conspire/constitutive/solid/hyperelastic/yeoh/
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, Modulus, Stress},
12};
13
14const SEVEN_THIRDS: Scalar = 7.0 / 3.0;
15
16#[doc = include_str!("doc.md")]
17#[derive(Clone, Debug)]
18pub struct Yeoh {
19    /// The bulk modulus $`\kappa`$.
20    pub bulk_modulus: Quantity<Stress>,
21    /// The shear moduli $`\mu_n`$.
22    pub shear_moduli: Vec<Quantity<Modulus>>,
23}
24
25impl Solid for Yeoh {
26    fn bulk_modulus(&self) -> Quantity<Stress> {
27        self.bulk_modulus
28    }
29    fn shear_modulus(&self) -> Quantity<Stress> {
30        self.shear_moduli.first().copied().unwrap_or_default()
31    }
32}
33
34impl Elastic for Yeoh {
35    #[doc = include_str!("cauchy_stress.md")]
36    fn cauchy_stress(
37        &self,
38        deformation_gradient: &DeformationGradient,
39    ) -> Result<CauchyStress, ConstitutiveError> {
40        let jacobian = self.jacobian(deformation_gradient)?;
41        let (deviatoric_left_cauchy_green_deformation, left_cauchy_green_deformation_trace) =
42            deformation_gradient
43                .left_cauchy_green()
44                .deviatoric_and_trace();
45        let scalar_term = left_cauchy_green_deformation_trace / jacobian.powf(TWO_THIRDS) - 3.0;
46        Ok(deviatoric_left_cauchy_green_deformation
47            * self
48                .shear_moduli
49                .iter()
50                .enumerate()
51                .map(|(n, &modulus)| modulus * (((n as Scalar) + 1.0) * scalar_term.powi(n as i32)))
52                .sum::<Quantity<Modulus>>()
53            / jacobian.powf(FIVE_THIRDS)
54            + IDENTITY * self.bulk_modulus() * 0.5 * (jacobian - 1.0 / jacobian))
55    }
56    #[doc = include_str!("cauchy_tangent_stiffness.md")]
57    fn cauchy_tangent_stiffness(
58        &self,
59        deformation_gradient: &DeformationGradient,
60    ) -> Result<CauchyTangentStiffness, ConstitutiveError> {
61        let jacobian = self.jacobian(deformation_gradient)?;
62        let inverse_transpose_deformation_gradient = deformation_gradient.inverse_transpose();
63        let left_cauchy_green_deformation = deformation_gradient.left_cauchy_green();
64        let scalar_term = left_cauchy_green_deformation.trace() / jacobian.powf(TWO_THIRDS) - 3.0;
65        let scaled_modulus = self
66            .shear_moduli
67            .iter()
68            .enumerate()
69            .map(|(n, &modulus)| modulus * (((n as Scalar) + 1.0) * scalar_term.powi(n as i32)))
70            .sum::<Quantity<Modulus>>()
71            / jacobian.powf(FIVE_THIRDS);
72        let deviatoric_left_cauchy_green_deformation = left_cauchy_green_deformation.deviatoric();
73        let last_term = TensorRank4::dyad_ij_kl(
74            &deviatoric_left_cauchy_green_deformation,
75            &((left_cauchy_green_deformation.deviatoric()
76                * &inverse_transpose_deformation_gradient)
77                * (self
78                    .shear_moduli
79                    .iter()
80                    .enumerate()
81                    .skip(1)
82                    .map(|(n, &modulus)| {
83                        modulus
84                            * (2.0
85                                * ((n as Scalar) + 1.0)
86                                * (n as Scalar)
87                                * scalar_term.powi(n as i32 - 1))
88                    })
89                    .sum::<Quantity<Modulus>>()
90                    / jacobian.powf(SEVEN_THIRDS))),
91        );
92        Ok((TensorRank4::dyad_ik_jl(&IDENTITY, deformation_gradient)
93            + TensorRank4::dyad_il_jk(deformation_gradient, &IDENTITY)
94            - TensorRank4::dyad_ij_kl(&IDENTITY, deformation_gradient) * (TWO_THIRDS))
95            * scaled_modulus
96            + TensorRank4::dyad_ij_kl(
97                &(IDENTITY * (self.bulk_modulus() * 0.5 * (jacobian + 1.0 / jacobian))
98                    - deviatoric_left_cauchy_green_deformation * (scaled_modulus * FIVE_THIRDS)),
99                &inverse_transpose_deformation_gradient,
100            )
101            + last_term)
102    }
103}
104
105impl Hyperelastic for Yeoh {
106    #[doc = include_str!("helmholtz_free_energy_density.md")]
107    fn helmholtz_free_energy_density(
108        &self,
109        deformation_gradient: &DeformationGradient,
110    ) -> Result<Quantity<EnergyDensity>, ConstitutiveError> {
111        let jacobian = self.jacobian(deformation_gradient)?;
112        let scalar_term =
113            deformation_gradient.left_cauchy_green().trace() / jacobian.powf(TWO_THIRDS) - 3.0;
114        Ok(0.5
115            * (self
116                .shear_moduli
117                .iter()
118                .enumerate()
119                .map(|(n, &modulus)| modulus * scalar_term.powi((n + 1) as i32))
120                .sum::<Quantity<Modulus>>()
121                + self.bulk_modulus() * (0.5 * (jacobian.powi(2) - 1.0) - jacobian.ln())))
122    }
123}
conspire/constitutive/solid/hyperelastic/yeoh/mod.rs

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