conspire/constitutive/solid/elastic/saint_venant_kirchhoff/
mod.rs

1#[cfg(test)]
2mod test;
3
4use crate::{
5    constitutive::{
6        Constitutive, ConstitutiveError,
7        solid::{Solid, TWO_THIRDS, elastic::Elastic},
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 SaintVenantKirchhoff {
16    /// The bulk modulus $`\kappa`$.
17    pub bulk_modulus: Scalar,
18    /// The shear modulus $`\mu`$.
19    pub shear_modulus: Scalar,
20}
21
22impl Solid for SaintVenantKirchhoff {
23    fn bulk_modulus(&self) -> &Scalar {
24        &self.bulk_modulus
25    }
26    fn shear_modulus(&self) -> &Scalar {
27        &self.shear_modulus
28    }
29}
30
31impl Elastic for SaintVenantKirchhoff {
32    #[doc = include_str!("cauchy_stress.md")]
33    fn cauchy_stress(
34        &self,
35        deformation_gradient: &DeformationGradient,
36    ) -> Result<CauchyStress, ConstitutiveError> {
37        let jacobian = self.jacobian(deformation_gradient)?;
38        let (deviatoric_strain, strain_trace) =
39            ((deformation_gradient.left_cauchy_green() - IDENTITY) * 0.5).deviatoric_and_trace();
40        Ok(deviatoric_strain * (2.0 * self.shear_modulus() / jacobian)
41            + IDENTITY * (self.bulk_modulus() * strain_trace / jacobian))
42    }
43    #[doc = include_str!("cauchy_tangent_stiffness.md")]
44    fn cauchy_tangent_stiffness(
45        &self,
46        deformation_gradient: &DeformationGradient,
47    ) -> Result<CauchyTangentStiffness, ConstitutiveError> {
48        let jacobian = self.jacobian(deformation_gradient)?;
49        let inverse_transpose_deformation_gradient = deformation_gradient.inverse_transpose();
50        let scaled_deformation_gradient = deformation_gradient * (self.shear_modulus() / jacobian);
51        let (deviatoric_strain, strain_trace) =
52            ((deformation_gradient.left_cauchy_green() - IDENTITY) * 0.5).deviatoric_and_trace();
53        Ok(
54            (CauchyTangentStiffness::dyad_il_jk(&scaled_deformation_gradient, &IDENTITY)
55                + CauchyTangentStiffness::dyad_ik_jl(&IDENTITY, &scaled_deformation_gradient))
56                + CauchyTangentStiffness::dyad_ij_kl(
57                    &IDENTITY,
58                    &(deformation_gradient
59                        * ((self.bulk_modulus() - self.shear_modulus() * TWO_THIRDS) / jacobian)),
60                )
61                - CauchyTangentStiffness::dyad_ij_kl(
62                    &(deviatoric_strain * (2.0 * self.shear_modulus() / jacobian)
63                        + IDENTITY * (self.bulk_modulus() * strain_trace / jacobian)),
64                    &inverse_transpose_deformation_gradient,
65                ),
66        )
67    }
68}
conspire/constitutive/solid/elastic/saint_venant_kirchhoff/mod.rs

conspire/constitutive/solid/elastic/saint_venant_kirchhoff/
mod.rs
