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Smooth finite strain plasticity with non‐local pressure support
Author(s) -
Areias P. M. A.,
Rabczuk T.
Publication year - 2009
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.2686
Subject(s) - hyperelastic material , finite element method , linearization , discretization , constitutive equation , mathematics , solver , isotropy , linear elasticity , plasticity , nonlinear system , finite strain theory , mathematical optimization , computer science , mathematical analysis , structural engineering , engineering , physics , quantum mechanics , thermodynamics
The aim of this work is to introduce an alternative framework to solve problems of finite strain elastoplasticity including anisotropy and kinematic hardening coupled with any isotropic hyperelastic law. After deriving the constitutive equations and inequalities without any of the customary simplifications, we arrive at a new general elasto‐plastic system. We integrate the elasto‐plastic algebraico‐differential system and replace the loading–unloading condition by a Chen–Mangasarian smooth function to obtain a non‐linear system solved by a trust region method. Despite being non‐standard, this approach is advantageous, since quadratic convergence is always obtained by the non‐linear solver and very large steps can be used with negligible effect in the results. Discretized equilibrium is, in contrast with traditional approaches, smooth and well behaved. In addition, since no return mapping algorithm is used, there is no need to use a predictor. The work follows our previous studies of element technology and highly non‐linear visco‐elasticity. From a general framework, with exact linearization, systematic particularization is made to prototype constitutive models shown as examples. Our element with non‐local pressure support is used. Examples illustrating the generality of the method are presented with excellent results. Copyright © 2009 John Wiley & Sons, Ltd.