From 5eedbd78a51df2509b33ac60286b65a57d53ef68 Mon Sep 17 00:00:00 2001
From: singularitti <singularitti@outlook.com>
Date: Fri, 13 Oct 2023 01:44:08 -0400
Subject: [PATCH 1/5] Add module `EffectiveModuli` with `bulk_modulus` &
 `shear_modulus`

---
 src/EffectiveModuli.jl | 36 ++++++++++++++++++++++++++++++++++++
 1 file changed, 36 insertions(+)
 create mode 100644 src/EffectiveModuli.jl

diff --git a/src/EffectiveModuli.jl b/src/EffectiveModuli.jl
new file mode 100644
index 0000000..27361b8
--- /dev/null
+++ b/src/EffectiveModuli.jl
@@ -0,0 +1,36 @@
+module EffectiveModuli
+
+abstract type Model end
+struct Voigt <: Model end
+struct Reuss <: Model end
+struct VoigtReussHill <: Model end
+
+bulk_modulus(c::StiffnessMatrix, ::Voigt) =
+    (c[1, 1] + c[2, 2] + c[3, 3] + 2(c[1, 2] + c[2, 3] + c[3, 1])) / 9
+bulk_modulus(s::ComplianceMatrix, ::Voigt) = bulk_modulus(inv(s), Voigt())
+bulk_modulus(s::ComplianceMatrix, ::Reuss) =
+    inv(s[1, 1] + s[2, 2] + s[3, 3] + 2(s[1, 2] + s[2, 3] + s[3, 1]))
+bulk_modulus(c::StiffnessMatrix, ::Reuss) = bulk_modulus(inv(c), Voigt())
+bulk_modulus(c::StiffnessMatrix, ::VoigtReussHill) =
+    (bulk_modulus(c, Voigt()) + bulk_modulus(inv(c), Reuss())) / 2
+bulk_modulus(s::ComplianceMatrix, ::VoigtReussHill) =
+    (bulk_modulus(inv(s), Voigt()) + bulk_modulus(s, Reuss())) / 2
+
+shear_modulus(c::StiffnessMatrix, ::Voigt) =
+    (
+        c[1, 1] + c[2, 2] + c[3, 3] - (c[1, 2] + c[2, 3] + c[3, 1]) +
+        3(c[4, 4] + c[5, 5] + c[6, 6])
+    ) / 15
+shear_modulus(s::ComplianceMatrix, ::Voigt) = shear_modulus(inv(s), Voigt())
+shear_modulus(s::ComplianceMatrix, ::Reuss) =
+    inv(
+        4(s[1, 1] + s[2, 2] + s[3, 3] - (s[1, 2] + s[2, 3] + s[3, 1])) +
+        3(s[4, 4] + s[5, 5] + s[6, 6]),
+    ) * 15
+shear_modulus(c::StiffnessMatrix, ::Reuss) = shear_modulus(inv(c), Voigt())
+shear_modulus(c::StiffnessMatrix, ::VoigtReussHill) =
+    (shear_modulus(c, Voigt()) + shear_modulus(inv(c), Reuss())) / 2
+shear_modulus(s::ComplianceMatrix, ::VoigtReussHill) =
+    (shear_modulus(inv(s), Voigt()) + shear_modulus(s, Reuss())) / 2
+
+end

From 145c714e7298a53ffe85a89ea0a74158fddcfb55 Mon Sep 17 00:00:00 2001
From: singularitti <singularitti@outlook.com>
Date: Fri, 13 Oct 2023 01:46:01 -0400
Subject: [PATCH 2/5] Fix exports

---
 src/EffectiveModuli.jl | 4 ++++
 1 file changed, 4 insertions(+)

diff --git a/src/EffectiveModuli.jl b/src/EffectiveModuli.jl
index 27361b8..4b08c36 100644
--- a/src/EffectiveModuli.jl
+++ b/src/EffectiveModuli.jl
@@ -1,5 +1,9 @@
 module EffectiveModuli
 
+import ..Isotropic: bulk_modulus, shear_modulus
+
+export Voigt, Reuss, VoigtReussHill, bulk_modulus, shear_modulus
+
 abstract type Model end
 struct Voigt <: Model end
 struct Reuss <: Model end

From 949434c35736b6679ea23a65acdce4012aff46be Mon Sep 17 00:00:00 2001
From: singularitti <singularitti@outlook.com>
Date: Fri, 13 Oct 2023 01:46:11 -0400
Subject: [PATCH 3/5] Include code

---
 src/LinearElasticity.jl | 1 +
 1 file changed, 1 insertion(+)

diff --git a/src/LinearElasticity.jl b/src/LinearElasticity.jl
index 44e8871..dea71b4 100644
--- a/src/LinearElasticity.jl
+++ b/src/LinearElasticity.jl
@@ -7,6 +7,7 @@ using Reexport: @reexport
 include("Symmetry.jl")
 # include("Stability.jl")
 include("Isotropic.jl")
+include("EffectiveModuli.jl")
 include("misc.jl")
 include("Solve/Solve.jl")
 include("ULICS.jl")

From 6f678a52cbbfd62ed18225a0c8c97d707b49b1b8 Mon Sep 17 00:00:00 2001
From: singularitti <singularitti@outlook.com>
Date: Fri, 13 Oct 2023 01:47:16 -0400
Subject: [PATCH 4/5] Fix imports in src/EffectiveModuli.jl

---
 src/EffectiveModuli.jl | 2 ++
 1 file changed, 2 insertions(+)

diff --git a/src/EffectiveModuli.jl b/src/EffectiveModuli.jl
index 4b08c36..54a1b54 100644
--- a/src/EffectiveModuli.jl
+++ b/src/EffectiveModuli.jl
@@ -1,5 +1,7 @@
 module EffectiveModuli
 
