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

1#[cfg(test)]
2mod test;
3
4use super::*;
5
6#[doc = include_str!("model.md")]
7#[derive(Debug)]
8pub struct MooneyRivlin<P> {
9    parameters: P,
10}
11
12impl<P> MooneyRivlin<P>
13where
14    P: Parameters,
15{
16    /// Returns the extra modulus.
17    pub fn extra_modulus(&self) -> &Scalar {
18        self.parameters.get(2)
19    }
20}
21
22impl<P> Constitutive<P> for MooneyRivlin<P>
23where
24    P: Parameters,
25{
26    fn new(parameters: P) -> Self {
27        Self { parameters }
28    }
29}
30
31impl<P> Solid for MooneyRivlin<P>
32where
33    P: Parameters,
34{
35    fn bulk_modulus(&self) -> &Scalar {
36        self.parameters.get(0)
37    }
38    fn shear_modulus(&self) -> &Scalar {
39        self.parameters.get(1)
40    }
41}
42
43impl<P> Elastic for MooneyRivlin<P>
44where
45    P: Parameters,
46{
47    #[doc = include_str!("cauchy_stress.md")]
48    fn cauchy_stress(
49        &self,
50        deformation_gradient: &DeformationGradient,
51    ) -> Result<CauchyStress, ConstitutiveError> {
52        let jacobian = self.jacobian(deformation_gradient)?;
53        let isochoric_left_cauchy_green_deformation =
54            deformation_gradient.left_cauchy_green() / jacobian.powf(TWO_THIRDS);
55        Ok(((isochoric_left_cauchy_green_deformation.deviatoric()
56            * (self.shear_modulus() - self.extra_modulus())
57            - isochoric_left_cauchy_green_deformation
58                .inverse()
59                .deviatoric()
60                * self.extra_modulus())
61            + IDENTITY * (self.bulk_modulus() * 0.5 * (jacobian.powi(2) - 1.0)))
62            / jacobian)
63    }
64    #[doc = include_str!("cauchy_tangent_stiffness.md")]
65    fn cauchy_tangent_stiffness(
66        &self,
67        deformation_gradient: &DeformationGradient,
68    ) -> Result<CauchyTangentStiffness, ConstitutiveError> {
69        let jacobian = self.jacobian(deformation_gradient)?;
70        let inverse_transpose_deformation_gradient = deformation_gradient.inverse_transpose();
71        let scaled_delta_shear_modulus =
72            (self.shear_modulus() - self.extra_modulus()) / jacobian.powf(FIVE_THIRDS);
73        let inverse_isochoric_left_cauchy_green_deformation =
74            (deformation_gradient.left_cauchy_green() / jacobian.powf(TWO_THIRDS)).inverse();
75        let deviatoric_inverse_isochoric_left_cauchy_green_deformation =
76            inverse_isochoric_left_cauchy_green_deformation.deviatoric();
77        let term_1 = CauchyTangentStiffness::dyad_ij_kl(
78            &inverse_isochoric_left_cauchy_green_deformation,
79            &inverse_transpose_deformation_gradient,
80        ) * TWO_THIRDS
81            - CauchyTangentStiffness::dyad_ik_jl(
82                &inverse_isochoric_left_cauchy_green_deformation,
83                &inverse_transpose_deformation_gradient,
84            )
85            - CauchyTangentStiffness::dyad_il_jk(
86                &inverse_transpose_deformation_gradient,
87                &inverse_isochoric_left_cauchy_green_deformation,
88            );
89        let term_3 = CauchyTangentStiffness::dyad_ij_kl(
90            &deviatoric_inverse_isochoric_left_cauchy_green_deformation,
91            &inverse_transpose_deformation_gradient,
92        );
93        let term_2 = CauchyTangentStiffness::dyad_ij_kl(
94            &IDENTITY,
95            &((deviatoric_inverse_isochoric_left_cauchy_green_deformation * TWO_THIRDS)
96                * &inverse_transpose_deformation_gradient),
97        );
98        Ok(
99            (CauchyTangentStiffness::dyad_ik_jl(&IDENTITY, deformation_gradient)
100                + CauchyTangentStiffness::dyad_il_jk(deformation_gradient, &IDENTITY)
101                - CauchyTangentStiffness::dyad_ij_kl(&IDENTITY, deformation_gradient)
102                    * (TWO_THIRDS))
103                * scaled_delta_shear_modulus
104                + CauchyTangentStiffness::dyad_ij_kl(
105                    &(IDENTITY * (0.5 * self.bulk_modulus() * (jacobian + 1.0 / jacobian))
106                        - deformation_gradient.left_cauchy_green().deviatoric()
107                            * (scaled_delta_shear_modulus * FIVE_THIRDS)),
108                    &inverse_transpose_deformation_gradient,
109                )
110                - (term_1 + term_2 - term_3) * self.extra_modulus() / jacobian,
111        )
112    }
113}
114
115impl<P> Hyperelastic for MooneyRivlin<P>
116where
117    P: Parameters,
118{
119    #[doc = include_str!("helmholtz_free_energy_density.md")]
120    fn helmholtz_free_energy_density(
121        &self,
122        deformation_gradient: &DeformationGradient,
123    ) -> Result<Scalar, ConstitutiveError> {
124        let jacobian = self.jacobian(deformation_gradient)?;
125        let isochoric_left_cauchy_green_deformation =
126            deformation_gradient.left_cauchy_green() / jacobian.powf(TWO_THIRDS);
127        Ok(0.5
128            * ((self.shear_modulus() - self.extra_modulus())
129                * (isochoric_left_cauchy_green_deformation.trace() - 3.0)
130                + self.extra_modulus()
131                    * (isochoric_left_cauchy_green_deformation.second_invariant() - 3.0)
132                + self.bulk_modulus() * (0.5 * (jacobian.powi(2) - 1.0) - jacobian.ln())))
133    }
134}
conspire/constitutive/solid/hyperelastic/mooney_rivlin/mod.rs

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