stress**2))) # scalar
MP.dev_dstress = 2.*P.S[p].G*(de_ij - dev_work_norm/(2.*(P.S[p].k**2))*
((dev_stress_norm/(sqrt(2.)*P.S[p].k))**(P.S[p].s-2.))*MP.dev_stress) # matrix
MP.sigma_kk += dsigma_kk # scalar
MP.dev_stress += MP.dev_dstress # matrix
MP.dstress = (MP.dev_stress + MP.sigma_kk*eye(3)/3.) - MP.stress # matrix
# for visualisation
MP.yieldfunction = dev_stress_norm/(sqrt(2.)*P.S[p].k) - 1. # scalar
MP.gammadot = sqrt(sum(sum(de_ij**2)))
MP.pressure = trace(MP.stress)/3.
MP.sigmav = MP.stress[1,1]
MP.sigmah = MP.stress[0,0]
for r in range(4):
n = G.nearby_nodes(MP.n_star,r,P)
G.pressure[n] += MP.N[r]*MP.pressure*MP.m
G.yieldfunction[n] += MP.N[r]*MP.yieldfunction*MP.m
G.gammadot[n] += MP.N[r]*MP.gammadot/P.dt*MP.m
G.sigmav[n] += MP.N[r]*MP.sigmav*MP.m
G.sigmah[n] += MP.N[r]*MP.sigmah*MP.m
G.dev_stress[n] += MP.N[r]*norm(MP.dev_stress)*MP.m
G.dev_stress_dot[n] += MP.N[r]*norm(MP.dev_dstress)/P.dt*MP.m
def dp(MP,P,G,p): # UNVALIDATED
"""Drucker-Prager :math:`H^2` yield criterion.
This material model is ONLY PARTIALLY WORKING - NOT YET VALIDATED!
:param MP: A particle.Particle instance.
:param P: A param.Param instance.
:param G: A grid.Grid instance
:param p: The particle number.
:type p: int
"""
def dp_guts(dstrain2d,stress2d):
de_kk = trace(dstrain2d)
de_ij = dstrain2d - de_kk*eye(2)/2. # shear strain
MP.p = trace(stress2d)/2. # pressure, positive for compression
s_ij = stress2d - eye(2)*MP.p # shear stress
MP.q = sqrt(3.*sum(sum(s_ij*s_ij))/2.)
if MP.p > 0: K = P.S[p].K
else: K = 0
# K = P.S[p].K
lambda_2 = ((3.*P.S[p].G*MP.p*sum(sum(s_ij*de_ij)) - K*MP.q**2.*de_kk)/
(3.*P.S[p].G*MP.mu*MP.p**2 + beta*MP.q**2))
# Gamma_2 = lambda_2*(lambda_2>0) # Macauley bracket
Gamma_2 = abs(nan_to_num(lambda_2)) # absolute value
dstress = (2.*P.S[p].G*(de_ij - 3./2.*s_ij/MP.q*Gamma_2*(MP.q/(MP.mu*MP.p))**(P.S[p].s-1.)) +
K*eye(2)*(de_kk + beta*Gamma_2*(MP.q/(MP.mu*MP.p))**P.S[p].s))
dstress = nan_to_num(dstress)
# print(dstress)
return dstress
dstrain = -MP.dstrain[:2,:2] # convert from fluid mechanics to soil mechanics convention, just 2d
stress = -MP.stress[:2,:2] # convert from fluid mechanics to soil mechanics convention, just 2d
s_bar = 0.
for i in range(P.G.ns): s_bar += MP.phi[i]*P.G.s[i]
MP.gammadot = sqrt(sum(sum((2.*MP.de_ij/P.dt)**2))) # norm of shear strain rate
MP.I = MP.gammadot*s_bar*sqrt(P.S[p].rho_s/abs(MP.pressure))
MP.I = nan_to_num(MP.I)
mu_target = P.S[p].mu_0 + P.S[p].delta_mu/(P.S[p].I_0/MP.I + 1.)
