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

1#[cfg(test)]
2mod test;
3
4use crate::{
5    constitutive::{
6        ConstitutiveError,
7        solid::{Solid, TWO_THIRDS, elastic::Elastic},
8    },
9    math::{ContractThirdFourthWithFirstSecond, IDENTITY, Quantity, Rank2, Spectrum, TensorRank4},
10    mechanics::{CauchyStress, CauchyTangentStiffness, Deformation, DeformationGradient, Scalar},
11    units::Stress,
12};
13
14#[doc = include_str!("doc.md")]
15#[derive(Clone, Debug)]
16pub struct SethHillEulerian {
17    /// The bulk modulus $`\kappa`$.
18    pub bulk_modulus: Quantity<Stress>,
19    /// The shear modulus $`\mu`$.
20    pub shear_modulus: Quantity<Stress>,
21    /// The exponent $`m`$.
22    pub exponent: Scalar,
23}
24
25impl SethHillEulerian {
26    /// Returns the exponent.
27    pub fn exponent(&self) -> Scalar {
28        self.exponent
29    }
30}
31
32impl Solid for SethHillEulerian {
33    fn bulk_modulus(&self) -> Quantity<Stress> {
34        self.bulk_modulus
35    }
36    fn shear_modulus(&self) -> Quantity<Stress> {
37        self.shear_modulus
38    }
39}
40
41impl Elastic for SethHillEulerian {
42    #[doc = include_str!("cauchy_stress.md")]
43    fn cauchy_stress(
44        &self,
45        deformation_gradient: &DeformationGradient,
46    ) -> Result<CauchyStress, ConstitutiveError> {
47        let jacobian = self.jacobian(deformation_gradient)?;
48        let left_cauchy_green = deformation_gradient.left_cauchy_green();
49        let (deviatoric_strain, strain_trace) = if self.exponent() == 0.0 {
50            (left_cauchy_green
51                .logm()
52                .map_err(|error| ConstitutiveError::upstream(error, self))?
53                * 0.5)
54                .deviatoric_and_trace()
55        } else {
56            ((left_cauchy_green
57                .powm(0.5 * self.exponent())
58                .map_err(|error| ConstitutiveError::upstream(error, self))?
59                - IDENTITY)
60                / self.exponent())
61            .deviatoric_and_trace()
62        };
63        Ok(deviatoric_strain * (2.0 * self.shear_modulus() / jacobian)
64            + IDENTITY * (self.bulk_modulus() * strain_trace / jacobian))
65    }
66    #[doc = include_str!("cauchy_tangent_stiffness.md")]
67    fn cauchy_tangent_stiffness(
68        &self,
69        deformation_gradient: &DeformationGradient,
70    ) -> Result<CauchyTangentStiffness, ConstitutiveError> {
71        let jacobian = self.jacobian(deformation_gradient)?;
72        let left_cauchy_green = deformation_gradient.left_cauchy_green();
73        let inverse_transpose_deformation_gradient = deformation_gradient.inverse_transpose();
74        if self.exponent() == 0.0 {
75            let (deviatoric_strain, strain_trace) = (left_cauchy_green
76                .logm()
77                .map_err(|error| ConstitutiveError::upstream(error, self))?
78                * 0.5)
79                .deviatoric_and_trace();
80            let scaled_deformation_gradient =
81                deformation_gradient * (self.shear_modulus() / jacobian);
82            return Ok((left_cauchy_green
83                .dlogm()
84                .map_err(|error| ConstitutiveError::upstream(error, self))?
85                .contract_third_fourth_with_first_second(
86                    &(TensorRank4::dyad_il_jk(&scaled_deformation_gradient, &IDENTITY)
87                        + TensorRank4::dyad_ik_jl(&IDENTITY, &scaled_deformation_gradient)),
88                ))
89                + TensorRank4::dyad_ij_kl(
90                    &(IDENTITY
91                        * ((self.bulk_modulus() - TWO_THIRDS * self.shear_modulus()) / jacobian)
92                        - deviatoric_strain * (2.0 * self.shear_modulus() / jacobian)
93                        - IDENTITY * (self.bulk_modulus() * strain_trace / jacobian)),
94                    &inverse_transpose_deformation_gradient,
95                ));
96        }
97        let half_exponent = 0.5 * self.exponent();
98        let spectrum = Spectrum::new(&left_cauchy_green)
99            .map_err(|error| ConstitutiveError::upstream(error, self))?;
100        let (deviatoric_strain, strain_trace) = ((spectrum
101            .powm(half_exponent)
102            .map_err(|error| ConstitutiveError::upstream(error, self))?
103            - IDENTITY)
104            / self.exponent())
105        .deviatoric_and_trace();
106        let cauchy_stress = deviatoric_strain * (2.0 * self.shear_modulus() / jacobian)
107            + IDENTITY * (self.bulk_modulus() * strain_trace / jacobian);
108        let scaled_deformation_gradient =
109            deformation_gradient * (2.0 * self.shear_modulus() / (self.exponent() * jacobian));
110        let trace_term = spectrum
111            .powm(half_exponent - 1.0)
112            .map_err(|error| ConstitutiveError::upstream(error, self))?
113            * deformation_gradient;
114        Ok(spectrum
115            .dpowm(half_exponent)
116            .map_err(|error| ConstitutiveError::upstream(error, self))?
117            .contract_third_fourth_with_first_second(
118                &(TensorRank4::dyad_il_jk(&scaled_deformation_gradient, &IDENTITY)
119                    + TensorRank4::dyad_ik_jl(&IDENTITY, &scaled_deformation_gradient)),
120            )
121            + TensorRank4::dyad_ij_kl(
122                &(IDENTITY
123                    * ((self.bulk_modulus() - TWO_THIRDS * self.shear_modulus()) / jacobian)),
124                &trace_term,
125            )
126            - TensorRank4::dyad_ij_kl(&cauchy_stress, &inverse_transpose_deformation_gradient))
127    }
128}
conspire/constitutive/solid/elastic/seth_hill_eulerian/mod.rs

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