Add power law strain/stress functions

src/ConstitutiveRelationships.jl

@@ -69,7 +69,7 @@ export param_info,
 # add methods programmatically 
 for myType in (:LinearViscous, :LinearMeltViscosity, :ViscosityPartialMelt_Costa_etal_2009, 
                 :DiffusionCreep, :DislocationCreep, :ConstantElasticity, :DruckerPrager, :ArrheniusType, 
-                :GrainBoundarySliding, :PeierlsCreep, :NonLinearPeierlsCreep)
+                :GrainBoundarySliding, :PeierlsCreep, :NonLinearPeierlsCreep, :PowerlawViscous)
     @eval begin
         @inline compute_εII(a::$(myType), TauII, args) = compute_εII(a, TauII; args...)
         @inline compute_εvol(a::$(myType), P, args) = compute_εvol(a, P; args...)

src/CreepLaw/CreepLaw.jl

@@ -194,7 +194,7 @@
 where ``\\eta_0`` is the reference viscosity [Pa*s] at reference strain rate ``\\dot{\\varepsilon}_0``[1/s], and ``n`` the power law exponent []. 
 """
 @with_kw_noshow struct ArrheniusType{_T,U1,U2,U3} <: AbstractCreepLaw{_T}
-    η_0::GeoUnit{_T,U1} = 1.0NoUnits      # Pre-exponential factor
+    η0::GeoUnit{_T,U1} = 1.0NoUnits      # Pre-exponential factor
     E_η::GeoUnit{_T,U2} = 23.03NoUnits    # Activation energy (non-dimensional)
     T_O::GeoUnit{_T,U3} = 1.0NoUnits      # Offset temperature 
     T_η::GeoUnit{_T,U3} = 1.0NoUnits      # Reference temperature at which viscosity is unity
@@ -215,10 +215,11 @@
         Equation=L"\tau_{ij} = 2 \eta_0 exp( E_η/(T + T_O) + E_η/(T_η + T_O))  \dot{\varepsilon}_{ij}",
     )
 end
+
 # Calculation routines for linear viscous rheologies
 function compute_εII(a::ArrheniusType, TauII; T=one(precision(a)), kwargs...)
-    @unpack_val η_0, E_η, T_O, T_η = a
-    η = η_0 * exp(E_η / (T + T_O) - E_η / (T_η + T_O))
+    @unpack_val η0, E_η, T_O, T_η = a
+    η = η0 * exp(E_η / (T + T_O) - E_η / (T_η + T_O))
     return (TauII / η) * 0.5
 end
 
@@ -241,8 +242,8 @@
 end
 
 function dεII_dτII(a::ArrheniusType, TauII; T=one(precision(a)), kwargs...)
-    @unpack_val η_0, E_η, T_O, T_η = a
-    η = η_0 * exp(E_η / (T + T_O) - E_η / (T_η + T_O))
+    @unpack_val η0, E_η, T_O, T_η = a
+    η = η0 * exp(E_η / (T + T_O) - E_η / (T_η + T_O))
     return 0.5 * inv(η)
 end
 
@@ -252,9 +253,9 @@
 Returns second invariant of the stress tensor given a 2nd invariant of strain rate tensor 
 """
 function compute_τII(a::ArrheniusType, EpsII; T=one(precision(a)), kwargs...)
-    @unpack_val η_0, E_η, T_O, T_η = a
+    @unpack_val η0, E_η, T_O, T_η = a
 
-    η = η_0 * exp(E_η / (T + T_O) - E_η / (T_η + T_O))
+    η = η0 * exp(E_η / (T + T_O) - E_η / (T_η + T_O))
 
     return 2 * (η * EpsII)
 end
@@ -274,8 +275,8 @@
 end
 
 function dτII_dεII(a::ArrheniusType, EpsII; T=one(precision(a)), kwargs...)
-    @unpack_val η_0, E_η, T_O, T_η = a
-    η = η_0 * exp(E_η / (T + T_O) - E_η / (T_η + T_O))
+    @unpack_val η0, E_η, T_O, T_η = a
+    η = η0 * exp(E_η / (T + T_O) - E_η / (T_η + T_O))
 
     return 2 * η
 end
@@ -284,7 +285,7 @@
 function show(io::IO, g::ArrheniusType)
     return print(
         io,
-        "ArrheniusType: η_0 = $(Value(g.η_0)), E_η = $(Value(g.E_η)), T_O = $(Value(g.T_O)), T_η = $(Value(g.T_η))",
+        "ArrheniusType: η0 = $(Value(g.η0)), E_η = $(Value(g.E_η)), T_O = $(Value(g.T_O)), T_η = $(Value(g.T_η))",
     )
 end
 
