Smooth finite strain plasticity with non-local pressure support

P. M A Areias, Timon Rabczuk

Research output: Contribution to journalArticle

24 Citations (Scopus)

Abstract

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.

Original languageEnglish
Pages (from-to)106-134
Number of pages29
JournalInternational Journal for Numerical Methods in Engineering
Volume81
Issue number1
DOIs
Publication statusPublished - 2010 Jan 1
Externally publishedYes

Fingerprint

Finite Strain
Elasto-plastic
Plasticity
Nonlinear Viscoelasticity
Elastoplasticity
Plastics
Trust Region Method
Quadratic Convergence
Viscoelasticity
Constitutive Model
Constitutive Equation
Constitutive equations
Hardening
Constitutive models
Unloading
Linearization
Smooth function
Differential System
Simplification
Anisotropy

Keywords

  • Complementarity
  • Finite strain
  • Mixed methods
  • Plasticity

ASJC Scopus subject areas

  • Engineering(all)
  • Applied Mathematics
  • Numerical Analysis

Cite this

Smooth finite strain plasticity with non-local pressure support. / Areias, P. M A; Rabczuk, Timon.

In: International Journal for Numerical Methods in Engineering, Vol. 81, No. 1, 01.01.2010, p. 106-134.

Research output: Contribution to journalArticle

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