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

1#[cfg(test)]
2mod test;
3
4use crate::{
5    constitutive::{
6        Constitutive, ConstitutiveError,
7        solid::{FIVE_THIRDS, Solid, TWO_THIRDS, elastic::Elastic, hyperelastic::Hyperelastic},
8    },
9    math::{IDENTITY, Rank2},
10    mechanics::{CauchyStress, CauchyTangentStiffness, Deformation, DeformationGradient, Scalar},
11};
12
13#[doc = include_str!("doc.md")]
14#[derive(Debug)]
15pub struct Fung {
16    /// The bulk modulus $`\kappa`$.
17    pub bulk_modulus: Scalar,
18    /// The shear modulus $`\mu`$.
19    pub shear_modulus: Scalar,
20    /// The extra modulus $`\mu_m`$.
21    pub extra_modulus: Scalar,
22    /// The exponent $`c`$.
23    pub exponent: Scalar,
24}
25
26impl Fung {
27    /// Returns the extra modulus.
28    pub fn extra_modulus(&self) -> &Scalar {
29        &self.extra_modulus
30    }
31    /// Returns the exponent.
32    pub fn exponent(&self) -> &Scalar {
33        &self.exponent
34    }
35}
36
37impl Solid for Fung {
38    fn bulk_modulus(&self) -> &Scalar {
39        &self.bulk_modulus
40    }
41    fn shear_modulus(&self) -> &Scalar {
42        &self.shear_modulus
43    }
44}
45
46impl Elastic for Fung {
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        let (
56            deviatoric_isochoric_left_cauchy_green_deformation,
57            isochoric_left_cauchy_green_deformation_trace,
58        ) = isochoric_left_cauchy_green_deformation.deviatoric_and_trace();
59        Ok(deviatoric_isochoric_left_cauchy_green_deformation
60            * ((self.shear_modulus()
61                + self.extra_modulus()
62                    * ((self.exponent() * (isochoric_left_cauchy_green_deformation_trace - 3.0))
63                        .exp()
64                        - 1.0))
65                / jacobian)
66            + IDENTITY * self.bulk_modulus() * 0.5 * (jacobian - 1.0 / jacobian))
67    }
68    #[doc = include_str!("cauchy_tangent_stiffness.md")]
69    fn cauchy_tangent_stiffness(
70        &self,
71        deformation_gradient: &DeformationGradient,
72    ) -> Result<CauchyTangentStiffness, ConstitutiveError> {
73        let jacobian = self.jacobian(deformation_gradient)?;
74        let inverse_transpose_deformation_gradient = deformation_gradient.inverse_transpose();
75        let isochoric_left_cauchy_green_deformation =
76            deformation_gradient.left_cauchy_green() / jacobian.powf(TWO_THIRDS);
77        let (
78            deviatoric_isochoric_left_cauchy_green_deformation,
79            isochoric_left_cauchy_green_deformation_trace,
80        ) = isochoric_left_cauchy_green_deformation.deviatoric_and_trace();
81        let exponential =
82            (self.exponent() * (isochoric_left_cauchy_green_deformation_trace - 3.0)).exp();
83        let scaled_shear_modulus_0 = (self.shear_modulus()
84            + self.extra_modulus() * (exponential - 1.0))
85            / jacobian.powf(FIVE_THIRDS);
86        Ok(
87            (CauchyTangentStiffness::dyad_ik_jl(&IDENTITY, deformation_gradient)
88                + CauchyTangentStiffness::dyad_il_jk(deformation_gradient, &IDENTITY)
89                - CauchyTangentStiffness::dyad_ij_kl(&IDENTITY, deformation_gradient)
90                    * (TWO_THIRDS))
91                * scaled_shear_modulus_0
92                + CauchyTangentStiffness::dyad_ij_kl(
93                    &deviatoric_isochoric_left_cauchy_green_deformation,
94                    &((&deviatoric_isochoric_left_cauchy_green_deformation
95                        * &inverse_transpose_deformation_gradient)
96                        * (2.0 * self.exponent() * self.extra_modulus() * exponential / jacobian)),
97                )
98                + CauchyTangentStiffness::dyad_ij_kl(
99                    &(IDENTITY * (0.5 * self.bulk_modulus() * (jacobian + 1.0 / jacobian))
100                        - deformation_gradient.left_cauchy_green().deviatoric()
101                            * (scaled_shear_modulus_0 * FIVE_THIRDS)),
102                    &inverse_transpose_deformation_gradient,
103                ),
104        )
105    }
106}
107
108impl Hyperelastic for Fung {
109    #[doc = include_str!("helmholtz_free_energy_density.md")]
110    fn helmholtz_free_energy_density(
111        &self,
112        deformation_gradient: &DeformationGradient,
113    ) -> Result<Scalar, ConstitutiveError> {
114        let jacobian = self.jacobian(deformation_gradient)?;
115        let scalar_term =
116            deformation_gradient.left_cauchy_green().trace() / jacobian.powf(TWO_THIRDS) - 3.0;
117        Ok(0.5
118            * ((self.shear_modulus() - self.extra_modulus()) * scalar_term
119                + self.extra_modulus() / self.exponent()
120                    * ((self.exponent() * scalar_term).exp() - 1.0)
121                + self.bulk_modulus() * (0.5 * (jacobian.powi(2) - 1.0) - jacobian.ln())))
122    }
123}
conspire/constitutive/solid/hyperelastic/fung/mod.rs

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