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abstractmaterial_full_workflow.jl
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abstractmaterial_full_workflow.jl
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using Tensors
using Parameters
using NLsolve
using ForwardDiff
using Profile
abstract type AbstractMaterial end
abstract type AbstractMaterialState end
@generated function Base.:+(state::T, dstate::T) where {T <: AbstractMaterialState}
expr = [:(state.$p+ dstate.$p) for p in fieldnames(T)]
return :(T($(expr...)))
end
@with_kw mutable struct ChabocheDriverState <: AbstractMaterialState
time :: Float64 = zero(Float64)
strain :: Symm2 = zero(Symm2{Float64})
end
@with_kw struct ChabocheParameterState <: AbstractMaterialState
E :: Float64 = 0.0
nu :: Float64 = 0.0
R0 :: Float64 = 0.0
Kn :: Float64 = 0.0
nn :: Float64 = 0.0
C1 :: Float64 = 0.0
D1 :: Float64 = 0.0
C2 :: Float64 = 0.0
D2 :: Float64 = 0.0
Q :: Float64 = 0.0
b :: Float64 = 0.0
end
@with_kw struct ChabocheVariableState <: AbstractMaterialState
stress :: Symm2 = zero(Symm2{Float64})
X1 :: Symm2 = zero(Symm2{Float64})
X2 :: Symm2 = zero(Symm2{Float64})
plastic_strain :: Symm2 = zero(Symm2{Float64})
cumeq :: Float64 = zero(Float64)
R :: Float64 = zero(Float64)
jacobian :: Symm4 = zero(Symm4{Float64})
end
@with_kw mutable struct Chaboche <: AbstractMaterial
drivers :: ChabocheDriverState = ChabocheDriverState()
ddrivers :: ChabocheDriverState = ChabocheDriverState()
variables :: ChabocheVariableState = ChabocheVariableState()
variables_new :: ChabocheVariableState = ChabocheVariableState()
parameters :: ChabocheParameterState = ChabocheParameterState()
dparameters :: ChabocheParameterState = ChabocheParameterState()
end
@with_kw mutable struct PerfectPlasticDriverState <: AbstractMaterialState
time :: Float64 = zero(Float64)
strain :: Symm2 = zero(Symm2{Float64})
end
@with_kw struct PerfectPlasticParameterState <: AbstractMaterialState
youngs_modulus :: Float64 = zero(Float64)
poissons_ratio :: Float64 = zero(Float64)
yield_stress :: Float64 = zero(Float64)
end
@with_kw struct PerfectPlasticVariableState <: AbstractMaterialState
stress :: Symm2 = zero(Symm2{Float64})
plastic_strain :: Symm2 = zero(Symm2{Float64})
cumeq :: Float64 = zero(Float64)
end
function update!(material::M) where {M <: AbstractMaterial}
material.drivers += material.ddrivers
material.parameters += material.dparameters
material.variables = material.variables_new
# material.ddrivers = typeof(material.ddrivers)()
# material.dparameters = typeof(material.dparameters)()
# material.variables_new = typeof(material.variables_new)()
reset!(material)
end
function reset!(material::M) where {M <: AbstractMaterial}
material.ddrivers = typeof(material.ddrivers)()
material.dparameters = typeof(material.dparameters)()
material.variables_new = typeof(material.variables_new)()
end
# @with_kw mutable struct Material{M <: AbstractMaterial}
# drivers :: DriverState{M} = DriverState{M}()
# ddrivers :: DriverState{M} = DriverState{M}()
# variables :: VariableState{M} = VariableState{M}()
# dvariables :: VariableState{M} = VariableState{M}()
# parameters :: ParameterState{M} = ParameterState{M}()
# dparameters :: ParameterState{M} = ParameterState{M}()
# end
@with_kw mutable struct PerfectPlastic <: AbstractMaterial
drivers :: PerfectPlasticDriverState = PerfectPlasticDriverState()
ddrivers :: PerfectPlasticDriverState = PerfectPlasticDriverState()
