conspire/constitutive/solid/hyperelastic/carroll/
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 Carroll {
19    /// The bulk modulus $`\kappa`$.
20    pub bulk_modulus: Quantity<Stress>,
21    /// The linear modulus $`\mu_1`$.
22    pub linear_modulus: Quantity<Stress>,
23    /// The quartic modulus $`\mu_2`$.
24    pub quartic_modulus: Quantity<Stress>,
25    /// The second-invariant modulus $`\mu_3`$.
26    pub second_invariant_modulus: Quantity<Stress>,
27}
28
29impl Carroll {
30    /// Returns the quartic modulus.
31    pub fn quartic_modulus(&self) -> Quantity<Stress> {
32        self.quartic_modulus
33    }
34    /// Returns the second-invariant modulus.
35    pub fn second_invariant_modulus(&self) -> Quantity<Stress> {
36        self.second_invariant_modulus
37    }
38}
39
40impl Solid for Carroll {
41    fn bulk_modulus(&self) -> Quantity<Stress> {
42        self.bulk_modulus
43    }
44    fn shear_modulus(&self) -> Quantity<Stress> {
45        self.linear_modulus * 2.0
46            + self.quartic_modulus * 216.0
47            + self.second_invariant_modulus / 3.0_f64.sqrt()
48    }
49}
50
51impl Elastic for Carroll {
52    #[doc = include_str!("cauchy_stress.md")]
53    fn cauchy_stress(
54        &self,
55        deformation_gradient: &DeformationGradient,
56    ) -> Result<CauchyStress, ConstitutiveError> {
57        let jacobian = self.jacobian(deformation_gradient)?;
58        let isochoric_left_cauchy_green_deformation =
59            deformation_gradient.left_cauchy_green() / jacobian.powf(TWO_THIRDS);
60        let first_invariant = isochoric_left_cauchy_green_deformation.trace();
61        let second_invariant = isochoric_left_cauchy_green_deformation.second_invariant();
62        let dw_di1 = self.linear_modulus + self.quartic_modulus * (4.0 * first_invariant.powi(3));
63        let dw_di2 = self.second_invariant_modulus / (2.0 * second_invariant.sqrt());
64        Ok(
65            ((isochoric_left_cauchy_green_deformation.deviatoric() * (dw_di1 * 2.0)
66                - isochoric_left_cauchy_green_deformation
67                    .inverse()
68                    .deviatoric()
69                    * (dw_di2 * 2.0))
70                + IDENTITY * (self.bulk_modulus() * 0.5 * (jacobian.powi(2) - 1.0)))
71                / jacobian,
72        )
73    }
74    #[doc = include_str!("cauchy_tangent_stiffness.md")]
75    fn cauchy_tangent_stiffness(
76        &self,
77        deformation_gradient: &DeformationGradient,
78    ) -> Result<CauchyTangentStiffness, ConstitutiveError> {
79        let jacobian = self.jacobian(deformation_gradient)?;
80        let inverse_transpose_deformation_gradient = deformation_gradient.inverse_transpose();
81        let isochoric_left_cauchy_green_deformation =
82            deformation_gradient.left_cauchy_green() / jacobian.powf(TWO_THIRDS);
83        let first_invariant = isochoric_left_cauchy_green_deformation.trace();
84        let second_invariant = isochoric_left_cauchy_green_deformation.second_invariant();
85        let dw_di1 = self.linear_modulus + self.quartic_modulus * (4.0 * first_invariant.powi(3));
86        let dw_di2 = self.second_invariant_modulus / (2.0 * second_invariant.sqrt());
87        let scaled_dw_di1 = dw_di1 * 2.0 / jacobian.powf(FIVE_THIRDS);
88        let inverse_isochoric_left_cauchy_green_deformation =
89            isochoric_left_cauchy_green_deformation.inverse();
90        let deviatoric_inverse_isochoric_left_cauchy_green_deformation =
91            inverse_isochoric_left_cauchy_green_deformation.deviatoric();
92        let term_1 = TensorRank4::dyad_ij_kl(
93            &inverse_isochoric_left_cauchy_green_deformation,
94            &inverse_transpose_deformation_gradient,
95        ) * TWO_THIRDS
