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Merged
jmartfrut merged 1 commit into from
Apr 8, 2026
Merged

Add χt parameter to HardMagnetic models #148

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12 changes: 8 additions & 4 deletions src/PhysicalModels/MagneticModels.jl
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Original file line number Diff line number Diff line change
Expand Up @@ -117,10 +117,12 @@ struct HardMagnetic <: Magneto
αr::Float64
χe::Float64
χr::Float64
χt::Float64
βmok::Float64
βcoup::Float64
function HardMagnetic(; μ0::Float64, αr::Float64, χe::Float64=0.0, χr::Float64=8.0, βmok::Float64=0.0, βcoup::Float64=0.0)
new(μ0, αr, χe, χr, βmok, βcoup)
function HardMagnetic(; μ0::Float64, αr::Float64, χe::Float64=0.0, χr::Float64=8.0, χt::Union{Float64,Nothing}=nothing, βmok::Float64=0.0, βcoup::Float64=0.0)
χt_val = isnothing(χt) ? χe : χt
new(μ0, αr, χe, χr, χt_val, βmok, βcoup)
end

function (obj::HardMagnetic)(Λ::Float64=1.0)
Expand Down Expand Up @@ -165,10 +167,12 @@ struct HardMagnetic2D <: Magneto
αr::Ref{Float64}
χe::Float64
χr::Float64
χt::Float64
βmok::Float64
βcoup::Float64
function HardMagnetic2D(; μ0::Float64, αr::Float64, χe::Float64=0.0, χr::Float64=8.0, βmok::Float64=0.0, βcoup::Float64=0.0)
new(μ0, Ref(αr), χe, χr, βmok, βcoup)
function HardMagnetic2D(; μ0::Float64, αr::Float64, χe::Float64=0.0, χr::Float64=8.0, χt::Union{Float64,Nothing}=nothing, βmok::Float64=0.0, βcoup::Float64=0.0)
χt_val = isnothing(χt) ? χe : χt
new(μ0, Ref(αr), χe, χr, χt_val, βmok, βcoup)
end

function (obj::HardMagnetic2D)(Λ::Float64=1.0)
Expand Down
40 changes: 20 additions & 20 deletions src/PhysicalModels/MagnetoMechanicalModels.jl
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Expand Up @@ -69,7 +69,7 @@ function _getCoupling(mag::HardMagnetic, ::Mechano, Λ::Float64=1.0)
# delay crack propagation, Journal of the Mechanics and Physics of Solids,


μ, αr, χe, χr, βcoup, βmok = mag.μ, mag.αr, mag.χe, mag.χr, mag.βcoup, mag.βmok
μ, αr, χr, χt, βcoup, βmok = mag.μ, mag.αr, mag.χr, mag.χt, mag.βcoup, mag.βmok
J(F) = det(F)
H(F) = det(F) * inv(F)'

Expand Down Expand Up @@ -108,15 +108,15 @@ function _getCoupling(mag::HardMagnetic, ::Mechano, Λ::Float64=1.0)
# FOURTH TERM
#-------------------------------------------------------------------------------------
Hℋᵣ(F, N) = H(F) * ℋᵣ(N)
Ψtorq(F, ℋ₀, N) = (μ * (1 + χe) / J(F)) * (Hℋ₀(F, ℋ₀) ⋅ Hℋᵣ(F, N))
∂Ψtorq_∂H(F, ℋ₀, N) = (μ * (1 + χe) / J(F)) * (Hℋᵣ(F, N) ⊗ ℋ₀ + Hℋ₀(F, ℋ₀) ⊗ ℋᵣ(N))
∂Ψtorq_∂J(F, ℋ₀, N) = -(μ * (1 + χe) / J(F)^2) * (Hℋ₀(F, ℋ₀) ⋅ Hℋᵣ(F, N))
Ψtorq(F, ℋ₀, N) = (μ * (1 + χt) / J(F)) * (Hℋ₀(F, ℋ₀) ⋅ Hℋᵣ(F, N))
∂Ψtorq_∂H(F, ℋ₀, N) = (μ * (1 + χt) / J(F)) * (Hℋᵣ(F, N) ⊗ ℋ₀ + Hℋ₀(F, ℋ₀) ⊗ ℋᵣ(N))
∂Ψtorq_∂J(F, ℋ₀, N) = -(μ * (1 + χt) / J(F)^2) * (Hℋ₀(F, ℋ₀) ⋅ Hℋᵣ(F, N))
∂Ψtorq_∂u(F, ℋ₀, N) = ∂Ψtorq_∂H(F, ℋ₀, N) × F + ∂Ψtorq_∂J(F, ℋ₀, N) * H(F)
∂Ψtorq_∂φ(F, ℋ₀, N) = (μ * (1 + χe) / J(F)) * (H(F)' * Hℋᵣ(F, N))
∂Ψtorq_∂φ(F, ℋ₀, N) = (μ * (1 + χt) / J(F)) * (H(F)' * Hℋᵣ(F, N))

