conspire/constitutive/solid/hyperelastic/arruda_boyce/
mod.rs

1#[cfg(test)]
2mod test;
3
4use crate::{
5    constitutive::{
6        Constitutive, ConstitutiveError, Parameters,
7        solid::{FIVE_THIRDS, Solid, TWO_THIRDS, elastic::Elastic, hyperelastic::Hyperelastic},
8    },
9    math::{
10        IDENTITY, Rank2,
11        special::{inverse_langevin, langevin_derivative},
12    },
13    mechanics::{CauchyStress, CauchyTangentStiffness, Deformation, DeformationGradient, Scalar},
14};
15
16#[doc = include_str!("doc.md")]
17#[derive(Debug)]
18pub struct ArrudaBoyce<P> {
19    parameters: P,
20}
21
22impl<P> ArrudaBoyce<P>
23where
24    P: Parameters,
25{
26    /// Returns the number of links.
27    pub fn number_of_links(&self) -> &Scalar {
28        self.parameters.get(2)
29    }
30}
31
32impl<P> Constitutive<P> for ArrudaBoyce<P>
33where
34    P: Parameters,
35{
36    fn new(parameters: P) -> Self {
37        Self { parameters }
38    }
39}
40
41impl<P> Solid for ArrudaBoyce<P>
42where
43    P: Parameters,
44{
45    fn bulk_modulus(&self) -> &Scalar {
46        self.parameters.get(0)
47    }
48    fn shear_modulus(&self) -> &Scalar {
49        self.parameters.get(1)
50    }
51}
52
53impl<P> Elastic for ArrudaBoyce<P>
54where
55    P: Parameters,
56{
57    #[doc = include_str!("cauchy_stress.md")]
58    fn cauchy_stress(
59        &self,
60        deformation_gradient: &DeformationGradient,
61    ) -> Result<CauchyStress, ConstitutiveError> {
62        let jacobian = self.jacobian(deformation_gradient)?;
63        let (
64            deviatoric_isochoric_left_cauchy_green_deformation,
65            isochoric_left_cauchy_green_deformation_trace,
66        ) = (deformation_gradient.left_cauchy_green() / jacobian.powf(TWO_THIRDS))
67            .deviatoric_and_trace();
68        let gamma =
69            (isochoric_left_cauchy_green_deformation_trace / 3.0 / self.number_of_links()).sqrt();
70        if gamma >= 1.0 {
71            Err(ConstitutiveError::Custom(
72                "Maximum extensibility reached.".to_string(),
73                deformation_gradient.clone(),
74                format!("{:?}", &self),
75            ))
76        } else {
77            let gamma_0 = (1.0 / self.number_of_links()).sqrt();
78            Ok(deviatoric_isochoric_left_cauchy_green_deformation
79                * (self.shear_modulus() * inverse_langevin(gamma) / inverse_langevin(gamma_0)
80                    * gamma_0
81                    / gamma
82                    / jacobian)
83                + IDENTITY * self.bulk_modulus() * 0.5 * (jacobian - 1.0 / jacobian))
84        }
85    }
86    #[doc = include_str!("cauchy_tangent_stiffness.md")]
87    fn cauchy_tangent_stiffness(
88        &self,
89        deformation_gradient: &DeformationGradient,
90    ) -> Result<CauchyTangentStiffness, ConstitutiveError> {
91        let jacobian = self.jacobian(deformation_gradient)?;
92        let inverse_transpose_deformation_gradient = deformation_gradient.inverse_transpose();
93        let left_cauchy_green_deformation = deformation_gradient.left_cauchy_green();
94        let deviatoric_left_cauchy_green_deformation = left_cauchy_green_deformation.deviatoric();
95        let (
96            deviatoric_isochoric_left_cauchy_green_deformation,
97            isochoric_left_cauchy_green_deformation_trace,
98        ) = (left_cauchy_green_deformation / jacobian.powf(TWO_THIRDS)).deviatoric_and_trace();
99        let gamma =
100            (isochoric_left_cauchy_green_deformation_trace / 3.0 / self.number_of_links()).sqrt();
101        if gamma >= 1.0 {
102            Err(ConstitutiveError::Custom(
