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fem, model: Mooney-Rivlin and Yeoh hyperelasticity in nonlinear steps

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Two more large-strain options on the isotropic constants, decoupled like
neo-Hookean with the volume kappa/2 (J - 1)^2: Mooney-Rivlin with C10 = mu/2 - C01
(0 <= C01 <= mu/2) and Yeoh with C10 = mu/2 and the higher terms C20, C30, so the
small-strain material is the elastic one everywhere. MaterialModel::Polynomial
gives the isochoric stress and tangent from Holzapfel's fictitious quantities
(eqs. 6.168, 6.193), consistent by central differences, equal to neo-Hookean
with C10 alone; hybrid elements take it. Abaqus writes *HYPERELASTIC,
MOONEY-RIVLIN and YEOH; LS-DYNA keeps refusing hyperelastic materials in
nonlinear steps by name. Verified in uniaxial and equibiaxial tension and pure
shear against the compressible closed form (exact).

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01NmAttHhUZTokgPeEJia8sm
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jyvikoandClaude Opus 5.5 authored and Irakli Kourtis committed 2026-10-14 07:23:06 -04:00
1 parent 7a69fe5e2f
commit 53adab54c2
7 files changed
+272 -21
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crates/decks/src/abaqus.rs
+18 -8
View File
@@ -108,7 +108,8 @@
//!
//! Isotropic elasticity is `*ELASTIC, TYPE=ISOTROPIC` (or, for a neo-Hookean material in a deck
//! with nonlinear steps, `*HYPERELASTIC, NEO HOOKE` with C₁₀ = μ/2 and D₁ = 2/κ, the same strain
//! energy; a linear static step is then refused, since Abaqus's general static step would apply
//! energy, and likewise `MOONEY-RIVLIN` (C₁₀, C₀₁, D₁) and `YEOH` (C₁₀, C₂₀, C₃₀, D₁, the higher
//! volumetric terms zero); a linear static step is then refused, since Abaqus's general static step would apply
//! the hyperelastic law), engineering constants
//! `TYPE=ENGINEERING CONSTANTS`, density `*DENSITY`. Von Mises plasticity is `*PLASTIC`: a
//! hardening table as its (yield stress, plastic strain) lines; bilinear isotropic hardening as
@@ -129,8 +130,8 @@ use std::collections::{BTreeMap, BTreeSet};
use std::fmt::Write as _;
use fieldcraft_model::{
BeamProfile, BoundaryCondition, CouplingKind, Elastic, Element, ElementKind, Hardening, Integration, Load, Model, OutputVariable, Plastic,
Procedure, Resolved, Section, SectionKind, Step, Symmetry, Target,
BeamProfile, BoundaryCondition, CouplingKind, Elastic, Element, ElementKind, Hardening, Hyperelastic, Integration, Load, Model, OutputVariable,
Plastic, Procedure, Resolved, Section, SectionKind, Step, Symmetry, Target,
};
use crate::{Error, Result, unsupported};
@@ -809,11 +810,20 @@ impl Deck {
for (name, m) in model.materials() {
self.line(&format!("*MATERIAL, NAME={name}"));
match m.elastic {
Some(Elastic::Isotropic { young, poisson }) if m.hyperelastic.is_some() && has_nonlinear_step(model) => {
// W = C10 (Ī1 − 3) + (J − 1)²/D1 with C10 = μ/2 and D1 = 2/κ.
let (shear, bulk) = fieldcraft_model::Hyperelastic::moduli(young, poisson);
self.line("*HYPERELASTIC, NEO HOOKE");
self.numbers_line("", &[shear / 2.0, 2.0 / bulk])?;
Some(Elastic::Isotropic { young, poisson })
if has_nonlinear_step(model)
&& let Some(h) = m.hyperelastic =>
{
// The polynomial constants of the option and U = (J − 1)²/D1 with D1 = 2/κ.
let (shear, bulk) = Hyperelastic::moduli(young, poisson);
let [c10, c01, c20, c30] = h.constants(shear);
let (keyword, values) = match h {
Hyperelastic::NeoHookean {} => ("NEO HOOKE", vec![c10, 2.0 / bulk]),
Hyperelastic::MooneyRivlin { .. } => ("MOONEY-RIVLIN", vec![c10, c01, 2.0 / bulk]),
Hyperelastic::Yeoh { .. } => ("YEOH", vec![c10, c20, c30, 2.0 / bulk]),
};
self.line(&format!("*HYPERELASTIC, {keyword}"));
self.numbers_line("", &values)?;
}
Some(Elastic::Isotropic { young, poisson }) => {
self.line("*ELASTIC, TYPE=ISOTROPIC");