# MP.eta = mu_target*abs(MP.pressure)/MP.gammadot # HACK: 2*SQRT(2) FIXES ISSUES WITH DEFINITION OF STRAIN
# MP.eta_limited = minimum(nan_to_num(MP.eta),P.S[p].eta_max) # COPYING FROM HERE: http://www.lmm.jussieu.fr/~lagree/TEXTES/PDF/JFMcollapsePYLLSSP11.pdf
# MP.mu = nan_to_num(abs(MP.pressure)/(MP.eta_limited*MP.gammadot))
# MP.dev_stress = MP.eta_limited*MP.de_ij/P.dt
# beta = P.S[p].beta
beta = MP.mu
dstress = RK4(dp_guts,dstrain,stress) # RK4
# dstress = dp_guts(dstrain,stress) # Euler
MP.dstress[:2,:2] = -dstress
# For visualisation
MP.gammadot = sqrt(sum(sum((dstrain - trace(dstrain)*eye(2)/2.)**2)))
MP.pressure = trace(MP.stress)/2. # 3
# MP.dev_stress = MP.stress - eye(3)*MP.pressure
# MP.dev_stress_dot = MP.dstress - eye(3)*trace(MP.dstress)/2. # 3
MP.sigmav = MP.stress[1,1]
MP.sigmah = MP.stress[0,0]
# MP.yieldfunction = MP.q/(P.S[p].beta*MP.p - (P.S[p].mu-P.S[p].beta)*K*trace(strain)) - 1
# MP.yieldfunction = MP.q/(P.S[p].mu*MP.p) - 1. # Associated flow only!
# MP.p = -(MP.stress[0,0]+MP.stress[1,1])/2. # pressure, positive for compression
# s_ij = -MP.stress[:2,:2] - eye(2)*MP.p # shear stress
# MP.q = sqrt(3.*sum(sum(s_ij*s_ij))/2.)
for r in range(4):
n = G.nearby_nodes(MP.n_star,r,P)
G.pressure[n] += MP.N[r]*MP.m*MP.p
# G.yieldfunction[n] += MP.N[r]*MP.yieldfunction*MP.m
G.gammadot[n] += MP.N[r]*MP.gammadot/P.dt*MP.m
# G.sigmav[n] += MP.N[r]*MP.sigmav*MP.m
# G.sigmah[n] += MP.N[r]*MP.sigmah*MP.m
G.dev_stress[n] += MP.N[r]*MP.q*MP.m
# G.dev_stress_dot[n] += MP.N[r]*norm(MP.dev_stress_dot)/P.dt*MP.m
def dp_rate(MP,P,G,p): # UNVALIDATED
"""Drucker-Prager yield criterion with rate dependent behaviour.
This material model is PROBALBLY WORKING - NOT YET VALIDATED!
:param MP: A particle.Particle instance.
:param P: A param.Param instance.
:param G: A grid.Grid instance
:param p: The particle number.
:type p: int
"""
def dp_guts(dstrain,stress):
# calculate strain components
de_kk = trace(dstrain)
de_ij = dstrain - de_kk*eye(2)/2.
# calculate stress components
MP.p = trace(stress)/2.
s_ij = stress - eye(2)*MP.p
MP.q = sqrt(3.*sum(sum(s_ij*s_ij))/2.)
# find plasticity multiplier
lambda_2 = MP.q - P.S[0].mu*MP.p
# take macaulay
Gamma_2 = lambda_2*(lambda_2>0)
dstress = (2.*P.S[0].G*(de_ij - 3.*s_ij/(2.*MP.q*MP.p*P.S[0].t_star)*Gamma_2) +
P.S[0].K*eye(2)*(de_kk + P.S[0].beta*MP.q/(P.S[0].mu*MP.p*MP.p*P.S[0].t_star)*Gamma_2))
return dstress
dstrain = -MP.dstrain[:2,:2] # convert from fluid mechanics to soil mechanics convention, just 2d
stress = -MP.stress[:2,:2] # convert from fluid mechanics to soil mechanics convention, just 2d
