conspire/constitutive/solid/hyperelastic/isihara/
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, Scalar},
11    units::{EnergyDensity, Stress},
12};
13
14const FOUR_THIRDS: Scalar = 4.0 / 3.0;
15
16#[doc = include_str!("doc.md")]
17#[derive(Clone, Debug)]
18pub struct Isihara {
19    /// The bulk modulus $`\kappa`$.
20    pub bulk_modulus: Quantity<Stress>,
21    /// The shear modulus $`\mu`$.
22    pub shear_modulus: Quantity<Stress>,
23    /// The extra modulus $`\mu_m`$.
24    pub extra_modulus: Quantity<Stress>,
25    /// The quadratic modulus $`\mu_q`$.
26    pub quadratic_modulus: Quantity<Stress>,
27}
28
29impl Isihara {
30    /// Returns the extra modulus.
31    pub fn extra_modulus(&self) -> Quantity<Stress> {
32        self.extra_modulus
33    }
34    /// Returns the quadratic modulus.
35    pub fn quadratic_modulus(&self) -> Quantity<Stress> {
36        self.quadratic_modulus
37    }
38}
39
40impl Solid for Isihara {
41    fn bulk_modulus(&self) -> Quantity<Stress> {
42        self.bulk_modulus
43    }
44    fn shear_modulus(&self) -> Quantity<Stress> {
45        self.shear_modulus
46    }
47}
48
49impl Elastic for Isihara {
50    #[doc = include_str!("cauchy_stress.md")]
51    fn cauchy_stress(
52        &self,
53        deformation_gradient: &DeformationGradient,
54    ) -> Result<CauchyStress, ConstitutiveError> {
55        let jacobian = self.jacobian(deformation_gradient)?;
56        let isochoric_left_cauchy_green_deformation =
57            deformation_gradient.left_cauchy_green() / jacobian.powf(TWO_THIRDS);
58        let first_invariant = isochoric_left_cauchy_green_deformation.trace();
59        let dw_di1 = 0.5 * (self.shear_modulus() - self.extra_modulus())
60            + self.quadratic_modulus() * (first_invariant - 3.0);
61        Ok(
62            ((isochoric_left_cauchy_green_deformation.deviatoric() * (dw_di1 * 2.0)
63                - isochoric_left_cauchy_green_deformation
64                    .inverse()
65                    .deviatoric()
66                    * self.extra_modulus())
67                + IDENTITY * (self.bulk_modulus() * 0.5 * (jacobian.powi(2) - 1.0)))
68                / jacobian,
69        )
70    }
71    #[doc = include_str!("cauchy_tangent_stiffness.md")]
72    fn cauchy_tangent_stiffness(
73        &self,
74        deformation_gradient: &DeformationGradient,
75    ) -> Result<CauchyTangentStiffness, ConstitutiveError> {
76        let jacobian = self.jacobian(deformation_gradient)?;
77        let inverse_transpose_deformation_gradient = deformation_gradient.inverse_transpose();
78        let left_cauchy_green_deformation = deformation_gradient.left_cauchy_green();
79        let isochoric_left_cauchy_green_deformation =
80            left_cauchy_green_deformation.clone() / jacobian.powf(TWO_THIRDS);
81        let first_invariant = isochoric_left_cauchy_green_deformation.trace();
82        let dw_di1 = 0.5 * (self.shear_modulus() - self.extra_modulus())
83            + self.quadratic_modulus() * (first_invariant - 3.0);
84        let scaled_dw_di1 = dw_di1 * 2.0 / jacobian.powf(FIVE_THIRDS);
85        let inverse_isochoric_left_cauchy_green_deformation =
86            isochoric_left_cauchy_green_deformation.inverse();
87        let deviatoric_inverse_isochoric_left_cauchy_green_deformation =
88            inverse_isochoric_left_cauchy_green_deformation.deviatoric();
89        let term_1 = TensorRank4::dyad_ij_kl(
90            &inverse_isochoric_left_cauchy_green_deformation,
91            &inverse_transpose_deformation_gradient,
92        ) * TWO_THIRDS
93            - TensorRank4::dyad_ik_jl(
94                &inverse_isochoric_left_cauchy_green_deformation,
95                &inverse_transpose_deformation_gradient,
96            )
97            - TensorRank4::dyad_il_jk(
98                &inverse_transpose_deformation_gradient,
99                &inverse_isochoric_left_cauchy_green_deformation,
100            );
101        let term_3 = TensorRank4::dyad_ij_kl(
102            &deviatoric_inverse_isochoric_left_cauchy_green_deformation,
103            &inverse_transpose_deformation_gradient,
104        );
105        let term_2 = TensorRank4::dyad_ij_kl(
106            &IDENTITY,
107            &((deviatoric_inverse_isochoric_left_cauchy_green_deformation * TWO_THIRDS)
108                * &inverse_transpose_deformation_gradient),
109        );
110        let d_first_invariant_dw_di1_df = deformation_gradient
111            * (4.0 * self.quadratic_modulus() / jacobian.powf(TWO_THIRDS))
112            - inverse_transpose_deformation_gradient.clone()
113                * (FOUR_THIRDS * self.quadratic_modulus() * first_invariant);
114        let extra_term_1 = TensorRank4::dyad_ij_kl(
115            &isochoric_left_cauchy_green_deformation.deviatoric(),
116            &d_first_invariant_dw_di1_df,
117        ) / jacobian;
118        Ok((TensorRank4::dyad_ik_jl(&IDENTITY, deformation_gradient)
119            + TensorRank4::dyad_il_jk(deformation_gradient, &IDENTITY)
120            - TensorRank4::dyad_ij_kl(&IDENTITY, deformation_gradient) * (TWO_THIRDS))
121            * scaled_dw_di1
122            + TensorRank4::dyad_ij_kl(
123                &(IDENTITY * (0.5 * self.bulk_modulus() * (jacobian + 1.0 / jacobian))
124                    - left_cauchy_green_deformation.deviatoric() * (scaled_dw_di1 * FIVE_THIRDS)),
125                &inverse_transpose_deformation_gradient,
126            )
127            - (term_1 + term_2 - term_3) * self.extra_modulus() / jacobian
128            + extra_term_1)
129    }
130}
131
132impl Hyperelastic for Isihara {
133    #[doc = include_str!("helmholtz_free_energy_density.md")]
134    fn helmholtz_free_energy_density(
135        &self,
136        deformation_gradient: &DeformationGradient,
137    ) -> Result<Quantity<EnergyDensity>, ConstitutiveError> {
138        let jacobian = self.jacobian(deformation_gradient)?;
139        let isochoric_left_cauchy_green_deformation =
140            deformation_gradient.left_cauchy_green() / jacobian.powf(TWO_THIRDS);
141        let first_invariant = isochoric_left_cauchy_green_deformation.trace();
142        let second_invariant = isochoric_left_cauchy_green_deformation.second_invariant();
143        Ok(0.5
144            * ((self.shear_modulus() - self.extra_modulus()) * (first_invariant - 3.0)
145                + self.extra_modulus() * (second_invariant - 3.0)
146                + self.quadratic_modulus() * (first_invariant - 3.0).powi(2)
147                + self.bulk_modulus() * (0.5 * (jacobian.powi(2) - 1.0) - jacobian.ln())))
148    }
149}
conspire/constitutive/solid/hyperelastic/isihara/mod.rs

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