variables :: PerfectPlasticVariableState = PerfectPlasticVariableState()
variables_new :: PerfectPlasticVariableState = PerfectPlasticVariableState()
parameters :: PerfectPlasticParameterState = PerfectPlasticParameterState()
dparameters :: PerfectPlasticParameterState = PerfectPlasticParameterState()
end
mat = Chaboche()
mat2 = PerfectPlastic()
function isotropic_elasticity_tensor(lambda, mu)
delta(i,j) = i==j ? 1.0 : 0.0
g(i,j,k,l) = lambda*delta(i,j)*delta(k,l) + mu*(delta(i,k)*delta(j,l)+delta(i,l)*delta(j,k))
jacobian = Symm4{Float64}(g)
return jacobian
end
function integrate_material!(material::Chaboche)
p = material.parameters
v = material.variables
dd = material.ddrivers
d = material.drivers
@unpack E, nu, R0, Kn, nn, C1, D1, C2, D2, Q, b = p
mu = E/(2.0*(1.0+nu))
lambda = E*nu/((1.0+nu)*(1.0-2.0*nu))
@unpack strain, time = d
dstrain = dd.strain
dtime = dd.time
@unpack stress, X1, X2, plastic_strain, cumeq, R, jacobian = v
jacobian = isotropic_elasticity_tensor(lambda, mu)
stress += dcontract(jacobian, dstrain)
seff = stress - X1 - X2
seff_dev = dev(seff)
f = sqrt(1.5)*norm(seff_dev) - (R0 + R)
if f > 0.0
g! = create_nonlinear_system_of_equations(material)
x0 = [tovoigt(stress); R; tovoigt(X1); tovoigt(X2)]
F = similar(x0)
res = nlsolve(g!, x0; autodiff = :forward)
x = res.zero
res.f_converged || error("Nonlinear system of equations did not converge!")
stress = fromvoigt(Symm2{Float64}, @view x[1:6])
R = x[7]
X1 = fromvoigt(Symm2{Float64}, @view x[8:13])
X2 = fromvoigt(Symm2{Float64}, @view x[14:19])
seff = stress - X1 - X2
seff_dev = dev(seff)
f = sqrt(1.5)*norm(seff_dev) - (R0 + R)
dotp = ((f >= 0.0 ? f : 0.0)/Kn)^nn
dp = dotp*dtime
n = 1.5*seff_dev/norm(seff_dev)
plastic_strain += dp*n
cumeq += dp
# Compute Jacobian
function residuals(x)
F = similar(x)
g!(F, x)
return F
end
drdx = ForwardDiff.jacobian(residuals, x)
drde = zeros((length(x),6))
drde[1:6, 1:6] = -tovoigt(jacobian)
jacobian = fromvoigt(Symm4, (drdx\drde)[1:6, 1:6])
end
variables_new = ChabocheVariableState(stress = stress,
X1 = X1,
X2 = X2,
R = R,
plastic_strain = plastic_strain,
cumeq = cumeq,
jacobian = jacobian)
material.variables_new = variables_new
end
function create_nonlinear_system_of_equations(material::Chaboche)
p = material.parameters
v = material.variables
dd = material.ddrivers
d = material.drivers
@unpack E, nu, R0, Kn, nn, C1, D1, C2, D2, Q, b = p
mu = E/(2.0*(1.0+nu))
lambda = E*nu/((1.0+nu)*(1.0-2.0*nu))
@unpack strain, time = d
dstrain = dd.strain
dtime = dd.time
@unpack stress, X1, X2, plastic_strain, cumeq, R = v
function g!(F, x::Vector{T}) where {T} # System of non-linear equations
jacobian = isotropic_elasticity_tensor(lambda, mu)
stress_ = fromvoigt(Symm2{T}, @view x[1:6])
R_ = x[7]
X1_ = fromvoigt(Symm2{T}, @view x[8:13])
X2_ = fromvoigt(Symm2{T}, @view x[14:19])
seff = stress_ - X1_ - X2_
seff_dev = dev(seff)
f = sqrt(1.5)*norm(seff_dev) - (R0 + R_)
dotp = ((f >= 0.0 ? f : 0.0)/Kn)^nn
dp = dotp*dtime
n = 1.5*seff_dev/norm(seff_dev)
dstrain_plastic = dp*n
tovoigt!(view(F, 1:6), stress - stress_ + dcontract(jacobian, dstrain - dstrain_plastic))
F[7] = R - R_ + b*(Q-R_)*dp
if isapprox(C1, 0.0)
tovoigt!(view(F,8:13),X1 - X1_)
else
tovoigt!(view(F,8:13), X1 - X1_ + 2.0/3.0*C1*dp*(n - 1.5*D1/C1*X1_))
end
if isapprox(C2, 0.0)
tovoigt!(view(F,14:19), X2 - X2_)
else
tovoigt!(view(F, 14:19), X2 - X2_ + 2.0/3.0*C2*dp*(n - 1.5*D2/C2*X2_))
end
end
return g!