# dstress1 = dp_guts(dstrain,stress)
# dstress2 = dp_guts(dstrain,stress + 0.5*dstress1)
# dstress3 = dp_guts(dstrain,stress + 0.5*dstress2)
# dstress4 = dp_guts(dstrain,stress + dstress3)
# dstress = (dstress1 + 2.*dstress2 + 2.*dstress3 + dstress4)/6.
dstress = dp_guts(dstrain,stress)
MP.dstress[:2,:2] = -dstress
# print(MP.stress)
# print(MP.p,MP.q)
# For visualisation
MP.gammadot = sqrt(sum(sum((dstrain - trace(dstrain)*eye(2)/2.)**2)))
MP.pressure = trace(MP.stress)/2. # 3
# MP.dev_stress = MP.stress - eye(3)*MP.pressure
# MP.dev_stress_dot = MP.dstress - eye(3)*trace(MP.dstress)/2. # 3
MP.sigmav = MP.stress[1,1]
MP.sigmah = MP.stress[0,0]
# MP.yieldfunction = MP.q/(P.S[p].beta*MP.p - (P.S[p].mu-P.S[p].beta)*K*trace(strain)) - 1
MP.yieldfunction = MP.q/(P.S[p].mu*MP.p) - 1. # Associated flow only!
MP.p = -(MP.stress[0,0]+MP.stress[1,1])/2. # pressure, positive for compression
s_ij = -MP.stress[:2,:2] - eye(2)*MP.p # shear stress
MP.q = sqrt(3.*sum(sum(s_ij*s_ij))/2.)
for r in range(4):
n = G.nearby_nodes(MP.n_star,r,P)
G.pressure[n] += MP.N[r]*MP.m*MP.p
# G.yieldfunction[n] += MP.N[r]*MP.yieldfunction*MP.m
G.gammadot[n] += MP.N[r]*MP.gammadot/P.dt*MP.m
# G.sigmav[n] += MP.N[r]*MP.sigmav*MP.m
# G.sigmah[n] += MP.N[r]*MP.sigmah*MP.m
G.dev_stress[n] += MP.N[r]*MP.q*MP.m
# G.dev_stress_dot[n] += MP.N[r]*norm(MP.dev_stress_dot)/P.dt*MP.m
def viscous(MP,P,G,p):
"""Linear viscosity.
This material model has been validated and is functional.
:param MP: A particle.Particle instance.
:param P: A param.Param instance.
:param G: A grid.Grid instance
:param p: The particle number.
:type p: int
"""
MP.de_kk = trace(MP.dstrain)/3.
MP.de_ij = MP.dstrain - MP.de_kk*eye(3)
MP.dp = P.S[p].K*MP.de_kk
MP.pressure += MP.dp
MP.dev_stress = 2.*P.S[p].mu_s*MP.de_ij/P.dt
viscous_volumetric = P.S[p].mu_v*MP.de_kk*eye(3)/P.dt
# MP.stress = MP.pressure*eye(3) + MP.dev_stress - viscous_volumetric
MP.dstress = MP.pressure*eye(3) + MP.dev_stress - viscous_volumetric - MP.stress
MP.gammadot = sqrt(sum(sum(MP.de_ij**2)))/P.dt
for r in range(4):
n = G.nearby_nodes(MP.n_star,r,P)
G.pressure[n] += MP.N[r]*MP.pressure*MP.m
# G.gammadot[n] += MP.N[r]*MP.gammadot*MP.m
G.dev_stress[n] += MP.N[r]*norm(MP.dev_stress)*MP.m
def bingham(MP,P,G,p):
"""Bingham fluid.
This material model has not been validated but may be functional. YMMV.
:param MP: A particle.Particle instance.
:param P: A param.Param instance.
:param G: A grid.Grid instance
:param p: The particle number.
:type p: int
"""
MP.de_kk = trace(MP.dstrain)/3.
