conspire/constitutive/solid/elastic/hencky/
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::{ContractThirdFourthIndicesWithFirstSecondIndicesOf, IDENTITY_00, Rank2},
10    mechanics::{
11        Deformation, DeformationGradient, Scalar, SecondPiolaKirchhoffStress,
12        SecondPiolaKirchhoffTangentStiffness,
13    },
14};
15
16#[doc = include_str!("doc.md")]
17#[derive(Debug)]
18pub struct Hencky {
19    /// The bulk modulus $`\kappa`$.
20    pub bulk_modulus: Scalar,
21    /// The shear modulus $`\mu`$.
22    pub shear_modulus: Scalar,
23}
24
25impl Solid for Hencky {
26    fn bulk_modulus(&self) -> &Scalar {
27        &self.bulk_modulus
28    }
29    fn shear_modulus(&self) -> &Scalar {
30        &self.shear_modulus
31    }
32}
33
34impl Elastic for Hencky {
35    #[doc = include_str!("second_piola_kirchhoff_stress.md")]
36    fn second_piola_kirchhoff_stress(
37        &self,
38        deformation_gradient: &DeformationGradient,
39    ) -> Result<SecondPiolaKirchhoffStress, ConstitutiveError> {
40        let _jacobian = self.jacobian(deformation_gradient)?;
41        let (deviatoric_strain, strain_trace) =
42            (deformation_gradient.right_cauchy_green().logm() * 0.5).deviatoric_and_trace();
43        Ok(deviatoric_strain * (2.0 * self.shear_modulus())
44            + IDENTITY_00 * (self.bulk_modulus() * strain_trace))
45    }
46    #[doc = include_str!("second_piola_kirchhoff_tangent_stiffness.md")]
47    fn second_piola_kirchhoff_tangent_stiffness(
48        &self,
49        deformation_gradient: &DeformationGradient,
50    ) -> Result<SecondPiolaKirchhoffTangentStiffness, ConstitutiveError> {
51        let _jacobian = self.jacobian(deformation_gradient)?;
52        let right_cauchy_green = deformation_gradient.right_cauchy_green();
53        let deformation_gradient_transpose = deformation_gradient.transpose();
54        let scaled_deformation_gradient_transpose =
55            &deformation_gradient_transpose * self.shear_modulus();
56        Ok((right_cauchy_green
57            .dlogm()
58            .contract_third_fourth_indices_with_first_second_indices_of(
59                &(SecondPiolaKirchhoffTangentStiffness::dyad_il_jk(
60                    &IDENTITY_00,
61                    &scaled_deformation_gradient_transpose,
62                ) + SecondPiolaKirchhoffTangentStiffness::dyad_ik_jl(
63                    &scaled_deformation_gradient_transpose,
64                    &IDENTITY_00,
65                )),
66            ))
67            + (SecondPiolaKirchhoffTangentStiffness::dyad_ij_kl(
68                &(IDENTITY_00 * (self.bulk_modulus() - TWO_THIRDS * self.shear_modulus())),
69                &deformation_gradient_transpose.inverse(),
70            )))
71    }
72}
conspire/constitutive/solid/elastic/hencky/mod.rs

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