On the formulation of closest-point projection algorithms in elastoplasticity-part I: The variational structure

We present in this paper the characterization of the variational structure behind the discrete equations defining the closest‐point projection approximation in elastoplasticity. Rate‐independent and viscoplastic formulations are considered in the infinitesimal and the finite deformation range, the l...

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Bibliographic Details
Published in:International journal for numerical methods in engineering Vol. 53; no. 2; pp. 297 - 329
Main Authors: Armero, F., Pérez-Foguet, A.
Format: Journal Article
Language:English
Published: Chichester, UK John Wiley & Sons, Ltd 20.01.2002
Subjects:
augmented Lagrangian
closest-point projection
plasticity and viscoplasticity
primal and dual variational principles
return mapping algorithms
ISSN:0029-5981, 1097-0207
Online Access:Get full text
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Summary:We present in this paper the characterization of the variational structure behind the discrete equations defining the closest‐point projection approximation in elastoplasticity. Rate‐independent and viscoplastic formulations are considered in the infinitesimal and the finite deformation range, the later in the context of isotropic finite‐strain multiplicative plasticity. Primal variational principles in terms of the stresses and stress‐like hardening variables are presented first, followed by the formulation of dual principles incorporating explicitly the plastic multiplier. Augmented Lagrangian extensions are also presented allowing a complete regularization of the problem in the constrained rate‐independent limit. The variational structure identified in this paper leads to the proper framework for the development of new improved numerical algorithms for the integration of the local constitutive equations of plasticity as it is undertaken in Part II of this work. Copyright © 2001 John Wiley & Sons, Ltd.
Bibliography:Commission for Cultural, Educational and Scientific Exchange, (1999) U.S.A./Spain - No. 99258
ArticleID:NME278
NSF - No. CMS-9703000
ark:/67375/WNG-MP643H73-F
ONR - No. N00014-96-1-0818
Generalitat de Catalunya - No. 1998 BEA1200042
istex:D208475A5EE42B75EC9D3DCF9FCC493E4673B281
On leave from the Departament de Matemàtica Aplicada III, ETSECCPB, UPC, Barcelona, Spain, during the Fall semester 1999.
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ISSN:0029-5981
1097-0207
DOI:10.1002/nme.278