conspire/constitutive/solid/hyperelastic/mooney_rivlin/
mod.rs

1#[cfg(test)]
2mod test;
3
4use crate::{
5    constitutive::{
6        ConstitutiveError,
7        solid::{FIVE_THIRDS, Solid, TWO_THIRDS, elastic::Elastic, hyperelastic::Hyperelastic},
8    },
9    math::{IDENTITY, Quantity, Rank2, TensorRank4},
10    mechanics::{CauchyStress, CauchyTangentStiffness, Deformation, DeformationGradient},
11    units::{EnergyDensity, Stress},
12};
13
14#[doc = include_str!("doc.md")]
15#[derive(Clone, Debug)]
16pub struct MooneyRivlin {
17    /// The bulk modulus $`\kappa`$.
18    pub bulk_modulus: Quantity<Stress>,
19    /// The shear modulus $`\mu`$.
20    pub shear_modulus: Quantity<Stress>,
21    /// The extra modulus $`\mu_m`$.
22    pub extra_modulus: Quantity<Stress>,
23}
24
25impl MooneyRivlin {
26    /// Returns the extra modulus.
27    pub fn extra_modulus(&self) -> Quantity<Stress> {
28        self.extra_modulus
29    }
30}
31
32impl Solid for MooneyRivlin {
33    fn bulk_modulus(&self) -> Quantity<Stress> {
34        self.bulk_modulus
35    }
36    fn shear_modulus(&self) -> Quantity<Stress> {
37        self.shear_modulus
38    }
39}
40
41impl Elastic for MooneyRivlin {
42    #[doc = include_str!("cauchy_stress.md")]
43    fn cauchy_stress(
44        &self,
45        deformation_gradient: &DeformationGradient,
46    ) -> Result<CauchyStress, ConstitutiveError> {
47        let jacobian = self.jacobian(deformation_gradient)?;
48        let isochoric_left_cauchy_green_deformation =
49            deformation_gradient.left_cauchy_green() / jacobian.powf(TWO_THIRDS);
50        Ok(((isochoric_left_cauchy_green_deformation.deviatoric()
51            * (self.shear_modulus() - self.extra_modulus())
52            - isochoric_left_cauchy_green_deformation
53                .inverse()
54                .deviatoric()
55                * self.extra_modulus())
56            + IDENTITY * (self.bulk_modulus() * 0.5 * (jacobian.powi(2) - 1.0)))
57            / jacobian)
58    }
59    #[doc = include_str!("cauchy_tangent_stiffness.md")]
60    fn cauchy_tangent_stiffness(
61        &self,
62        deformation_gradient: &DeformationGradient,
63    ) -> Result<CauchyTangentStiffness, ConstitutiveError> {
64        let jacobian = self.jacobian(deformation_gradient)?;
65        let inverse_transpose_deformation_gradient = deformation_gradient.inverse_transpose();
66        let scaled_delta_shear_modulus =
67            (self.shear_modulus() - self.extra_modulus()) / jacobian.powf(FIVE_THIRDS);
68        let inverse_isochoric_left_cauchy_green_deformation =
69            (deformation_gradient.left_cauchy_green() / jacobian.powf(TWO_THIRDS)).inverse();
70        let deviatoric_inverse_isochoric_left_cauchy_green_deformation =
71            inverse_isochoric_left_cauchy_green_deformation.deviatoric();
72        let term_1 = TensorRank4::dyad_ij_kl(
73            &inverse_isochoric_left_cauchy_green_deformation,
74            &inverse_transpose_deformation_gradient,
75        ) * TWO_THIRDS
76            - TensorRank4::dyad_ik_jl(
77                &inverse_isochoric_left_cauchy_green_deformation,
78                &inverse_transpose_deformation_gradient,
79            )
80            - TensorRank4::dyad_il_jk(
81                &inverse_transpose_deformation_gradient,
82                &inverse_isochoric_left_cauchy_green_deformation,
83            );
84        let term_3 = TensorRank4::dyad_ij_kl(
85            &deviatoric_inverse_isochoric_left_cauchy_green_deformation,
86            &inverse_transpose_deformation_gradient,
87        );
88        let term_2 = TensorRank4::dyad_ij_kl(
89            &IDENTITY,
90            &((deviatoric_inverse_isochoric_left_cauchy_green_deformation * TWO_THIRDS)
91                * &inverse_transpose_deformation_gradient),
92        );
93        Ok((TensorRank4::dyad_ik_jl(&IDENTITY, deformation_gradient)
94            + TensorRank4::dyad_il_jk(deformation_gradient, &IDENTITY)
95            - TensorRank4::dyad_ij_kl(&IDENTITY, deformation_gradient) * (TWO_THIRDS))
96            * scaled_delta_shear_modulus
97            + TensorRank4::dyad_ij_kl(
98                &(IDENTITY * (0.5 * self.bulk_modulus() * (jacobian + 1.0 / jacobian))
99                    - deformation_gradient.left_cauchy_green().deviatoric()
100                        * (scaled_delta_shear_modulus * FIVE_THIRDS)),
101                &inverse_transpose_deformation_gradient,
102            )
103            - (term_1 + term_2 - term_3) * self.extra_modulus() / jacobian)
104    }
105}
106
107impl Hyperelastic for MooneyRivlin {
108    #[doc = include_str!("helmholtz_free_energy_density.md")]
109    fn helmholtz_free_energy_density(
110        &self,
111        deformation_gradient: &DeformationGradient,
112    ) -> Result<Quantity<EnergyDensity>, ConstitutiveError> {
113        let jacobian = self.jacobian(deformation_gradient)?;
114        let isochoric_left_cauchy_green_deformation =
115            deformation_gradient.left_cauchy_green() / jacobian.powf(TWO_THIRDS);
116        Ok(0.5
117            * ((self.shear_modulus() - self.extra_modulus())
118                * (isochoric_left_cauchy_green_deformation.trace() - 3.0)
119                + self.extra_modulus()
120                    * (isochoric_left_cauchy_green_deformation.second_invariant() - 3.0)
121                + self.bulk_modulus() * (0.5 * (jacobian.powi(2) - 1.0) - jacobian.ln())))
122    }
123}
conspire/constitutive/solid/hyperelastic/mooney_rivlin/mod.rs

conspire/constitutive/solid/hyperelastic/mooney_rivlin/
mod.rs