@@ -300,33 +301,51 @@
 where ``\\eta`` is the effective viscosity [Pa*s].
 """
 @with_kw_noshow struct PowerlawViscous{T,U1,U2,U3} <: AbstractCreepLaw{T}
-    η0::GeoUnit{T,U1} = 1e18Pa * s            # reference viscosity 
-    n::GeoUnit{T,U2} = 2.0 * NoUnits         # powerlaw exponent
-    ε0::GeoUnit{T,U3} = 1e-15 * 1 / s          # reference strainrate
+    η0::GeoUnit{T,U1} = 1e18Pa * s       # reference viscosity 
+    n::GeoUnit{T,U2} = 2.0 * NoUnits     # powerlaw exponent
+    ε0::GeoUnit{T,U3} = 1e-15/s          # reference strainrate
 end
 PowerlawViscous(a...) = PowerlawViscous(convert.(GeoUnit, a)...)
 
 # Print info 
 function show(io::IO, g::PowerlawViscous)
     return print(io, "Powerlaw viscosity: η0=$(g.η0.val), n=$(g.n.val), ε0=$(g.ε0.val) ")
 end
-#-------------------------------------------------------------------------
 
-#=
-# add methods programmatically 
-#for myType in (:LinearViscous, :DiffusionCreep, :DislocationCreep, :ConstantElasticity)
-for myType in (:LinearViscous, :DiffusionCreep, :DislocationCreep)
-
-    @eval begin
-        compute_εII(TauII, a::$(myType), args) = compute_εII(TauII, a; args...) 
-        dεII_dτII(TauII, a::$(myType), args) = dεII_dτII(TauII, a; args...) 
-        compute_τII(EpsII, a::$(myType), args) = compute_τII(EpsII, a; args...) 
-        if Symbol($myType) !== :ConstantElasticity
-            dτII_dεII(EpsII, a::$(myType), args) = dτII_dεII(EpsII, a; args...)
-        end
-    end
+# Calculation routines for linear viscous rheologies
+function compute_εII(a::PowerlawViscous, TauII; kwargs...)
+    @unpack_val η0, n, ε0 = a
+
+    @pow EpsII = (TauII / η0)^(1/n) * ε0
+
+    return EpsII
 end
-=#
+
+function dεII_dτII(a::PowerlawViscous, TauII; kwargs...)
+    @unpack_val η0, n, ε0 = a
+
+    return @pow (TauII^((1 - n) / n)) / (n*(η0^(1 / n)))
+end
+
+"""
+    compute_τII(s::PowerlawViscous, EpsII; kwargs...)
+
+Returns second invariant of the stress tensor given a 2nd invariant of strain rate tensor 
+"""
+function compute_τII(a::PowerlawViscous, EpsII; kwargs...)
+    @unpack_val η0, n, ε0 = a
+
+    τII  = @pow ε0 * η0 * (EpsII / ε0)^n
+
+    return τII
+end
+
+function dτII_dεII(a::PowerlawViscous, EpsII; kwargs...)
+    @unpack_val η0, n, ε0 = a
+
+    return @pow η0 * EpsII^(n - 1) * (1 / ε0)^n
+end
+#-------------------------------------------------------------------------
 
 # Help info for the calculation routines
 """

src/MeltFraction/MeltingParameterization.jl

@@ -581,7 +581,7 @@ julia> T,phi,dϕdT =  PlotMeltFraction(p,T=T);
 The same but with smoothening:
 ```julia
 julia> p_s = SmoothMelting(p=MeltingParam_4thOrder(), k_liq=0.21/K);
-4th order polynomial melting curve: phi = -7.594512597174117e-10T^4 + 3.469192091489447e-6T^3 + -0.00592352980926T^2 + 4.482855645604745T + -1268.730161921053  963.15 K ≤ T ≤ 1270.15 K with smooth Heaviside function smoothening using k_sol=0.1 K⁻¹·⁰, k_liq=0.11 K⁻¹·⁰
+4th order polynomial melting curve: phi = -7.594512597174117e-10T^4 + 3.469192091489447e-6T^3 + -0.00592352980926T^2 + 4.482855645604745T + -1268.730161921053  963.15 K ≤ T ≤ 1270.15 K with smooth Heaviside function smoothening using k_sol=0.1 K⁻¹·⁰, k_liq=0.11 K⁻¹·⁰
 julia> T_s,phi_s,dϕdT_s =  PlotMeltFraction(p_s,T=T);
 ```
 