end
function simple_integration_test()
parameters = ChabocheParameterState(E = 200.0e3,
nu = 0.3,
R0 = 100.0,
Kn = 100.0,
nn = 10.0,
C1 = 10000.0,
D1 = 100.0,
C2 = 50000.0,
D2 = 1000.0,
Q = 50.0,
b = 0.1)
dstrain_dtime = fromvoigt(Symm2{Float64}, 1e-3*[1.0, -0.3, -0.3, 0.0, 0.0, 0.0]; offdiagscale=2.0)
ddrivers = ChabocheDriverState(time = 0.25, strain = 0.25*dstrain_dtime)
chabmat = Chaboche(parameters = parameters, ddrivers = ddrivers)
@info "time = $(chabmat.drivers.time), stress = $(chabmat.variables.stress)"
integrate_material!(chabmat)
update!(chabmat)
@info "time = $(chabmat.drivers.time), stress = $(chabmat.variables.stress)"
chabmat.ddrivers = ddrivers
integrate_material!(chabmat)
update!(chabmat)
@info "time = $(chabmat.drivers.time), stress = $(chabmat.variables.stress)"
chabmat.ddrivers = ddrivers
integrate_material!(chabmat)
update!(chabmat)
@info "time = $(chabmat.drivers.time), stress = $(chabmat.variables.stress)"
end
using DelimitedFiles, Test
path = joinpath(@__DIR__, "one_elem_disp_chaboche", "unitelement_results.rpt")
data = readdlm(path, Float64; skipstart=4)
ts = data[:,1]
s11_ = data[:,2]
s12_ = data[:,3]
s13_ = data[:,4]
s22_ = data[:,5]
s23_ = data[:,6]
s33_ = data[:,7]
e11_ = data[:,8]
e12_ = data[:,9]
e13_ = data[:,10]
e22_ = data[:,11]
e23_ = data[:,12]
e33_ = data[:,13]
strains = [[e11_[i], e22_[i], e33_[i], e23_[i], e13_[i], e12_[i]] for i in 1:length(ts)]
function test_chaboche()
parameters = ChabocheParameterState(E = 200.0e3,
nu = 0.3,
R0 = 100.0,
Kn = 100.0,
nn = 10.0,
C1 = 10000.0,
D1 = 100.0,
C2 = 50000.0,
D2 = 1000.0,
Q = 50.0,
b = 0.1)
chabmat = Chaboche(parameters = parameters)
s33s = [chabmat.variables.stress[3,3]]
for i=2:length(ts)
dtime = ts[i]-ts[i-1]
dstrain = fromvoigt(Symm2{Float64}, strains[i]-strains[i-1]; offdiagscale=2.0)
chabmat.ddrivers = ChabocheDriverState(time = dtime, strain = dstrain)
integrate_material!(chabmat)
update!(chabmat)
push!(s33s, chabmat.variables.stress[3,3])
end
# @test isapprox(s33s, s33_; rtol=0.01)
end
test_chaboche()
Profile.clear_malloc_data()
test_chaboche()
# using BenchmarkTools
# @btime test_chaboche()
function simple_integration_test_fd_tangent()
parameters = ChabocheParameterState(E = 200.0e3,
nu = 0.3,
R0 = 100.0,
Kn = 100.0,
nn = 10.0,
C1 = 10000.0,
D1 = 100.0,
C2 = 50000.0,
D2 = 1000.0,
Q = 50.0,
b = 0.1)
dstrain_dtime = fromvoigt(Symm2{Float64}, 1e-3*[1.0, -0.3, -0.3, 0.0, 0.0, 0.0]; offdiagscale=2.0)
ddrivers = ChabocheDriverState(time = 0.25, strain = 0.25*dstrain_dtime)
chabmat = Chaboche(parameters = parameters, ddrivers = ddrivers)
