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

1#[cfg(test)]
2mod test;
3
4use crate::{
5    constitutive::{
6        ConstitutiveError,
7        fluid::{
8            plastic::Plastic,
9            viscoplastic::{Viscoplastic, ViscoplasticStateVariables, default_plastic_evolution},
10        },
11        solid::{
12            Solid, TWO_THIRDS,
13            elastic_viscoplastic::{ElasticPlasticOrViscoplastic, ElasticViscoplastic},
14            hyperelastic_viscoplastic::HyperelasticViscoplastic,
15        },
16    },
17    math::{ContractThirdFourthIndicesWithFirstSecondIndicesOf, IDENTITY, Rank2, TensorArray},
18    mechanics::{
19        CauchyStress, CauchyTangentStiffness, CauchyTangentStiffnessElastic, Deformation,
20        DeformationGradient, DeformationGradientPlastic, MandelStressElastic, Scalar,
21    },
22};
23
24#[doc = include_str!("doc.md")]
25#[derive(Clone, Debug)]
26pub struct Hencky {
27    /// The bulk modulus $`\kappa`$.
28    pub bulk_modulus: Scalar,
29    /// The shear modulus $`\mu`$.
30    pub shear_modulus: Scalar,
31    /// The initial yield stress $`Y_0`$.
32    pub yield_stress: Scalar,
33    /// The isotropic hardening slope $`H`$.
34    pub hardening_slope: Scalar,
35    /// The rate sensitivity parameter $`m`$.
36    pub rate_sensitivity: Scalar,
37    /// The reference flow rate $`d_0`$.
38    pub reference_flow_rate: Scalar,
39}
40
41impl Solid for Hencky {
42    fn bulk_modulus(&self) -> Scalar {
43        self.bulk_modulus
44    }
45    fn shear_modulus(&self) -> Scalar {
46        self.shear_modulus
47    }
48}
49
50impl Plastic for Hencky {
51    fn initial_yield_stress(&self) -> Scalar {
52        self.yield_stress
53    }
54    fn hardening_slope(&self) -> Scalar {
55        self.hardening_slope
56    }
57}
58
59impl Viscoplastic<Scalar> for Hencky {
60    fn initial_state(&self) -> ViscoplasticStateVariables<Scalar> {
61        (DeformationGradientPlastic::identity(), 0.0).into()
62    }
63    fn plastic_evolution(
64        &self,
65        mandel_stress: MandelStressElastic,
66        state_variables: &ViscoplasticStateVariables<Scalar>,
67    ) -> Result<ViscoplasticStateVariables<Scalar>, ConstitutiveError> {
68        default_plastic_evolution(self, mandel_stress, state_variables)
69    }
70    fn rate_sensitivity(&self) -> Scalar {
71        self.rate_sensitivity
72    }
73    fn reference_flow_rate(&self) -> Scalar {
74        self.reference_flow_rate
75    }
76}
77
78impl ElasticPlasticOrViscoplastic for Hencky {
79    #[doc = include_str!("cauchy_stress.md")]
80    fn cauchy_stress(
81        &self,
82        deformation_gradient: &DeformationGradient,
83        deformation_gradient_p: &DeformationGradientPlastic,
84    ) -> Result<CauchyStress, ConstitutiveError> {
85        let jacobian = self.jacobian(deformation_gradient)?;
86        let deformation_gradient_e = deformation_gradient * deformation_gradient_p.inverse();
87        let (deviatoric_strain_e, strain_trace_e) =
88            (deformation_gradient_e.left_cauchy_green().logm()? * 0.5).deviatoric_and_trace();
89        Ok(
90            deviatoric_strain_e * (2.0 * self.shear_modulus() / jacobian)
91                + IDENTITY * (self.bulk_modulus() * strain_trace_e / jacobian),
92        )
93    }
94    #[doc = include_str!("cauchy_tangent_stiffness.md")]
95    fn cauchy_tangent_stiffness(
96        &self,
97        deformation_gradient: &DeformationGradient,
98        deformation_gradient_p: &DeformationGradientPlastic,
99    ) -> Result<CauchyTangentStiffness, ConstitutiveError> {
100        let jacobian = self.jacobian(deformation_gradient)?;
101        let deformation_gradient_inverse_p = deformation_gradient_p.inverse();
102        let deformation_gradient_e = deformation_gradient * &deformation_gradient_inverse_p;
103        let left_cauchy_green_e = deformation_gradient_e.left_cauchy_green();
104        let (deviatoric_strain_e, strain_trace_e) =
105            (left_cauchy_green_e.logm()? * 0.5).deviatoric_and_trace();
106        let scaled_deformation_gradient_e =
107            &deformation_gradient_e * self.shear_modulus() / jacobian;
108        Ok((left_cauchy_green_e
109            .dlogm()?
110            .contract_third_fourth_indices_with_first_second_indices_of(
111                &(CauchyTangentStiffnessElastic::dyad_il_jk(
112                    &scaled_deformation_gradient_e,
113                    &IDENTITY,
114                ) + CauchyTangentStiffnessElastic::dyad_ik_jl(
115                    &IDENTITY,
116                    &scaled_deformation_gradient_e,
117                )),
118            ))
119            * deformation_gradient_inverse_p.transpose()
120            + (CauchyTangentStiffness::dyad_ij_kl(
121                &(IDENTITY
122                    * ((self.bulk_modulus() - TWO_THIRDS * self.shear_modulus()) / jacobian)
123                    - deviatoric_strain_e * (2.0 * self.shear_modulus() / jacobian)
124                    - IDENTITY * (self.bulk_modulus() * strain_trace_e / jacobian)),
125                &deformation_gradient.inverse_transpose(),
126            )))
127    }
128}
129
130impl ElasticViscoplastic<Scalar> for Hencky {}
131
132impl HyperelasticViscoplastic<Scalar> for Hencky {
133    #[doc = include_str!("helmholtz_free_energy_density.md")]
134    fn helmholtz_free_energy_density(
135        &self,
136        deformation_gradient: &DeformationGradient,
137        deformation_gradient_p: &DeformationGradientPlastic,
138    ) -> Result<Scalar, ConstitutiveError> {
139        let _jacobian = self.jacobian(deformation_gradient)?;
140        let deformation_gradient_e = deformation_gradient * deformation_gradient_p.inverse();
141        let strain_e = deformation_gradient_e.left_cauchy_green().logm()? * 0.5;
142        Ok(self.shear_modulus() * strain_e.squared_trace()
143            + 0.5
144                * (self.bulk_modulus() - TWO_THIRDS * self.shear_modulus())
145                * strain_e.trace().powi(2))
146    }
147}
conspire/constitutive/solid/hyperelastic_viscoplastic/hencky/mod.rs

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