@@ -767,7 +767,7 @@ end
 Computation of melt fraction ϕ for the whole domain and all phases, in case an array with phase properties `MatParam` is provided, along with `P` and `T` arrays.
 """
 compute_meltfraction(args::Vararg{Any,N}) where {N} =
-    clamp(compute_param(compute_meltfraction, args...), 0e0, 1e0)
+    clamp(compute_param(compute_meltfraction, args...), 0, 1)
 
 """
     compute_meltfraction(ϕ::AbstractArray{<:AbstractFloat}, Phases::AbstractArray{<:Integer}, P::AbstractArray{<:AbstractFloat},T::AbstractArray{<:AbstractFloat}, MatParam::AbstractArray{<:AbstractMaterialParamsStruct})
@@ -802,4 +802,4 @@ This is employed, for example, in computing latent heat terms in an implicit man
 """
 compute_dϕdT!(args::Vararg{Any,N}) where {N} = compute_param!(compute_dϕdT, args...)
 
-end
+end

test/test_CreepLaw.jl

@@ -29,7 +29,7 @@ using GeoParams
 
     x1_ND = LinearViscous(; η=1e18Pa * s)
     @test isDimensional(x1_ND) == true
-    x1_ND = nondimensionalize(x1_ND, CharUnits_GEO)                 # check that we can nondimensionalize all entries within the struct
+    x1_ND = nondimensionalize(x1_ND, CharUnits_GEO)                # check that we can nondimensionalize all entries within the struct
     @test isDimensional(x1_ND) == false
     @test x1_ND.η * 1.0 == 0.1
     x1_D = dimensionalize(x1_ND, CharUnits_GEO)                    # check that we can dimensionalize it again
@@ -53,14 +53,28 @@ using GeoParams
     ε = [0.0; 0.0]
     compute_τII!(ε, x1_ND, [1e0; 2.0], args)
     @test ε == [0.2; 0.4]     # vector input
-
     # -------------------------------------------------------------------
 
     # -------------------------------------------------------------------
     # Define powerlaw viscous rheology
+    η0 = 10
+    n  = 2.3
+    ε0 = 1
+    x2 = PowerlawViscous(; η0 = 10, n=2.3, ε0 = 1)
+
+    τII = 1e0
+    εII = 1e0
+
+    (τII / η0)^(1/n)
+    @test compute_τII(x2, τII) == η0 * εII^n
+    @test compute_εII(x2, εII) ≈ (τII / η0)^(1/n)
+
+    @test compute_viscosity_εII(x2, τII, (;)) == 5e0
+    @test compute_viscosity_τII(x2, εII, (;)) == 1.3606693841876538
+
     x2 = PowerlawViscous()
     x2 = nondimensionalize(x2, CharUnits_GEO)
-    @test NumValue(x2.ε0) == 0.001                                 # powerlaw
+    @test NumValue(x2.ε0) == 0.001 # powerlaw
 
     # Given strainrate
     compute_τII(x1, 1e-13 / s, args)
@@ -147,33 +161,26 @@ using GeoParams
     @test ε ≈ [2.553516169022911e-6; 5.107032338045822e-6]     # vector input
 
     # With vector as input
-    T = Vector(800.0:1400)*K
-    η_basalt = zeros(size(T))*Pas
+    T          = Vector(800.0:1400)*K
+    η_basalt   = zeros(size(T))*Pas
     η_rhyolite = zeros(size(T))*Pas
-
     x_basalt   = LinearMeltViscosity()
     x_rhyolite = LinearMeltViscosity(A = -8.1590, B = 2.4050e+04K, T0 = -430.9606K)   # Rhyolite
 
     for i in eachindex(T)
-        args_D  = (; T = T[i])
-        η_basalt[i]     = compute_viscosity_τII(x_basalt, 1e6Pa, (; T=T[i]))
-        η_rhyolite[i]   = compute_viscosity_τII(x_rhyolite, 1e6Pa, (; T=T[i]))
+        args_D        = (; T = T[i])
+        η_basalt[i]   = compute_viscosity_τII(x_basalt, 1e6Pa, (; T=T[i]))
+        η_rhyolite[i] = compute_viscosity_τII(x_rhyolite, 1e6Pa, (; T=T[i]))
     end
 
