conspire/constitutive/solid/hyperelastic/neo_hookean/
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},
11    units::{EnergyDensity, Stress},
12};
13
14#[doc = include_str!("doc.md")]
15#[derive(Clone, Debug)]
16pub struct NeoHookean {
17    /// The bulk modulus $`\kappa`$.
18    pub bulk_modulus: Quantity<Stress>,
19    /// The shear modulus $`\mu`$.
20    pub shear_modulus: Quantity<Stress>,
21}
22
23impl Solid for NeoHookean {
24    fn bulk_modulus(&self) -> Quantity<Stress> {
25        self.bulk_modulus
26    }
27    fn shear_modulus(&self) -> Quantity<Stress> {
28        self.shear_modulus
29    }
30}
31
32impl Elastic for NeoHookean {
33    #[doc = include_str!("cauchy_stress.md")]
34    fn cauchy_stress(
35        &self,
36        deformation_gradient: &DeformationGradient,
37    ) -> Result<CauchyStress, ConstitutiveError> {
38        let jacobian = self.jacobian(deformation_gradient)?;
39        Ok(
40            deformation_gradient.left_cauchy_green().deviatoric() / jacobian.powf(FIVE_THIRDS)
41                * self.shear_modulus()
42                + IDENTITY * self.bulk_modulus() * 0.5 * (jacobian - 1.0 / jacobian),
43        )
44    }
45    #[doc = include_str!("cauchy_tangent_stiffness.md")]
46    fn cauchy_tangent_stiffness(
47        &self,
48        deformation_gradient: &DeformationGradient,
49    ) -> Result<CauchyTangentStiffness, ConstitutiveError> {
50        let jacobian = self.jacobian(deformation_gradient)?;
51        let inverse_transpose_deformation_gradient = deformation_gradient.inverse_transpose();
52        let scaled_shear_modulus = self.shear_modulus() / jacobian.powf(FIVE_THIRDS);
53        Ok((TensorRank4::dyad_ik_jl(&IDENTITY, deformation_gradient)
54            + TensorRank4::dyad_il_jk(deformation_gradient, &IDENTITY)
55            - TensorRank4::dyad_ij_kl(&IDENTITY, deformation_gradient) * (TWO_THIRDS))
56            * scaled_shear_modulus
57            + TensorRank4::dyad_ij_kl(
58                &(IDENTITY * (self.bulk_modulus() * 0.5 * (jacobian + 1.0 / jacobian))
59                    - deformation_gradient.left_cauchy_green().deviatoric()
60                        * (scaled_shear_modulus * FIVE_THIRDS)),
61                &inverse_transpose_deformation_gradient,
62            ))
63    }
64}
65
66impl Hyperelastic for NeoHookean {
67    #[doc = include_str!("helmholtz_free_energy_density.md")]
68    fn helmholtz_free_energy_density(
69        &self,
70        deformation_gradient: &DeformationGradient,
71    ) -> Result<Quantity<EnergyDensity>, ConstitutiveError> {
72        let jacobian = self.jacobian(deformation_gradient)?;
73        Ok(0.5
74            * (self.shear_modulus()
75                * (deformation_gradient.left_cauchy_green().trace() / jacobian.powf(TWO_THIRDS)
76                    - 3.0)
77                + self.bulk_modulus() * (0.5 * (jacobian.powi(2) - 1.0) - jacobian.ln())))
78    }
79}
conspire/constitutive/solid/hyperelastic/neo_hookean/mod.rs

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