conspire 0.6.0

The Rust interface to conspire.
Documentation 
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137

#[cfg(test)]
mod test;

use crate::{
    constitutive::{
        ConstitutiveError,
        solid::{Solid, TWO_THIRDS, elastic::Elastic, hyperelastic::Hyperelastic},
    },
    math::{IDENTITY, Rank2},
    mechanics::{CauchyStress, CauchyTangentStiffness, Deformation, DeformationGradient, Scalar},
};

#[doc = include_str!("doc.md")]
#[derive(Clone, Debug)]
pub struct Gent {
    /// The bulk modulus $`\kappa`$.
    pub bulk_modulus: Scalar,
    /// The shear modulus $`\mu`$.
    pub shear_modulus: Scalar,
    /// The extensibility $`J_m`$.
    pub extensibility: Scalar,
}

impl Gent {
    /// Returns the extensibility.
    pub fn extensibility(&self) -> Scalar {
        self.extensibility
    }
}

impl Solid for Gent {
    fn bulk_modulus(&self) -> Scalar {
        self.bulk_modulus
    }
    fn shear_modulus(&self) -> Scalar {
        self.shear_modulus
    }
}

impl Elastic for Gent {
    #[doc = include_str!("cauchy_stress.md")]
    fn cauchy_stress(
        &self,
        deformation_gradient: &DeformationGradient,
    ) -> Result<CauchyStress, ConstitutiveError> {
        let jacobian = self.jacobian(deformation_gradient)?;
        let isochoric_left_cauchy_green_deformation =
            deformation_gradient.left_cauchy_green() / jacobian.powf(TWO_THIRDS);
        let (
            deviatoric_isochoric_left_cauchy_green_deformation,
            isochoric_left_cauchy_green_deformation_trace,
        ) = isochoric_left_cauchy_green_deformation.deviatoric_and_trace();
        let denominator =
            self.extensibility() - isochoric_left_cauchy_green_deformation_trace + 3.0;
        if denominator <= 0.0 {
            Err(ConstitutiveError::Custom(
                "Maximum extensibility reached.".to_string(),
                format!("{:?}", &self),
            ))
        } else {
            Ok((deviatoric_isochoric_left_cauchy_green_deformation
                * self.shear_modulus()
                * self.extensibility()
                / jacobian)
                / denominator
                + IDENTITY * self.bulk_modulus() * 0.5 * (jacobian - 1.0 / jacobian))
        }
    }
    #[doc = include_str!("cauchy_tangent_stiffness.md")]
    fn cauchy_tangent_stiffness(
        &self,
        deformation_gradient: &DeformationGradient,
    ) -> Result<CauchyTangentStiffness, ConstitutiveError> {
        let jacobian = self.jacobian(deformation_gradient)?;
        let inverse_transpose_deformation_gradient = deformation_gradient.inverse_transpose();
        let isochoric_left_cauchy_green_deformation =
            deformation_gradient.left_cauchy_green() / jacobian.powf(TWO_THIRDS);
        let (
            deviatoric_isochoric_left_cauchy_green_deformation,
            isochoric_left_cauchy_green_deformation_trace,
        ) = isochoric_left_cauchy_green_deformation.deviatoric_and_trace();
        let denominator =
            self.extensibility() - isochoric_left_cauchy_green_deformation_trace + 3.0;
        if denominator <= 0.0 {
            Err(ConstitutiveError::Custom(
                "Maximum extensibility reached.".to_string(),
                format!("{:?}", &self),
            ))
        } else {
            let prefactor = self.shear_modulus() * self.extensibility() / jacobian / denominator;
            Ok(
                (CauchyTangentStiffness::dyad_ik_jl(&IDENTITY, deformation_gradient)
                    + CauchyTangentStiffness::dyad_il_jk(deformation_gradient, &IDENTITY)
                    - CauchyTangentStiffness::dyad_ij_kl(&IDENTITY, deformation_gradient)
                        * (TWO_THIRDS)
                    + CauchyTangentStiffness::dyad_ij_kl(
                        &deviatoric_isochoric_left_cauchy_green_deformation,
                        deformation_gradient,
                    ) * (2.0 / denominator))
                    * (prefactor / jacobian.powf(TWO_THIRDS))
                    + CauchyTangentStiffness::dyad_ij_kl(
                        &(IDENTITY * (0.5 * self.bulk_modulus() * (jacobian + 1.0 / jacobian))
                            - deviatoric_isochoric_left_cauchy_green_deformation
                                * prefactor
                                * ((5.0
                                    + 2.0 * isochoric_left_cauchy_green_deformation_trace
                                        / denominator)
                                    / 3.0)),
                        &inverse_transpose_deformation_gradient,
                    ),
            )
        }
    }
}

impl Hyperelastic for Gent {
    #[doc = include_str!("helmholtz_free_energy_density.md")]
    fn helmholtz_free_energy_density(
        &self,
        deformation_gradient: &DeformationGradient,
    ) -> Result<Scalar, ConstitutiveError> {
        let jacobian = self.jacobian(deformation_gradient)?;
        let factor = (deformation_gradient.left_cauchy_green().trace() / jacobian.powf(TWO_THIRDS)
            - 3.0)
            / self.extensibility();
        if factor >= 1.0 {
            Err(ConstitutiveError::Custom(
                "Maximum extensibility reached.".to_string(),
                format!("{:?}", &self),
            ))
        } else {
            Ok(0.5
                * (-self.shear_modulus() * self.extensibility() * (1.0 - factor).ln()
                    + self.bulk_modulus() * (0.5 * (jacobian.powi(2) - 1.0) - jacobian.ln())))
        }
    }
}