feat: Elastic energy #10
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| @@ -17,6 +17,21 @@ impl ConstitutiveModel for CorotatedLinearElasticity { | |||
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| } | |||
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| // https://www.math.ucla.edu/~cffjiang/research/mpmcourse/mpmcourse.pdf#subsection.6.3 | |||
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| // https://www.math.ucla.edu/~cffjiang/research/mpmcourse/mpmcourse.pdf#subsection.6.3 | |
| // https://www.math.ucla.edu/~cffjiang/research/mpmcourse/mpmcourse.pdf#subsection.6.3 | |
| // This is essentially the same calculation as `[pos_energy]` but without ignoring the negative part. |
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I added a reference to the pos_energy instead.
| fn elastic_energy_density(&self, deformation_gradient: Matrix<Real>) -> Real { | ||
| let singular_values = deformation_gradient | ||
| .svd_unordered(false, false) | ||
| .singular_values; | ||
| let determinant: Real = singular_values.iter().product(); | ||
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| self.mu | ||
| * singular_values | ||
| .iter() | ||
| .map(|sigma| (sigma - 1.).powi(2)) | ||
| .sum::<Real>() | ||
| + self.lambda / 2. * (determinant - 1.).powi(2) |
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I would recommend taking the whole &Particle as argument, for consistency with pos_energy and to take hardening into account the same way as in pos_energy.
Can be in another PR.
| fn elastic_energy_density(&self, deformation_gradient: Matrix<Real>) -> Real { | ||
| let determinant_log = deformation_gradient.determinant().ln(); | ||
| self.mu / 2. | ||
| * ((deformation_gradient.transpose() * deformation_gradient).trace() - DIM as Real) | ||
| - self.mu * determinant_log | ||
| + self.lambda / 2. * determinant_log.powi(2) | ||
| } | ||
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Same remark regarding taking hardening into account.
| @@ -76,7 +76,7 @@ impl CorotatedLinearElasticity { | |||
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| pub fn pos_energy(&self, deformation_gradient: Matrix<Real>, elastic_hardening: Real) -> Real { | |||
| let j = deformation_gradient.determinant(); | |||
| let mut pos_def = deformation_gradient.svd_unordered(true, true); | |||
| let mut pos_def = deformation_gradient.svd_unordered(true, true); // TODO: why compute U and V? | |||
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Probably just a refactoring leftover. It can be false, false.
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| // General elastic density function: https://dl.acm.org/doi/pdf/10.1145/3306346.3322949#section.5 (8) and (9) | ||
| // With degradation: https://dl.acm.org/doi/pdf/10.1145/3306346.3322949#subsection.3.2 (3) | ||
| // With hardening: https://www.math.ucla.edu/~cffjiang/research/mpmcourse/mpmcourse.pdf#subsection.6.5 (87) | ||
| #[allow(non_snake_case)] |
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Let’s not allow non_snake_case. It messes up with syntax highlighting, and is very unconventional in rust, even though I agree it makes it closer to the mathematical notation.
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We're now using more descriptive names (with proper snake case) while keeping aliases matching the paper in the comments.
| let Psi_mu = | ||
| |F: Matrix<Real>| hardened_mu / 2. * ((F.transpose() * F).trace() - DIM as Real); | ||
| let Psi_mu = Psi_mu(J_alpha * F); |
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The closure makes the code more difficult to read, especially since it’s only called once and bound to a variable with the same name.
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Once we've converged on style for the neo-hookean one, I'll update the corotated code to match. |
This adds functions to compute the elastic energy density function from a given deformation gradient.
The new code is different from the existing one.
See
pos_energy:sparkl/src/dynamics/models/elasticity_corotated_linear.rs
Lines 35 to 37 in 43c13a6
We may want to refactor.