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Title of Journal: Int J Mater Form

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Abbravation: International Journal of Material Forming

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Springer-Verlag

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DOI

10.1002/cber.19170500201

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1960-6214

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Regularization and perturbation technique to solve

Authors: Mohamed Assidi Hamid Zahrouni Noureddine Damil Michel PotierFerry
Publish Date: 2008/12/18
Volume: 2, Issue: 1, Pages: 1-14
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Abstract

This paper investigates new procedures to solve plasticity problems by using the asymptotic numerical method ANM As the elasticplastic behavior involves two unilateral conditions we replace these two conditions by regular functions depending upon the stress field and its time derivative which permits one to take into account elasticplastic transition and elastic unloading Several applications in structural plasticity problems are presented to assess the ability of the proposed algorithmIn the specific case of elastoplasticity one can distinguish two groups of equations The first group contains Eqs 50 51 52 53 and 54 and corresponds to the non linear relation between the stress rate and the strain rate These five equations will be combined to get the recurrence formula 38 that relates σ k and ε k The second group of equations 47 48 49 55 56 57 and 58 defines the yield function f k the normal n k the equivalent stress q k and the effective stress σ e k These variables f q and σ e appears in the first group but only via the orders lower than k As a consequence the second group of equations can be implemented after the first groupIt is convenient to eliminate the plastic strain the plastic multiplier H k − 1 and ξ k − 1 to recover the stressstrain relation 38 that can be introduced in a finite element framework see “Finite element applications” This condensation process is easy because the perturbation technique leads to linear equations


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