-    #using Plots
-    #plot(ustrip.(T) .- 273.15, log10.(ustrip.(η_basalt)), xlabel="T [C]", ylabel="log10(η [Pas])", label="basalt")
-    #plot!(ustrip.(T) .- 273.15, log10.(ustrip.(η_rhyolite)), label="rhyolite")
-
-    args_D=(;T=1000K)
-    η_basalt1 = compute_viscosity_τII(x_basalt, 1e6Pa, args_D)
-    @test η_basalt1 ≈ 5.2471745814062805e9Pa*s
-
-    η_rhyolite1 = compute_viscosity_τII(x_rhyolite, 1e6Pa, args_D)
+    args_D            = (;T=1000K)
+    η_basalt1         = compute_viscosity_τII(x_basalt, 1e6Pa, args_D)
+    @test η_basalt1   ≈ 5.2471745814062805e9Pa*s
+    η_rhyolite1       = compute_viscosity_τII(x_rhyolite, 1e6Pa, args_D)
     @test η_rhyolite1 ≈ 4.445205243727607e8Pa*s
     # -------------------------------------------------------------------
 
     # Test effective viscosity of partially molten rocks -----------------
-
     x1_D =ViscosityPartialMelt_Costa_etal_2009(η=LinearMeltViscosity(A = -8.1590, B = 2.4050e+04K, T0 = -430.9606K))   # Rhyolite
     @test isDimensional(x1_D) == true
     x1_ND = nondimensionalize(x1_D, CharUnits_GEO)                 # check that we can nondimensionalize all entries within the struct
@@ -186,71 +193,63 @@ using GeoParams
     args_D  = (; T = 700K, ϕ=0.5)
     args_ND = (; T =  nondimensionalize(700K, CharUnits_GEO), ϕ=0.5)
 
-    ε_D = compute_εII(x1_D, 1e6Pa, args_D)
-    @test ε_D ≈  1.5692922423522311e-10 / s                      # dimensional input
-    ε_ND  = compute_εII(x1_ND, nondimensionalize(1e6Pa, CharUnits_GEO), args_ND)
+    ε_D        = compute_εII(x1_D, 1e6Pa, args_D)
+    @test ε_D  ≈ 1.5692922423522311e-10 / s                      # dimensional input
+    ε_ND       = compute_εII(x1_ND, nondimensionalize(1e6Pa, CharUnits_GEO), args_ND)
     @test ε_ND ≈ 156.92922423522444                              # non-dimensional
-    @test ε_ND*CharUnits_GEO.strainrate ≈ ε_D   # check that non-dimensiional computations give the same results
+    @test ε_ND * CharUnits_GEO.strainrate ≈ ε_D   # check that non-dimensiional computations give the same results
 
     ε = [0.0; 0.0]
     τ = [1e6; 2e6]
     args_ND1 = (; T =  1000*ones(size(τ)), ϕ=0.5*ones(size(τ)))
     compute_εII!(ε, x1_D, τ, args_ND1)
     @test ε ≈ [0.0011248074556411618; 0.0022496149112823235]    # vector input
 
-
     # Given strainrate
     @test compute_τII(x1_D,  1e-13 / s, args_D) ≈ 643.9044043803415Pa      # dimensional input
-    @test compute_τII(x1_ND, 1e-13, args_ND) ≈ 5.64401178083053e-17                  # non-dimensional
+    @test compute_τII(x1_ND, 1e-13, args_ND)    ≈ 5.64401178083053e-17                  # non-dimensional
 
     ε = [0.0; 0.0]
     compute_τII!(ε, x1_ND, [1e0; 2.0], args_ND1)
     @test ε ≈ [3.65254588484434e-25, 7.305079089024537e-25]    # vector input
 