MP.de_ij = MP.dstrain - MP.de_kk*eye(3)
MP.dp = P.S[p].K*MP.de_kk
MP.gammadot = sqrt(sum(sum(MP.de_ij**2)))/P.dt
MP.pressure += MP.dp
if MP.gammadot <= P.S[p].gamma_c: MP.dev_stress = 2.*P.S[p].mu_0*MP.de_ij/P.dt
else: MP.dev_stress = 2.*(P.S[p].mu_s + P.S[p].tau_0/MP.gammadot)*MP.de_ij/P.dt
viscous_volumetric = P.S[p].mu_v*MP.de_kk*eye(3)/P.dt
MP.stress = MP.pressure*eye(3) + MP.dev_stress - viscous_volumetric
for r in range(4):
n = G.nearby_nodes(MP.n_star,r,P)
G.pressure[n] += MP.N[r]*MP.pressure*MP.m
# G.gammadot[n] += MP.N[r]*MP.gammadot*MP.m
G.dev_stress[n] += MP.N[r]*norm(MP.dev_stress)*MP.m
def ken_kamrin(MP,P,G,p):
""":math:`\mu(I)` rheology implemented from Ken Kamrin's MPM paper. Definitely _NOT_ functional.
:param MP: A particle.Particle instance.
:param P: A param.Param instance.
:param G: A grid.Grid instance
:param p: The particle number.
:type p: int
"""
MP.de_kk = trace(MP.dstrain)/3.
MP.de_ij = MP.dstrain - MP.de_kk*eye(3)
# MP.pressure = trace(MP.stress)/3.
MP.pressure += P.S[p].K*MP.de_kk
MP.gammadot_ij = 2.*MP.de_ij/P.dt
MP.gammadot = sqrt(0.5*sum(sum(MP.gammadot_ij**2))) # second invariant of strain rate tensor
MP.gammadot = maximum(MP.gammadot,1e-5) # no zero
d = 1. # MEAN DIAMETER
I = sqrt(2)*d*MP.gammadot/sqrt(abs(MP.pressure)/MP.rho)
mu = nan_to_num(P.S[p].mu_s + (P.S[p].mu_2 - P.S[p].mu_s)/(nan_to_num(P.S[p].I_0/I) + 1.))
eta = nan_to_num(mu*MP.pressure/(sqrt(2)*MP.gammadot)) # does this make sense for negative pressures???
eta = maximum(eta,0)
eta_max = 250.*MP.rho*P.max_g*(P.G.y_M-P.G.y_m)**3 # missing a g*H^3 !!
eta = minimum(eta,eta_max)
# print MP.gammadot, mu, eta, eta_max
MP.dev_stress = eta*MP.gammadot_ij
viscous_volumetric = P.S[p].mu_v*MP.de_kk*eye(3)/P.dt
# MP.stress = MP.pressure*eye(3) + MP.dev_stress - viscous_volumetric
MP.dstress = MP.pressure*eye(3) + MP.dev_stress - viscous_volumetric - MP.stress
for r in range(4):
n = G.nearby_nodes(MP.n_star,r,P)
G.pressure[n] += MP.N[r]*MP.pressure*MP.m
G.gammadot[n] += MP.N[r]*MP.gammadot/P.dt*MP.m
G.dev_stress[n] += MP.N[r]*norm(MP.dev_stress)*MP.m
def pouliquen(MP,P,G,p):
""":math:`\mu(I)` rheology implemented only for flowing regime.
This material model has been validated and is PROBABLY functional. (needs more mileage)
:param MP: A particle.Particle instance.
:param P: A param.Param instance.
:param G: A grid.Grid instance
:param p: The particle number.
:type p: int
"""
# Issues with the mu(I) model in general:
# 1. gammadot = 0
# 2. pressure = 0
# 3. large eta
# 4. no feedback to density
s_bar = 0.
mu_0 = 0.
delta_mu = 0.