96            - TensorRank4::dyad_ik_jl(
97                &inverse_isochoric_left_cauchy_green_deformation,
98                &inverse_transpose_deformation_gradient,
99            )
100            - TensorRank4::dyad_il_jk(
101                &inverse_transpose_deformation_gradient,
102                &inverse_isochoric_left_cauchy_green_deformation,
103            );
104        let term_3 = TensorRank4::dyad_ij_kl(
105            &deviatoric_inverse_isochoric_left_cauchy_green_deformation,
106            &inverse_transpose_deformation_gradient,
107        );
108        let term_2 = TensorRank4::dyad_ij_kl(
109            &IDENTITY,
110            &((deviatoric_inverse_isochoric_left_cauchy_green_deformation.clone() * TWO_THIRDS)
111                * &inverse_transpose_deformation_gradient),
112        );
113        let d_first_invariant_dw_di1_df = deformation_gradient
114            * (48.0 * self.quartic_modulus * first_invariant.powi(2) / jacobian.powf(TWO_THIRDS))
115            - inverse_transpose_deformation_gradient.clone()
116                * (16.0 * self.quartic_modulus * first_invariant.powi(3));
117        let identity_i1_minus_b =
118            IDENTITY * first_invariant - isochoric_left_cauchy_green_deformation.clone();
119        let d_second_invariant_dw_di2_df = (identity_i1_minus_b * deformation_gradient)
120            * (-2.0 * dw_di2 / second_invariant / jacobian.powf(TWO_THIRDS))
121            + inverse_transpose_deformation_gradient.clone() * (dw_di2 * FOUR_THIRDS);
122        let extra_term_1 = TensorRank4::dyad_ij_kl(
123            &isochoric_left_cauchy_green_deformation.deviatoric(),
124            &d_first_invariant_dw_di1_df,
125        ) / jacobian;
126        let extra_term_2 = TensorRank4::dyad_ij_kl(
127            &deviatoric_inverse_isochoric_left_cauchy_green_deformation,
128            &d_second_invariant_dw_di2_df,
129        ) / jacobian;
130        Ok((TensorRank4::dyad_ik_jl(&IDENTITY, deformation_gradient)
131            + TensorRank4::dyad_il_jk(deformation_gradient, &IDENTITY)
132            - TensorRank4::dyad_ij_kl(&IDENTITY, deformation_gradient) * (TWO_THIRDS))
133            * scaled_dw_di1
134            + TensorRank4::dyad_ij_kl(
135                &(IDENTITY * (0.5 * self.bulk_modulus() * (jacobian + 1.0 / jacobian))
136                    - deformation_gradient.left_cauchy_green().deviatoric()
137                        * (scaled_dw_di1 * FIVE_THIRDS)),
138                &inverse_transpose_deformation_gradient,
139            )
140            - (term_1 + term_2 - term_3) * (dw_di2 * 2.0) / jacobian
141            + extra_term_1
142            - extra_term_2)
143    }
144}
145
146impl Hyperelastic for Carroll {
147    #[doc = include_str!("helmholtz_free_energy_density.md")]
148    fn helmholtz_free_energy_density(
149        &self,
150        deformation_gradient: &DeformationGradient,
151    ) -> Result<Quantity<EnergyDensity>, ConstitutiveError> {
152        let jacobian = self.jacobian(deformation_gradient)?;
153        let isochoric_left_cauchy_green_deformation =
154            deformation_gradient.left_cauchy_green() / jacobian.powf(TWO_THIRDS);
155        let first_invariant = isochoric_left_cauchy_green_deformation.trace();
156        let second_invariant = isochoric_left_cauchy_green_deformation.second_invariant();
157        Ok(self.linear_modulus * (first_invariant - 3.0)
158            + self.quartic_modulus * (first_invariant.powi(4) - 81.0)
159            + self.second_invariant_modulus * (second_invariant.sqrt() - 3.0_f64.sqrt())
160            + self.bulk_modulus() * (0.5 * (jacobian.powi(2) - 1.0) - jacobian.ln()) * 0.5)
161    }
162}
conspire/constitutive/solid/hyperelastic/carroll/mod.rs

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