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On consistent stress rates in solid mechanics: Computational implications
Author(s) -
Perić Djordje
Publication year - 1992
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.1620330409
Subject(s) - hyperelastic material , mathematics , constitutive equation , elasticity (physics) , isotropy , cauchy elastic material , strain rate , cauchy stress tensor , finite strain theory , tensor (intrinsic definition) , stress (linguistics) , context (archaeology) , mathematical analysis , classical mechanics , geometry , finite element method , physics , thermodynamics , paleontology , linguistics , philosophy , quantum mechanics , biology
In the context of general isothermal elastic processes, issues related to work conjugacy and its effect on the choice of a stress rate are discussed for processes involving large strains. It is shown that a unique stress rate consistent with hyperelasticity can be defined for every conjugate pair chosen through the rate form of the associated hyperelastic constitutive equation. That results in non‐constant and generally anisotropic spatial elasticity tensors even for a linear isotropic material. The anisotropic spatial elasticity tensor connected with the Green–Naghdi rate of Kirchhoff stress is evaluated, which provides a basis for the spatial formulation of processes governed by the Hencky's strain energy function. 48,49 Notions of equivalent and irreducible form of stress rate are introduced using a ‘workless’ component of the deformation rate. The hyperelastic constitutive models for the conjugate pairs {S, E (2) } and {T, In U}, which are of significance for computation, are stated in their explicit form. Exact rate forms are derived and the order of approximation of currently employed computational algorithms discussed. Finally, computational implications of the work presented are reviewed.