function get_stress(dstrain)
chabmat.ddrivers.strain = dstrain
integrate_material!(chabmat)
return chabmat.variables_new.stress
end
# stress = get_stress(0.25*dstrain_dtime)
# @info "stress = $stress"
D, dstress = Tensors.gradient(get_stress, 0.25*dstrain_dtime, :all)
@info "D_mat = $(tovoigt(chabmat.variables_new.jacobian))"
@info "D = $(tovoigt(D))"
chabmat.variables_new = typeof(chabmat.variables_new)()
chabmat.ddrivers = ChabocheDriverState(time = 0.25, strain = 0.25*dstrain_dtime)
@info "time = $(chabmat.drivers.time), stress = $(chabmat.variables.stress)"
integrate_material!(chabmat)
update!(chabmat)
@info "time = $(chabmat.drivers.time), stress = $(chabmat.variables.stress)"
function get_stress(dstrain)
chabmat.ddrivers.strain = dstrain
integrate_material!(chabmat)
return chabmat.variables_new.stress
end
# stress = get_stress(0.25*dstrain_dtime)
# @info "stress = $stress"
D, dstress = Tensors.gradient(get_stress, 0.25*dstrain_dtime, :all)
@info "D = $(tovoigt(D))"
chabmat.variables_new = typeof(chabmat.variables_new)()
chabmat.ddrivers = ChabocheDriverState(time = 0.25, strain = 0.25*dstrain_dtime)
integrate_material!(chabmat)
update!(chabmat)
@info "time = $(chabmat.drivers.time), stress = $(chabmat.variables.stress)"
function get_stress(dstrain)
chabmat.ddrivers.strain = dstrain
integrate_material!(chabmat)
return chabmat.variables_new.stress
end
# stress = get_stress(0.25*dstrain_dtime)
# @info "stress = $stress"
D, dstress = Tensors.gradient(get_stress, 0.25*dstrain_dtime, :all)
@info "D = $(tovoigt(D))"
chabmat.variables_new = typeof(chabmat.variables_new)()
chabmat.ddrivers = ChabocheDriverState(time = 0.25, strain = 0.25*dstrain_dtime)
integrate_material!(chabmat)
update!(chabmat)
@info "time = $(chabmat.drivers.time), stress = $(chabmat.variables.stress)"
function get_stress(dstrain)
chabmat.ddrivers.strain = dstrain
integrate_material!(chabmat)
return chabmat.variables_new.stress
end
# stress = get_stress(0.25*dstrain_dtime)
# @info "stress = $stress"
D, dstress = Tensors.gradient(get_stress, 0.25*dstrain_dtime, :all)
@info "D = $(tovoigt(D))"
end
# simple_integration_test_fd_tangent()
function simple_integration_test_fd_tangent2()
parameters = ChabocheParameterState(E = 200.0e3,
nu = 0.3,
R0 = 100.0,
Kn = 100.0,
nn = 10.0,
C1 = 10000.0,
D1 = 100.0,
C2 = 50000.0,
D2 = 1000.0,
Q = 50.0,
b = 0.1)
dstrain_dtime = fromvoigt(Symm2{Float64}, 1e-3*[1.0, -0.3, -0.3, 0.0, 0.0, 0.0]; offdiagscale=2.0)
ddrivers = ChabocheDriverState(time = 0.25, strain = 0.25*dstrain_dtime)