-
-    x1_D = ViscosityPartialMelt_Costa_etal_2009()
-    args_D=(;T=1000K, ϕ=0.5)
-    ε_D    = compute_εII(x1_D, 1e6Pa, args_D)
-    @test ustrip(ε_D) ≈  3.4537433628446676e-6
-
-    η    =   compute_viscosity_τII(x1_D, 1e6Pa, args_D)
-    @test  ustrip(η) ≈  1.447704555523709e11
+    x1_D              = ViscosityPartialMelt_Costa_etal_2009()
+    args_D            = (;T=1000K, ϕ=0.5)
+    ε_D               = compute_εII(x1_D, 1e6Pa, args_D)
+    @test ustrip(ε_D) ≈ 3.4537433628446676e-6
+    η                 = compute_viscosity_τII(x1_D, 1e6Pa, args_D)
+    @test  ustrip(η)  ≈ 1.447704555523709e11
 
     @test dεII_dτII(x1_ND, 1e6, args_ND) ≈ 31884.63277076202
     @test dτII_dεII(x1_ND, 1e-15, args_ND) ≈ 0.0005644011780830529
-
     # -----
 
     # ----
     # Create plot
-    T = Vector(800.0:1400)*K
-    η_basalt  = zeros(size(T))*Pas
-    η_basalt1 = zeros(size(T))*Pas
-    η_rhyolite = zeros(size(T))*Pas
-    ϕ_basalt = zeros(size(T))
-    ϕ_rhyolite = zeros(size(T))
-
-    x_basalt   = ViscosityPartialMelt_Costa_etal_2009(η = LinearMeltViscosity())
-    x_rhyolite = ViscosityPartialMelt_Costa_etal_2009(η= LinearMeltViscosity(A = -8.1590, B = 2.4050e+04K, T0 = -430.9606K))   # Rhyolite
-
-    mf_basalt = MeltingParam_Smooth3rdOrder()
+    T           = Vector(800.0:1400)*K
+    η_basalt    = zeros(size(T))*Pas
+    η_basalt1   = zeros(size(T))*Pas
+    η_rhyolite  = zeros(size(T))*Pas
+    ϕ_basalt    = zeros(size(T))
+    ϕ_rhyolite  = zeros(size(T))
+    x_basalt    = ViscosityPartialMelt_Costa_etal_2009(η = LinearMeltViscosity())
+    x_rhyolite  = ViscosityPartialMelt_Costa_etal_2009(η= LinearMeltViscosity(A = -8.1590, B = 2.4050e+04K, T0 = -430.9606K))   # Rhyolite
+    mf_basalt   = MeltingParam_Smooth3rdOrder()
     mf_rhyolite = MeltingParam_Smooth3rdOrder( a=3043.0,  b=-10552.0, c=12204.9, d = -4709.0 )
 
     εII = 1e-5/s;
     for i in eachindex(T)
-        args_D  = (; T = T[i])
-        ϕ_basalt[i] = compute_meltfraction(mf_basalt, (; T=T[i]/K))
-        η_basalt[i]     = compute_viscosity_εII(x_basalt, εII, (; ϕ=ϕ_basalt[i], T=T[i]))
-
-        η_basalt1[i]     = compute_viscosity_εII(x_basalt, 1e-3/s, (; ϕ=ϕ_basalt[i], T=T[i]))
-
+        args_D        = (; T = T[i])
+        ϕ_basalt[i]   = compute_meltfraction(mf_basalt, (; T=T[i]/K))
+        η_basalt[i]   = compute_viscosity_εII(x_basalt, εII, (; ϕ=ϕ_basalt[i], T=T[i]))
+        η_basalt1[i]  = compute_viscosity_εII(x_basalt, 1e-3/s, (; ϕ=ϕ_basalt[i], T=T[i]))
         ϕ_rhyolite[i] = compute_meltfraction(mf_rhyolite, (; T=T[i]/K))
-        η_rhyolite[i]   = compute_viscosity_εII(x_rhyolite, εII, (; ϕ=ϕ_rhyolite[i], T=T[i]))
+        η_rhyolite[i] = compute_viscosity_εII(x_rhyolite, εII, (; ϕ=ϕ_rhyolite[i], T=T[i]))
 
     end
-    @test mean(η_rhyolite) ≈ 1.26143880075233e19Pas
-    @test mean(η_basalt) ≈ 5.822731206904198e24Pas
-    @test mean(η_basalt1) ≈ 8.638313729394237e21Pas
+    @test mean(η_rhyolite) ≈ 1.2614388007523279e19Pas
+    @test mean(η_basalt)   ≈ 5.822731206904198e24Pas
+    @test mean(η_basalt1)  ≈ 8.638313729394237e21Pas
 
     #=
     using Plots
@@ -269,3 +268,4 @@ using GeoParams
 
 
 end
+