I_0 = 0.
for i in range(P.G.ns):
s_bar += MP.phi[i]*P.G.s[i]
# HACK: THIS IS SOME GARBAGE I'M TRYING TO GET MORE SIZE EFFECTS
mu_0 += MP.phi[i]*P.S[p].mu_0[i]
delta_mu += MP.phi[i]*P.S[p].delta_mu[i]
I_0 += MP.phi[i]*P.S[p].I_0[i]
MP.de_kk = trace(MP.dstrain)/3. # tension positive
MP.de_ij = MP.dstrain - MP.de_kk*eye(3) # shear strain increment
MP.gammadot = sqrt(sum(sum((2.*MP.de_ij/P.dt)**2))) # norm of shear strain rate
MP.I = MP.gammadot*s_bar*sqrt(P.S[p].rho_s/abs(MP.pressure))
# if MP.I == inf: MP.I = 1e10 # HACK
# if MP.I < 1e-6: MP.I = 1e-6 # HACK
# NOTE: THIS IS THE CORRECT ONE THAT SHOULD BE USED
# MP.mu = P.S[p].mu_0 + P.S[p].delta_mu/(P.S[p].I_0/MP.I + 1.)
# HACK: THIS IS SOME GARBAGE I'M TRYING TO GET MORE SIZE EFFECTS
MP.mu = mu_0 + delta_mu/(I_0/MP.I + 1.)
MP.eta = 2.*sqrt(2)*MP.mu*abs(MP.pressure)/MP.gammadot # HACK: 2*SQRT(2) FIXES ISSUES WITH DEFINITION OF STRAIN
MP.eta_limited = minimum(nan_to_num(MP.eta),P.S[p].eta_max) # COPYING FROM HERE: http://www.lmm.jussieu.fr/~lagree/TEXTES/PDF/JFMcollapsePYLLSSP11.pdf
MP.dev_stress = MP.eta_limited*MP.de_ij/P.dt
MP.dp = P.S[p].K*MP.de_kk # tension positive # FIXME do I need to multiply this by 3??
MP.pressure += MP.dp
min_pressure = 0.0 # 1 Pa in compression
if (MP.pressure > min_pressure) or (MP.rho < P.S[p].rho*0.8): # can't go into tension - this is really important!!
MP.dp -= MP.pressure + min_pressure # set increment back to zero
MP.pressure = min_pressure
# if MP.rho < 2200:
# MP.dstress = - MP.stress # ADDED BY BENJY - CANNOT SUPPORT LOAD IF DENSITY LESS THAN CUTOFF
# MP.pressure = 0.
# else: MP.dstress = MP.pressure*eye(3) + MP.dev_stress - MP.stress
MP.dstress = MP.pressure*eye(3) + MP.dev_stress - MP.stress
if not isfinite(MP.dstress).all():
print('THIS IS GOING TO BE A PROBLEM! FOUND SOMETHING NON-FINITE IN CONSTITUTIVE MODEL')
print(MP.de_kk)
print(MP.de_ij)
print(s_bar)
print(MP.gammadot)
print(MP.I)
print(MP.mu)
print(MP.eta)
print(MP.dev_stress)
print(MP.dp)
print(MP.pressure)
print(MP.dstress)
sys.exit()
for r in range(4):
n = G.nearby_nodes(MP.n_star,r,P)
G.pressure[n] += MP.N[r]*MP.pressure*MP.m
G.dev_stress[n] += MP.N[r]*norm(MP.dev_stress)/sqrt(2.)*MP.m
G.mu[n] += MP.N[r]*MP.mu*MP.m
G.I[n] += MP.N[r]*MP.I*MP.m
G.eta[n] += MP.N[r]*MP.eta*MP.m
def linear_mu(MP,P,G,p):
""":math:`\mu(I)` rheology implemented only for flowing regime.
This material model has been validated and is PROBABLY functional. (needs more mileage)
:param MP: A particle.Particle instance.
:param P: A param.Param instance.
:param G: A grid.Grid instance
:param p: The particle number.