chabmat = Chaboche(parameters = parameters, ddrivers = ddrivers)
integrate_material!(chabmat)
update!(chabmat)
@info "time = $(chabmat.drivers.time), stress = $(chabmat.variables.stress)"
chabmat.ddrivers = ddrivers
integrate_material!(chabmat)
update!(chabmat)
@info "time = $(chabmat.drivers.time), stress = $(chabmat.variables.stress)"
chabmat.ddrivers = ddrivers
integrate_material!(chabmat)
g! = create_nonlinear_system_of_equations(chabmat)
function residuals(x)
F = similar(x)
g!(F, x)
return F
end
x0 = [tovoigt(chabmat.variables_new.stress); chabmat.variables_new.R; tovoigt(chabmat.variables_new.X1); tovoigt(chabmat.variables_new.X2)]
drdx = ForwardDiff.jacobian(residuals, x0)
@info "size(drdx) = $(size(drdx))"
@info "drdx = $drdx"
@unpack E, nu, R0, Kn, nn, C1, D1, C2, D2, Q, b = parameters
mu = E/(2.0*(1.0+nu))
lambda = E*nu/((1.0+nu)*(1.0-2.0*nu))
jacobian = isotropic_elasticity_tensor(lambda, mu)
drde = zeros((19,6))
drde[1:6, 1:6] = -tovoigt(jacobian)
@info "drde = $drde"
@info "size(drde) = $(size(drde))"
jacobian2 = (drdx\drde)[1:6, 1:6]
@info "jacobian = $(tovoigt(jacobian))"
@info "jacobian2 = $jacobian2"
jacobian3 = (drdx[1:6, 1:6] + drdx[1:6,7:end]*(drdx[7:end,7:end]\-drdx[7:end, 1:6]))\drde[1:6, 1:6]
@info "jacobian3 = $jacobian3"
@info "jacobian4 = $(tovoigt(chabmat.variables_new.jacobian))"
update!(chabmat)
@info "time = $(chabmat.drivers.time), stress = $(chabmat.variables.stress)"
chabmat.ddrivers = ddrivers
integrate_material!(chabmat)
g! = create_nonlinear_system_of_equations(chabmat)
function residuals(x)
F = similar(x)
g!(F, x)
return F
end
x0 = [tovoigt(chabmat.variables_new.stress); chabmat.variables_new.R; tovoigt(chabmat.variables_new.X1); tovoigt(chabmat.variables_new.X2)]
drdx = ForwardDiff.jacobian(residuals, x0)
@info "size(drdx) = $(size(drdx))"
@info "drdx = $drdx"
@unpack E, nu, R0, Kn, nn, C1, D1, C2, D2, Q, b = parameters
mu = E/(2.0*(1.0+nu))
lambda = E*nu/((1.0+nu)*(1.0-2.0*nu))
jacobian = isotropic_elasticity_tensor(lambda, mu)
drde = zeros((19,6))
drde[1:6, 1:6] = -tovoigt(jacobian)
@info "drde = $drde"
@info "size(drde) = $(size(drde))"
jacobian2 = (drdx\drde)[1:6, 1:6]
@info "jacobian = $(tovoigt(jacobian))"
@info "jacobian2 = $jacobian2"
jacobian3 = (drdx[1:6, 1:6] + drdx[1:6,7:end]*(drdx[7:end,7:end]\-drdx[7:end, 1:6]))\drde[1:6, 1:6]
@info "jacobian3 = $jacobian3"
@info "jacobian4 = $(tovoigt(chabmat.variables_new.jacobian))"
update!(chabmat)
@info "time = $(chabmat.drivers.time), stress = $(chabmat.variables.stress)"
end
#simple_integration_test_fd_tangent2()