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verification: hyperelastic and thermal oracle cases and documentation
Five cases against closed forms: a Mooney-Rivlin block in Treloar's uniaxial, equibiaxial and pure-shear modes and a Yeoh block in uniaxial tension (the compressible energy's stresses, exact); a stretched Mooney-Rivlin tube inflated by a follower pressure (Rivlin's incompressible solution, 0.6 % at nu = 0.4995); free and fully held thermal expansion at a thermal stretch of 1.2 (exact); a bar held at its ends heated past yield (exact). docs/fem.md, the literature, ROADMAP (M15, M17), parity and the oracle page follow. Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_01NmAttHhUZTokgPeEJia8sm
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@@ -1211,3 +1211,20 @@ update are written from (cited again in the module docs):
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B. G. Neal, *The Plastic Methods of Structural Analysis*, 3rd ed., Chapman & Hall 1977, and the
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continuum's velocity fields, W. Prager, P. G. Hodge, *Theory of Perfectly Plastic Solids*,
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Wiley 1951.
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## Part O: Polynomial hyperelasticity and thermal strain in nonlinear steps, as implemented
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- Decoupled invariant-based hyperelasticity, the fictitious stress and elasticity and their
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projection: G. A. Holzapfel, *Nonlinear Solid Mechanics*, Wiley 2000, §6.4–6.6 (eqs. 6.168,
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6.193).
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- Mooney–Rivlin: M. Mooney, *A theory of large elastic deformation*, J. Appl. Phys.
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11(9):582–592, 1940; R. S. Rivlin, *Large elastic deformations of isotropic materials IV*,
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Phil. Trans. R. Soc. A 241:379–397, 1948. Yeoh: O. H. Yeoh, *Some forms of the strain energy
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function for rubber*, Rubber Chem. Technol. 66(5):754–771, 1993.
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- The homogeneous modes of rubber testing: L. R. G. Treloar, *The Physics of Rubber
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Elasticity*, 3rd ed., Oxford 1975, ch. 10; the inflation and extension of a tube: R. S. Rivlin,
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Phil. Trans. R. Soc. A 242:173–195, 1949, and R. W. Ogden, *Non-Linear Elastic Deformations*,
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Dover 1997, §5.3.
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- Thermal strain by the multiplicative split F = F_m F_θ: V. A. Lubarda, *Constitutive
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theories based on the multiplicative decomposition of deformation gradient: thermoelasticity,
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elastoplasticity, and biomechanics*, Appl. Mech. Rev. 57(2):95–108, 2004.
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