conspire/constitutive/solid/hyperelastic/fung/
mod.rs1#[cfg(test)]
2mod test;
3
4use crate::{
5 constitutive::{
6 Constitutive, ConstitutiveError, Parameters,
7 solid::{FIVE_THIRDS, Solid, TWO_THIRDS, elastic::Elastic, hyperelastic::Hyperelastic},
8 },
9 math::{IDENTITY, Rank2},
10 mechanics::{CauchyStress, CauchyTangentStiffness, Deformation, DeformationGradient, Scalar},
11};
12
13#[doc = include_str!("model.md")]
14#[derive(Debug)]
15pub struct Fung<P> {
16 parameters: P,
17}
18
19impl<P> Fung<P>
20where
21 P: Parameters,
22{
23 pub fn extra_modulus(&self) -> &Scalar {
25 self.parameters.get(2)
26 }
27 pub fn exponent(&self) -> &Scalar {
29 self.parameters.get(3)
30 }
31}
32
33impl<P> Constitutive<P> for Fung<P>
34where
35 P: Parameters,
36{
37 fn new(parameters: P) -> Self {
38 Self { parameters }
39 }
40}
41
42impl<P> Solid for Fung<P>
43where
44 P: Parameters,
45{
46 fn bulk_modulus(&self) -> &Scalar {
47 self.parameters.get(0)
48 }
49 fn shear_modulus(&self) -> &Scalar {
50 self.parameters.get(1)
51 }
52}
53
54impl<P> Elastic for Fung<P>
55where
56 P: Parameters,
57{
58 #[doc = include_str!("cauchy_stress.md")]
59 fn cauchy_stress(
60 &self,
61 deformation_gradient: &DeformationGradient,
62 ) -> Result<CauchyStress, ConstitutiveError> {
63 let jacobian = self.jacobian(deformation_gradient)?;
64 let isochoric_left_cauchy_green_deformation =
65 deformation_gradient.left_cauchy_green() / jacobian.powf(TWO_THIRDS);
66 let (
67 deviatoric_isochoric_left_cauchy_green_deformation,
68 isochoric_left_cauchy_green_deformation_trace,
69 ) = isochoric_left_cauchy_green_deformation.deviatoric_and_trace();
70 Ok(deviatoric_isochoric_left_cauchy_green_deformation
71 * ((self.shear_modulus()
72 + self.extra_modulus()
73 * ((self.exponent() * (isochoric_left_cauchy_green_deformation_trace - 3.0))
74 .exp()
75 - 1.0))
76 / jacobian)
77 + IDENTITY * self.bulk_modulus() * 0.5 * (jacobian - 1.0 / jacobian))
78 }
79 #[doc = include_str!("cauchy_tangent_stiffness.md")]
80 fn cauchy_tangent_stiffness(
81 &self,
82 deformation_gradient: &DeformationGradient,
83 ) -> Result<CauchyTangentStiffness, ConstitutiveError> {
84 let jacobian = self.jacobian(deformation_gradient)?;
85 let inverse_transpose_deformation_gradient = deformation_gradient.inverse_transpose();
86 let isochoric_left_cauchy_green_deformation =
87 deformation_gradient.left_cauchy_green() / jacobian.powf(TWO_THIRDS);
88 let (
89 deviatoric_isochoric_left_cauchy_green_deformation,
90 isochoric_left_cauchy_green_deformation_trace,
91 ) = isochoric_left_cauchy_green_deformation.deviatoric_and_trace();
92 let exponential =
93 (self.exponent() * (isochoric_left_cauchy_green_deformation_trace - 3.0)).exp();
94 let scaled_shear_modulus_0 = (self.shear_modulus()
95 + self.extra_modulus() * (exponential - 1.0))
96 / jacobian.powf(FIVE_THIRDS);
97 Ok(
98 (CauchyTangentStiffness::dyad_ik_jl(&IDENTITY, deformation_gradient)
99 + CauchyTangentStiffness::dyad_il_jk(deformation_gradient, &IDENTITY)
100 - CauchyTangentStiffness::dyad_ij_kl(&IDENTITY, deformation_gradient)
101 * (TWO_THIRDS))
102 * scaled_shear_modulus_0
103 + CauchyTangentStiffness::dyad_ij_kl(
104 &deviatoric_isochoric_left_cauchy_green_deformation,
105 &((&deviatoric_isochoric_left_cauchy_green_deformation
106 * &inverse_transpose_deformation_gradient)
107 * (2.0 * self.exponent() * self.extra_modulus() * exponential / jacobian)),
108 )
109 + CauchyTangentStiffness::dyad_ij_kl(
110 &(IDENTITY * (0.5 * self.bulk_modulus() * (jacobian + 1.0 / jacobian))
111 - deformation_gradient.left_cauchy_green().deviatoric()
112 * (scaled_shear_modulus_0 * FIVE_THIRDS)),
113 &inverse_transpose_deformation_gradient,
114 ),
115 )
116 }
117}
118
119impl<P> Hyperelastic for Fung<P>
120where
121 P: Parameters,
122{
123 #[doc = include_str!("helmholtz_free_energy_density.md")]
124 fn helmholtz_free_energy_density(
125 &self,
126 deformation_gradient: &DeformationGradient,
127 ) -> Result<Scalar, ConstitutiveError> {
128 let jacobian = self.jacobian(deformation_gradient)?;
129 let scalar_term =
130 deformation_gradient.left_cauchy_green().trace() / jacobian.powf(TWO_THIRDS) - 3.0;
131 Ok(0.5
132 * ((self.shear_modulus() - self.extra_modulus()) * scalar_term
133 + self.extra_modulus() / self.exponent()
134 * ((self.exponent() * scalar_term).exp() - 1.0)
135 + self.bulk_modulus() * (0.5 * (jacobian.powi(2) - 1.0) - jacobian.ln())))
136 }
137}