103                "Maximum extensibility reached.".to_string(),
104                deformation_gradient.clone(),
105                format!("{:?}", &self),
106            ))
107        } else {
108            let gamma_0 = (1.0 / self.number_of_links()).sqrt();
109            let eta = inverse_langevin(gamma);
110            let scaled_shear_modulus =
111                gamma_0 / inverse_langevin(gamma_0) * self.shear_modulus() * eta
112                    / gamma
113                    / jacobian.powf(FIVE_THIRDS);
114            let scaled_deviatoric_isochoric_left_cauchy_green_deformation =
115                deviatoric_left_cauchy_green_deformation * scaled_shear_modulus;
116            let term = CauchyTangentStiffness::dyad_ij_kl(
117                &scaled_deviatoric_isochoric_left_cauchy_green_deformation,
118                &(deviatoric_isochoric_left_cauchy_green_deformation
119                    * &inverse_transpose_deformation_gradient
120                    * ((1.0 / eta / langevin_derivative(eta) - 1.0 / gamma)
121                        / 3.0
122                        / self.number_of_links()
123                        / gamma)),
124            );
125            Ok(
126                (CauchyTangentStiffness::dyad_ik_jl(&IDENTITY, deformation_gradient)
127                    + CauchyTangentStiffness::dyad_il_jk(deformation_gradient, &IDENTITY)
128                    - CauchyTangentStiffness::dyad_ij_kl(&IDENTITY, deformation_gradient)
129                        * (TWO_THIRDS))
130                    * scaled_shear_modulus
131                    + CauchyTangentStiffness::dyad_ij_kl(
132                        &(IDENTITY * (0.5 * self.bulk_modulus() * (jacobian + 1.0 / jacobian))
133                            - scaled_deviatoric_isochoric_left_cauchy_green_deformation
134                                * (FIVE_THIRDS)),
135                        &inverse_transpose_deformation_gradient,
136                    )
137                    + term,
138            )
139        }
140    }
141}
142
143impl<P> Hyperelastic for ArrudaBoyce<P>
144where
145    P: Parameters,
146{
147    #[doc = include_str!("helmholtz_free_energy_density.md")]
148    fn helmholtz_free_energy_density(
149        &self,
150        deformation_gradient: &DeformationGradient,
151    ) -> Result<Scalar, ConstitutiveError> {
152        let jacobian = self.jacobian(deformation_gradient)?;
153        let isochoric_left_cauchy_green_deformation =
154            deformation_gradient.left_cauchy_green() / jacobian.powf(TWO_THIRDS);
155        let gamma =
156            (isochoric_left_cauchy_green_deformation.trace() / 3.0 / self.number_of_links()).sqrt();
157        if gamma >= 1.0 {
158            Err(ConstitutiveError::Custom(
159                "Maximum extensibility reached.".to_string(),
160                deformation_gradient.clone(),
161                format!("{:?}", &self),
162            ))
163        } else {
164            let eta = inverse_langevin(gamma);
165            let gamma_0 = (1.0 / self.number_of_links()).sqrt();
166            let eta_0 = inverse_langevin(gamma_0);
167            Ok(3.0 * gamma_0 / eta_0
168                * self.shear_modulus()
169                * self.number_of_links()
170                * (gamma * eta
171                    - gamma_0 * eta_0
172                    - (eta_0 * eta.sinh() / (eta * eta_0.sinh())).ln())
173                + 0.5 * self.bulk_modulus() * (0.5 * (jacobian.powi(2) - 1.0) - jacobian.ln()))
174        }
175    }
176}
conspire/constitutive/solid/hyperelastic/arruda_boyce/mod.rs

conspire/constitutive/solid/hyperelastic/arruda_boyce/
mod.rs
