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

1#[cfg(test)]
2mod test;
3
4use crate::{
5    constitutive::{
6        ConstitutiveError,
7        fluid::{plastic::Plastic, viscoplastic::Viscoplastic},
8        solid::{
9            Solid, TWO_THIRDS, elastic_viscoplastic::ElasticViscoplastic,
10            hyperelastic_viscoplastic::HyperelasticViscoplastic,
11        },
12    },
13    math::{ContractThirdFourthIndicesWithFirstSecondIndicesOf, IDENTITY, Rank2},
14    mechanics::{
15        CauchyStress, CauchyTangentStiffness, CauchyTangentStiffnessElastic, Deformation,
16        DeformationGradient, DeformationGradientPlastic, Scalar,
17    },
18};
19
20#[doc = include_str!("doc.md")]
21#[derive(Clone, Debug)]
22pub struct Hencky {
23    /// The bulk modulus $`\kappa`$.
24    pub bulk_modulus: Scalar,
25    /// The shear modulus $`\mu`$.
26    pub shear_modulus: Scalar,
27    /// The initial yield stress $`Y_0`$.
28    pub initial_yield_stress: Scalar,
29    /// The isotropic hardening slope $`H`$.
30    pub hardening_slope: Scalar,
31    /// The rate sensitivity parameter $`m`$.
32    pub rate_sensitivity: Scalar,
33    /// The reference flow rate $`d_0`$.
34    pub reference_flow_rate: Scalar,
35}
36
37impl Solid for Hencky {
38    fn bulk_modulus(&self) -> Scalar {
39        self.bulk_modulus
40    }
41    fn shear_modulus(&self) -> Scalar {
42        self.shear_modulus
43    }
44}
45
46impl Plastic for Hencky {
47    fn initial_yield_stress(&self) -> Scalar {
48        self.initial_yield_stress
49    }
50    fn hardening_slope(&self) -> Scalar {
51        self.hardening_slope
52    }
53}
54
55impl Viscoplastic for Hencky {
56    fn rate_sensitivity(&self) -> Scalar {
57        self.rate_sensitivity
58    }
59    fn reference_flow_rate(&self) -> Scalar {
60        self.reference_flow_rate
61    }
62}
63
64impl ElasticViscoplastic for Hencky {
65    #[doc = include_str!("cauchy_stress.md")]
66    fn cauchy_stress(
67        &self,
68        deformation_gradient: &DeformationGradient,
69        deformation_gradient_p: &DeformationGradientPlastic,
70    ) -> Result<CauchyStress, ConstitutiveError> {
71        let jacobian = self.jacobian(deformation_gradient)?;
72        let deformation_gradient_e = deformation_gradient * deformation_gradient_p.inverse();
73        let (deviatoric_strain_e, strain_trace_e) =
74            (deformation_gradient_e.left_cauchy_green().logm()? * 0.5).deviatoric_and_trace();
75        Ok(
76            deviatoric_strain_e * (2.0 * self.shear_modulus() / jacobian)
77                + IDENTITY * (self.bulk_modulus() * strain_trace_e / jacobian),
78        )
79    }
80    #[doc = include_str!("cauchy_tangent_stiffness.md")]
81    fn cauchy_tangent_stiffness(
82        &self,
83        deformation_gradient: &DeformationGradient,
84        deformation_gradient_p: &DeformationGradientPlastic,
85    ) -> Result<CauchyTangentStiffness, ConstitutiveError> {
86        let jacobian = self.jacobian(deformation_gradient)?;
87        let deformation_gradient_inverse_p = deformation_gradient_p.inverse();
88        let deformation_gradient_e = deformation_gradient * &deformation_gradient_inverse_p;
89        let left_cauchy_green_e = deformation_gradient_e.left_cauchy_green();
90        let (deviatoric_strain_e, strain_trace_e) =
91            (left_cauchy_green_e.logm()? * 0.5).deviatoric_and_trace();
92        let scaled_deformation_gradient_e =
93            &deformation_gradient_e * self.shear_modulus() / jacobian;
94        Ok((left_cauchy_green_e
95            .dlogm()?
96            .contract_third_fourth_indices_with_first_second_indices_of(
97                &(CauchyTangentStiffnessElastic::dyad_il_jk(
98                    &scaled_deformation_gradient_e,
99                    &IDENTITY,
100                ) + CauchyTangentStiffnessElastic::dyad_ik_jl(
101                    &IDENTITY,
102                    &scaled_deformation_gradient_e,
103                )),
104            ))
105            * deformation_gradient_inverse_p.transpose()
106            + (CauchyTangentStiffness::dyad_ij_kl(
107                &(IDENTITY
108                    * ((self.bulk_modulus() - TWO_THIRDS * self.shear_modulus()) / jacobian)
109                    - deviatoric_strain_e * (2.0 * self.shear_modulus() / jacobian)
110                    - IDENTITY * (self.bulk_modulus() * strain_trace_e / jacobian)),
111                &deformation_gradient.inverse_transpose(),
112            )))
113    }
114}
115
116impl HyperelasticViscoplastic for Hencky {
117    #[doc = include_str!("helmholtz_free_energy_density.md")]
118    fn helmholtz_free_energy_density(
119        &self,
120        deformation_gradient: &DeformationGradient,
121        deformation_gradient_p: &DeformationGradientPlastic,
122    ) -> Result<Scalar, ConstitutiveError> {
123        let _jacobian = self.jacobian(deformation_gradient)?;
124        let deformation_gradient_e = deformation_gradient * deformation_gradient_p.inverse();
125        let strain_e = deformation_gradient_e.left_cauchy_green().logm()? * 0.5;
126        Ok(self.shear_modulus() * strain_e.squared_trace()
127            + 0.5
128                * (self.bulk_modulus() - TWO_THIRDS * self.shear_modulus())
129                * strain_e.trace().powi(2))
130    }
131}
conspire/constitutive/solid/hyperelastic_viscoplastic/hencky/mod.rs

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