+using ..LinearElasticity: StiffnessMatrix, ComplianceMatrix
+
 import ..Isotropic: bulk_modulus, shear_modulus
 
 export Voigt, Reuss, VoigtReussHill, bulk_modulus, shear_modulus

From d2ae2a87f681f0a6c315979e553694b276badb5a Mon Sep 17 00:00:00 2001
From: singularitti <singularitti@outlook.com>
Date: Fri, 13 Oct 2023 01:55:48 -0400
Subject: [PATCH 5/5] Add docs to `bulk_modulus` & `shear_modulus`

---
 src/EffectiveModuli.jl | 58 ++++++++++++++++++++++++++++++++++++++++++
 1 file changed, 58 insertions(+)

diff --git a/src/EffectiveModuli.jl b/src/EffectiveModuli.jl
index 54a1b54..0f001d9 100644
--- a/src/EffectiveModuli.jl
+++ b/src/EffectiveModuli.jl
@@ -11,29 +11,87 @@ struct Voigt <: Model end
 struct Reuss <: Model end
 struct VoigtReussHill <: Model end
 
+"""
+    bulk_modulus(c::StiffnessMatrix, ::Voigt)
+    bulk_modulus(s::ComplianceMatrix, ::Voigt)
+
+Calculate the bulk modulus of a material from its stiffness matrix by:
+
+```math
+K_V = \\frac{c_{11} + c_{22} + c_{33} + 2(c_{12} + c_{23} + c_{31})}{9}.
+```
+"""
 bulk_modulus(c::StiffnessMatrix, ::Voigt) =
     (c[1, 1] + c[2, 2] + c[3, 3] + 2(c[1, 2] + c[2, 3] + c[3, 1])) / 9
 bulk_modulus(s::ComplianceMatrix, ::Voigt) = bulk_modulus(inv(s), Voigt())
+"""
+    bulk_modulus(s::ComplianceMatrix, ::Reuss)
+    bulk_modulus(c::StiffnessMatrix, ::Reuss)
+
+Calculate the bulk modulus of a material from its compliance matrix by:
+
+```math
+K_R = \\frac{1}{s_{11} + s_{22} + s_{33} + 2(s_{12} + s_{23} + s_{31})}.
+```
+"""
 bulk_modulus(s::ComplianceMatrix, ::Reuss) =
     inv(s[1, 1] + s[2, 2] + s[3, 3] + 2(s[1, 2] + s[2, 3] + s[3, 1]))
 bulk_modulus(c::StiffnessMatrix, ::Reuss) = bulk_modulus(inv(c), Voigt())
+"""
+    bulk_modulus(c::StiffnessMatrix, ::VoigtReussHill)
+    bulk_modulus(s::ComplianceMatrix, ::VoigtReussHill)
+
+Calculate the bulk modulus of a material from its stiffness or compliance matrix by:
+
+```math
+K_{VRH} = \\frac{K_V + K_R}{2}.
+```
+"""
 bulk_modulus(c::StiffnessMatrix, ::VoigtReussHill) =
     (bulk_modulus(c, Voigt()) + bulk_modulus(inv(c), Reuss())) / 2
 bulk_modulus(s::ComplianceMatrix, ::VoigtReussHill) =
     (bulk_modulus(inv(s), Voigt()) + bulk_modulus(s, Reuss())) / 2
 
+"""
+    shear_modulus(c::StiffnessMatrix, ::Voigt)
+
+Calculate the shear modulus of a material from its stiffness matrix by:
+
+```math
+G_V = \\frac{(c_{11} + c_{22} + c_{33}) - (c_{12} + c_{23} + c_{31}) + 3(c_{44} + c_{55} + c_{66})}{15}.
+```
+"""
 shear_modulus(c::StiffnessMatrix, ::Voigt) =
     (
         c[1, 1] + c[2, 2] + c[3, 3] - (c[1, 2] + c[2, 3] + c[3, 1]) +
         3(c[4, 4] + c[5, 5] + c[6, 6])
     ) / 15
 shear_modulus(s::ComplianceMatrix, ::Voigt) = shear_modulus(inv(s), Voigt())
+"""
+    shear_modulus(s::ComplianceMatrix, ::Reuss)
+
+Calculate the shear modulus of a material from its compliance matrix by:
+
+```math
+G_R = \\frac{15}{4(s_{11} + s_{22} + s_{33}) - 4(s_{12} + s_{23} + s_{31}) + 3(s_{44} + s_{55} + s_{66})}.
+```
+"""
 shear_modulus(s::ComplianceMatrix, ::Reuss) =
     inv(
         4(s[1, 1] + s[2, 2] + s[3, 3] - (s[1, 2] + s[2, 3] + s[3, 1])) +
         3(s[4, 4] + s[5, 5] + s[6, 6]),
     ) * 15
 shear_modulus(c::StiffnessMatrix, ::Reuss) = shear_modulus(inv(c), Voigt())
+"""
+    shear_modulus(c::StiffnessMatrix, ::VoigtReussHill)
+    shear_modulus(s::ComplianceMatrix, ::VoigtReussHill)
+
+Calculate the shear modulus of a material from its stiffness or compliance matrix by:
+
+```math
+G_{VRH} = \\frac{G_V + G_R}{2}.
+```
+"""
 shear_modulus(c::StiffnessMatrix, ::VoigtReussHill) =
     (shear_modulus(c, Voigt()) + shear_modulus(inv(c), Reuss())) / 2
 shear_modulus(s::ComplianceMatrix, ::VoigtReussHill) =