conspire/constitutive/solid/elastic/bazant_itskov_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 BazantItskovEulerian {
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 BazantItskovEulerian {
26    /// Returns the exponent.
27    pub fn exponent(&self) -> Scalar {
28        self.exponent
29    }
30}
31
32impl Solid for BazantItskovEulerian {
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 BazantItskovEulerian {
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            let half_exponent = 0.5 * self.exponent();
57            let spectrum = Spectrum::new(&left_cauchy_green)
58                .map_err(|error| ConstitutiveError::upstream(error, self))?;
59            ((spectrum
60                .powm(half_exponent)
61                .map_err(|error| ConstitutiveError::upstream(error, self))?
62                - spectrum
63                    .powm(-half_exponent)
64                    .map_err(|error| ConstitutiveError::upstream(error, self))?)
65                / (2.0 * self.exponent()))
66            .deviatoric_and_trace()
67        };
68        Ok(deviatoric_strain * (2.0 * self.shear_modulus() / jacobian)
69            + IDENTITY * (self.bulk_modulus() * strain_trace / jacobian))
70    }
71    #[doc = include_str!("cauchy_tangent_stiffness.md")]
72    fn cauchy_tangent_stiffness(
73        &self,
74        deformation_gradient: &DeformationGradient,
75    ) -> Result<CauchyTangentStiffness, ConstitutiveError> {
76        let jacobian = self.jacobian(deformation_gradient)?;
77        let left_cauchy_green = deformation_gradient.left_cauchy_green();
78        let inverse_transpose_deformation_gradient = deformation_gradient.inverse_transpose();
79        if self.exponent() == 0.0 {
80            let (deviatoric_strain, strain_trace) = (left_cauchy_green
81                .logm()
82                .map_err(|error| ConstitutiveError::upstream(error, self))?
83                * 0.5)
84                .deviatoric_and_trace();
85            let scaled_deformation_gradient =
86                deformation_gradient * (self.shear_modulus() / jacobian);
87            return Ok((left_cauchy_green
88                .dlogm()
89                .map_err(|error| ConstitutiveError::upstream(error, self))?
90                .contract_third_fourth_with_first_second(
91                    &(TensorRank4::dyad_il_jk(&scaled_deformation_gradient, &IDENTITY)
92                        + TensorRank4::dyad_ik_jl(&IDENTITY, &scaled_deformation_gradient)),
93                ))
94                + TensorRank4::dyad_ij_kl(
95                    &(IDENTITY
96                        * ((self.bulk_modulus() - TWO_THIRDS * self.shear_modulus()) / jacobian)
97                        - deviatoric_strain * (2.0 * self.shear_modulus() / jacobian)
98                        - IDENTITY * (self.bulk_modulus() * strain_trace / jacobian)),
99                    &inverse_transpose_deformation_gradient,
100                ));
101        }
102        let half_exponent = 0.5 * self.exponent();
103        let spectrum = Spectrum::new(&left_cauchy_green)
104            .map_err(|error| ConstitutiveError::upstream(error, self))?;
105        let (deviatoric_strain, strain_trace) = ((spectrum
106            .powm(half_exponent)
107            .map_err(|error| ConstitutiveError::upstream(error, self))?
108            - spectrum
109                .powm(-half_exponent)
110                .map_err(|error| ConstitutiveError::upstream(error, self))?)
111            / (2.0 * self.exponent()))
112        .deviatoric_and_trace();
113        let cauchy_stress = deviatoric_strain * (2.0 * self.shear_modulus() / jacobian)
114            + IDENTITY * (self.bulk_modulus() * strain_trace / jacobian);
115        let scaled_deformation_gradient =
116            deformation_gradient * (self.shear_modulus() / (self.exponent() * jacobian));
117        let trace_term = (spectrum
118            .powm(half_exponent - 1.0)
119            .map_err(|error| ConstitutiveError::upstream(error, self))?
120            + spectrum
121                .powm(-half_exponent - 1.0)
122                .map_err(|error| ConstitutiveError::upstream(error, self))?)
123            * deformation_gradient
124            * 0.5;
125        Ok((spectrum
126            .dpowm(half_exponent)
127            .map_err(|error| ConstitutiveError::upstream(error, self))?
128            - spectrum
129                .dpowm(-half_exponent)
130                .map_err(|error| ConstitutiveError::upstream(error, self))?)
131        .contract_third_fourth_with_first_second(
132            &(TensorRank4::dyad_il_jk(&scaled_deformation_gradient, &IDENTITY)
133                + TensorRank4::dyad_ik_jl(&IDENTITY, &scaled_deformation_gradient)),
134        ) + TensorRank4::dyad_ij_kl(
135            &(IDENTITY * ((self.bulk_modulus() - TWO_THIRDS * self.shear_modulus()) / jacobian)),
136            &trace_term,
137        ) - TensorRank4::dyad_ij_kl(&cauchy_stress, &inverse_transpose_deformation_gradient))
138    }
139}
conspire/constitutive/solid/elastic/bazant_itskov_eulerian/mod.rs

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