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

1#[cfg(test)]
2mod test;
3
4use super::hencky::Hencky;
5use crate::{
6    constitutive::{
7        ConstitutiveError,
8        solid::{Solid, TWO_THIRDS, elastic::Elastic},
9    },
10    math::{
11        ContractThirdFourthWithFirstSecond, IDENTITY_00, Quantity, Rank2, Spectrum, TensorRank4,
12    },
13    mechanics::{
14        Deformation, DeformationGradient, Scalar, SecondPiolaKirchhoffStress,
15        SecondPiolaKirchhoffTangentStiffness,
16    },
17    units::Stress,
18};
19
20#[doc = include_str!("doc.md")]
21#[derive(Clone, Debug)]
22pub struct BazantItskovLagrangian {
23    /// The bulk modulus $`\kappa`$.
24    pub bulk_modulus: Quantity<Stress>,
25    /// The shear modulus $`\mu`$.
26    pub shear_modulus: Quantity<Stress>,
27    /// The exponent $`m`$.
28    pub exponent: Scalar,
29}
30
31impl BazantItskovLagrangian {
32    /// Returns the exponent.
33    pub fn exponent(&self) -> Scalar {
34        self.exponent
35    }
36    fn hencky(&self) -> Hencky {
37        Hencky {
38            bulk_modulus: self.bulk_modulus,
39            shear_modulus: self.shear_modulus,
40        }
41    }
42}
43
44impl Solid for BazantItskovLagrangian {
45    fn bulk_modulus(&self) -> Quantity<Stress> {
46        self.bulk_modulus
47    }
48    fn shear_modulus(&self) -> Quantity<Stress> {
49        self.shear_modulus
50    }
51}
52
53impl Elastic for BazantItskovLagrangian {
54    #[doc = include_str!("second_piola_kirchhoff_stress.md")]
55    fn second_piola_kirchhoff_stress(
56        &self,
57        deformation_gradient: &DeformationGradient,
58    ) -> Result<SecondPiolaKirchhoffStress, ConstitutiveError> {
59        if self.exponent() == 0.0 {
60            return self
61                .hencky()
62                .second_piola_kirchhoff_stress(deformation_gradient);
63        }
64        let _jacobian = self.jacobian(deformation_gradient)?;
65        let right_cauchy_green = deformation_gradient.right_cauchy_green();
66        let half_exponent = 0.5 * self.exponent();
67        let spectrum = Spectrum::new(&right_cauchy_green)
68            .map_err(|error| ConstitutiveError::upstream(error, self))?;
69        let (deviatoric_strain, strain_trace) = ((spectrum
70            .powm(half_exponent)
71            .map_err(|error| ConstitutiveError::upstream(error, self))?
72            - spectrum
73                .powm(-half_exponent)
74                .map_err(|error| ConstitutiveError::upstream(error, self))?)
75            / (2.0 * self.exponent()))
76        .deviatoric_and_trace();
77        Ok(deviatoric_strain * (2.0 * self.shear_modulus())
78            + IDENTITY_00 * (self.bulk_modulus() * strain_trace))
79    }
80    #[doc = include_str!("second_piola_kirchhoff_tangent_stiffness.md")]
81    fn second_piola_kirchhoff_tangent_stiffness(
82        &self,
83        deformation_gradient: &DeformationGradient,
84    ) -> Result<SecondPiolaKirchhoffTangentStiffness, ConstitutiveError> {
85        if self.exponent() == 0.0 {
86            return self
87                .hencky()
88                .second_piola_kirchhoff_tangent_stiffness(deformation_gradient);
89        }
90        let _jacobian = self.jacobian(deformation_gradient)?;
91        let right_cauchy_green = deformation_gradient.right_cauchy_green();
92        let half_exponent = 0.5 * self.exponent();
93        let spectrum = Spectrum::new(&right_cauchy_green)
94            .map_err(|error| ConstitutiveError::upstream(error, self))?;
95        let deformation_gradient_transpose = deformation_gradient.transpose();
96        let scaled_deformation_gradient_transpose =
97            &deformation_gradient_transpose * (self.shear_modulus() / self.exponent());
98        let trace_term = deformation_gradient
99            * (spectrum
100                .powm(half_exponent - 1.0)
101                .map_err(|error| ConstitutiveError::upstream(error, self))?
102                + spectrum
103                    .powm(-half_exponent - 1.0)
104                    .map_err(|error| ConstitutiveError::upstream(error, self))?)
105            * 0.5;
106        Ok((spectrum
107            .dpowm(half_exponent)
108            .map_err(|error| ConstitutiveError::upstream(error, self))?
109            - spectrum
110                .dpowm(-half_exponent)
111                .map_err(|error| ConstitutiveError::upstream(error, self))?)
112        .contract_third_fourth_with_first_second(
113            &(TensorRank4::dyad_il_jk(&IDENTITY_00, &scaled_deformation_gradient_transpose)
114                + TensorRank4::dyad_ik_jl(&scaled_deformation_gradient_transpose, &IDENTITY_00)),
115        ) + TensorRank4::dyad_ij_kl(
116            &(IDENTITY_00 * (self.bulk_modulus() - TWO_THIRDS * self.shear_modulus())),
117            &trace_term,
118        ))
119    }
120}
conspire/constitutive/solid/elastic/bazant_itskov_lagrangian/mod.rs

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