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

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

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