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Finite Elasticity,troduction of a strain-energy (or stored-energy) function into elasticity is due to George Green (1793–1841) and elastic solids for which such a function is assumed to exist are said to be Green elastic or hyperelastic. Elasticity without an underlying strain-energy function is called Cauchy elasticAgnosia 发表于 2025-3-22 13:09:05
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Polar Decomposition,olar decomposition theorem states that any deformation gradient tensor can be multiplicatively decomposed into the product of an orthogonal tensor, known as the rotation tensor, and a symmetric tensor called the right stretch tensor, or into the product of a symmetric tensor called the left stretch空中 发表于 2025-3-22 21:33:24
Strain-Energy Functions,unction of the three invariants of each of the two Cauchy-Green deformation tensors, given in terms of the principal extension ratios, or stretches. A number of different strain-energy formulations exist, having properties and characteristics that make them appropriate for characterizing different h单独 发表于 2025-3-23 04:18:44
Stress Measures,ensor, a Lagrangian formulation, is the most significant of the stress measures. The formulation and steps for computing it are presented in terms of the Mooney-Rivlin strain-energy function model. The Cauchy stress tensor, an Eulerian formulation, is obtained directly from the second Piola-Kirchhof切割 发表于 2025-3-23 08:32:53
Tangent Moduli, is linear, the stiffness does not change as deformation changes. However, for a hyperelastic model, differentiating the strain-energy function with respect to either the finite strain tensor or one of the two Cauchy-Green deformation tensors yields elastic “constants,” the magnitude of which depend