∂Ψtorq_∂HH(F, ℋ₀, N) = (μ * (1 + χe) / J(F)) * (I3 ⊗₁₃²⁴ (ℋᵣ(N) ⊗ ℋ₀ + ℋ₀ ⊗ ℋᵣ(N)))
∂Ψtorq_∂HJ(F, ℋ₀, N) = -(μ * (1 + χe) / J(F)^2) * (Hℋᵣ(F, N) ⊗ ℋ₀ + Hℋ₀(F, ℋ₀) ⊗ ℋᵣ(N))
∂Ψtorq_∂JJ(F, ℋ₀, N) = (μ * (1 + χe) / J(F)^3) * (Hℋ₀(F, ℋ₀) ⋅ Hℋᵣ(F, N))
∂Ψtorq_∂HH(F, ℋ₀, N) = (μ * (1 + χt) / J(F)) * (I3 ⊗₁₃²⁴ (ℋᵣ(N) ⊗ ℋ₀ + ℋ₀ ⊗ ℋᵣ(N)))
∂Ψtorq_∂HJ(F, ℋ₀, N) = -(μ * (1 + χt) / J(F)^2) * (Hℋᵣ(F, N) ⊗ ℋ₀ + Hℋ₀(F, ℋ₀) ⊗ ℋᵣ(N))
∂Ψtorq_∂JJ(F, ℋ₀, N) = (μ * (1 + χt) / J(F)^3) * (Hℋ₀(F, ℋ₀) ⋅ Hℋᵣ(F, N))

∂Ψtorq_∂uu(F, ℋ₀, N) = (F × (∂Ψtorq_∂HH(F, ℋ₀, N) × F)) +
H(F) ⊗₁₂³⁴ (∂Ψtorq_∂HJ(F, ℋ₀, N) × F) +
Expand All @@ -125,8 +125,8 @@ function _getCoupling(mag::HardMagnetic, ::Mechano, Λ::Float64=1.0)
×ᵢ⁴(∂Ψtorq_∂H(F, ℋ₀, N) + ∂Ψtorq_∂J(F, ℋ₀, N) * F)


∂Ψtorq_∂ℋ₀H(F, ℋ₀, N) = (μ / (J(F))) * ((I3 ⊗₁₃² Hℋᵣ(F, N)) + (H(F)' ⊗₁₂³ Hℋᵣ(F, N))) * (1 + χe)
∂Ψtorq_∂ℋ₀J(F, ℋ₀, N) = (-μ / (J(F))^2.0) * (H(F)' * Hℋᵣ(F, N)) * (1 + χe)
∂Ψtorq_∂ℋ₀H(F, ℋ₀, N) = (μ / (J(F))) * ((I3 ⊗₁₃² Hℋᵣ(F, N)) + (H(F)' ⊗₁₂³ Hℋᵣ(F, N))) * (1 + χt)
∂Ψtorq_∂ℋ₀J(F, ℋ₀, N) = (-μ / (J(F))^2.0) * (H(F)' * Hℋᵣ(F, N)) * (1 + χt)

∂Ψtorq_∂φu(F, ℋ₀, N) = (∂Ψtorq_∂ℋ₀H(F, ℋ₀, N) × F) + (∂Ψtorq_∂ℋ₀J(F, ℋ₀, N) ⊗₁²³ H(F))

Expand All @@ -150,7 +150,7 @@ function _getCoupling(mag::HardMagnetic2D, ::Mechano, Λ::Float64=1.0)
# Hard magnetics in ultra-soft magnetorheological elastomers enhance fracture toughness and
# delay crack propagation, Journal of the Mechanics and Physics of Solids,

μ, αr, χe, χr, βcoup, βmok = mag.μ, mag.αr, mag.χe, mag.χr, mag.βcoup, mag.βmok
μ, αr, χr, χt, βcoup, βmok = mag.μ, mag.αr, mag.χr, mag.χt, mag.βcoup, mag.βmok
J(F) = det(F)
H(F) = det(F) * inv(F)'