:type p: int
"""
s_bar = 0.
for i in range(P.G.ns): s_bar += MP.phi[i]*P.G.s[i]
MP.de_kk = trace(MP.dstrain)/3. # tension positive
MP.de_ij = MP.dstrain - MP.de_kk*eye(3) # shear strain increment
MP.gammadot = sqrt(sum(sum((2.*MP.de_ij/P.dt)**2))) # norm of shear strain rate
MP.I = MP.gammadot*s_bar*sqrt(P.S[p].rho_s/abs(MP.pressure))
# MP.I = minimum(MP.I,10.) # HACK - IF I DO THIS DO I NEED TO FIDDLE WITH ETA LATER?
# MP.mu = P.S[p].mu_0 + P.S[p].delta_mu/(P.S[p].I_0/MP.I + 1.)
MP.mu = P.S[p].mu_0 + P.S[p].b*MP.I
MP.eta = 2.*sqrt(2)*MP.mu*abs(MP.pressure)/MP.gammadot # HACK: 2*SQRT(2) FIXES ISSUES WITH DEFINITION OF STRAIN
MP.eta = minimum(MP.eta,P.S[p].eta_max) # COPYING FROM HERE: http://www.lmm.jussieu.fr/~lagree/TEXTES/PDF/JFMcollapsePYLLSSP11.pdf
MP.dev_stress = MP.eta*MP.de_ij/P.dt
MP.dp = P.S[p].K*MP.de_kk # tension positive
MP.pressure += MP.dp
if MP.pressure > 0.: MP.pressure = 0. # can't go into tension - this is really important!!
# MP.stress = MP.pressure*eye(3) + MP.dev_stress
MP.dstress = MP.pressure*eye(3) + MP.dev_stress - MP.stress
for r in range(4):
n = G.nearby_nodes(MP.n_star,r,P)
G.pressure[n] += MP.N[r]*MP.pressure*MP.m
G.dev_stress[n] += MP.N[r]*norm(MP.dev_stress)/sqrt(2.)*MP.m
# G.dev_stress[n] += MP.N[r]*MP.dev_stress[0,1]*MP.m
G.mu[n] += MP.N[r]*MP.mu*MP.m
G.I[n] += MP.N[r]*MP.I*MP.m
def ken_simple(MP,P,G,p):
""":math: constant `\mu` rheology with stress = 0 when rho < rho_c.
This material model is UNVALIDATED and is DEFINITELY NOT WORKING.
:param MP: A particle.Particle instance.
:param P: A param.Param instance.
:param G: A grid.Grid instance
:param p: The particle number.
:type p: int
"""
s_bar = 0.
for i in range(P.G.ns): s_bar += MP.phi[i]*P.G.s[i]
MP.de_kk = trace(MP.dstrain)/3. # tension positive
MP.de_ij = MP.dstrain - MP.de_kk*eye(3) # shear strain increment
MP.eta = 2.*sqrt(2)*P.S[p].mu_0*abs(MP.pressure)/MP.gammadot # HACK: 2*SQRT(2) FIXES ISSUES WITH DEFINITION OF STRAIN
MP.eta = minimum(nan_to_num(MP.eta),P.S[p].eta_max) # COPYING FROM HERE: http://www.lmm.jussieu.fr/~lagree/TEXTES/PDF/JFMcollapsePYLLSSP11.pdf
MP.dev_stress = MP.eta*MP.de_ij/P.dt
MP.dp = P.S[p].K*MP.de_kk # tension positive # FIXME do I need to multiply this by 3??
MP.pressure += MP.dp
if MP.pressure > 0: # can't go into tension - this is really important!!
MP.dp -= MP.pressure # set increment back to zero
MP.pressure = 0.
if MP.rho > 2500:
MP.dstress = MP.pressure*eye(3) + MP.dev_stress - MP.stress
else:
MP.dstress = -MP.stress
if not isfinite(MP.dstress).all():
print('THIS IS GOING TO BE A PROBLEM! FOUND SOMETHING NON-FINITE IN CONSTITUTIVE MODEL')
print(MP.de_kk)
print(MP.de_ij)
print(s_bar)
print(MP.eta)
print(MP.dev_stress)
print(MP.dp)
print(MP.pressure)
print(MP.dstress)
sys.exit()
for r in range(4):
n = G.nearby_nodes(MP.n_star,r,P)
G.pressure[n] += MP.N[r]*MP.pressure*MP.m
G.dev_stress[n] += MP.N[r]*norm(MP.dev_stress)/sqrt(2.)*MP.m
G.eta[n] += MP.N[r]*MP.eta*MP.m