Expand Down Expand Up @@ -187,24 +187,24 @@ function _getCoupling(mag::HardMagnetic2D, ::Mechano, Λ::Float64=1.0)
# FOURTH TERM
#-------------------------------------------------------------------------------------
Hℋᵣ(F, N) = H(F) * ℋᵣ(N)
Ψtorq(F, ℋ₀, N) = (μ * (1 + χe) / J(F)) * (Hℋ₀(F, ℋ₀) ⋅ Hℋᵣ(F, N))
∂Ψtorq_∂H(F, ℋ₀, N) = (μ * (1 + χe) / J(F)) * (Hℋᵣ(F, N) ⊗ ℋ₀ + Hℋ₀(F, ℋ₀) ⊗ ℋᵣ(N))
∂Ψtorq_∂J(F, ℋ₀, N) = -(μ * (1 + χe) / J(F)^2) * (Hℋ₀(F, ℋ₀) ⋅ Hℋᵣ(F, N))
Ψtorq(F, ℋ₀, N) = (μ * (1 + χt) / J(F)) * (Hℋ₀(F, ℋ₀) ⋅ Hℋᵣ(F, N))
∂Ψtorq_∂H(F, ℋ₀, N) = (μ * (1 + χt) / J(F)) * (Hℋᵣ(F, N) ⊗ ℋ₀ + Hℋ₀(F, ℋ₀) ⊗ ℋᵣ(N))
∂Ψtorq_∂J(F, ℋ₀, N) = -(μ * (1 + χt) / J(F)^2) * (Hℋ₀(F, ℋ₀) ⋅ Hℋᵣ(F, N))
∂Ψtorq_∂u(F, ℋ₀, N) = (tr(∂Ψtorq_∂H(F, ℋ₀, N)) * I2) - ∂Ψtorq_∂H(F, ℋ₀, N)' + ∂Ψtorq_∂J(F, ℋ₀, N) * H(F)
∂Ψtorq_∂φ(F, ℋ₀, N) = (μ * (1 + χe) / J(F)) * (H(F)' * Hℋᵣ(F, N))
∂Ψtorq_∂φ(F, ℋ₀, N) = (μ * (1 + χt) / J(F)) * (H(F)' * Hℋᵣ(F, N))

∂Ψtorq_∂HH(F, ℋ₀, N) = (μ * (1 + χe) / J(F)) * (I2 ⊗₁₃²⁴ (ℋᵣ(N) ⊗ ℋ₀ + ℋ₀ ⊗ ℋᵣ(N)))
∂Ψtorq_∂HJ(F, ℋ₀, N) = -(μ * (1 + χe) / J(F)^2) * (Hℋᵣ(F, N) ⊗ ℋ₀ + Hℋ₀(F, ℋ₀) ⊗ ℋᵣ(N))
∂Ψtorq_∂JJ(F, ℋ₀, N) = (μ * (1 + χe) / J(F)^3) * (Hℋ₀(F, ℋ₀) ⋅ Hℋᵣ(F, N))
∂Ψtorq_∂HH(F, ℋ₀, N) = (μ * (1 + χt) / J(F)) * (I2 ⊗₁₃²⁴ (ℋᵣ(N) ⊗ ℋ₀ + ℋ₀ ⊗ ℋᵣ(N)))
∂Ψtorq_∂HJ(F, ℋ₀, N) = -(μ * (1 + χt) / J(F)^2) * (Hℋᵣ(F, N) ⊗ ℋ₀ + Hℋ₀(F, ℋ₀) ⊗ ℋᵣ(N))
∂Ψtorq_∂JJ(F, ℋ₀, N) = (μ * (1 + χt) / J(F)^3) * (Hℋ₀(F, ℋ₀) ⋅ Hℋᵣ(F, N))

∂Ψtorq_∂uu(F, ℋ₀, N) = _∂H∂F_2D()' * ∂Ψtorq_∂HH(F, ℋ₀, N) * _∂H∂F_2D() +
_∂H∂F_2D()' * (∂Ψtorq_∂HJ(F, ℋ₀, N) ⊗ H(F)) +
(H(F) ⊗ ∂Ψtorq_∂HJ(F, ℋ₀, N)) * _∂H∂F_2D() +
∂Ψtorq_∂JJ(F, ℋ₀, N) * (H(F) ⊗ H(F)) +
∂Ψtorq_∂J(F, ℋ₀, N) * _∂H∂F_2D()

∂Ψtorq_∂ℋ₀H(F, ℋ₀, N) = (μ / (J(F))) * ((I2 ⊗₁₃² Hℋᵣ(F, N)) + (H(F)' ⊗₁₂³ Hℋᵣ(F, N))) * (1 + χe)
∂Ψtorq_∂ℋ₀J(F, ℋ₀, N) = (-μ / (J(F))^2.0) * (H(F)' * Hℋᵣ(F, N)) * (1 + χe)
∂Ψtorq_∂ℋ₀H(F, ℋ₀, N) = (μ / (J(F))) * ((I2 ⊗₁₃² Hℋᵣ(F, N)) + (H(F)' ⊗₁₂³ Hℋᵣ(F, N))) * (1 + χt)
∂Ψtorq_∂ℋ₀J(F, ℋ₀, N) = (-μ / (J(F))^2.0) * (H(F)' * Hℋᵣ(F, N)) * (1 + χt)


∂Ψtorq_∂φu(F, ℋ₀, N) = (∂Ψtorq_∂ℋ₀H(F, ℋ₀, N) * _∂H∂F_2D()) + (∂Ψtorq_∂ℋ₀J(F, ℋ₀, N) ⊗₁²³ H(F))
Expand Down
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