Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X



Approximation of dynamic and quasi-static evolution problems in elasto-plasticity by cap models

Authors: Jean-François Babadjian and Maria Giovanna Mora
Journal: Quart. Appl. Math. 73 (2015), 265-316
MSC (2010): Primary 74C05, 74C10; Secondary 74G65, 49J45, 35Q72
Published electronically: February 3, 2015
MathSciNet review: 3357495
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Abstract: This work is devoted to the analysis of elasto-plasticity models arising in soil mechanics. Contrary to the typical models mainly used for metals, it is required here to take into account plastic dilatancy due to the sensitivity of granular materials to hydrostatic pressure. The yield criterion thus depends on the mean stress, and the elasticity domain is unbounded and not invariant in the direction of hydrostatic matrices. In the mechanical literature, so-called cap models have been introduced, where the elasticity domain is cut in the direction of hydrostatic stresses by means of a strain-hardening yield surface, called a cap. The purpose of this article is to study the well-posedness of plasticity models with unbounded elasticity sets in dynamical and quasi-static regimes. An asymptotic analysis as the cap is moved to infinity is also performed, which enables one to recover solutions to the uncapped model of perfect elasto-plasticity.

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Jean-François Babadjian
Affiliation: Université Pierre et Marie Curie – Paris 6, CNRS, UMR 7598 Laboratoire Jacques-Louis Lions, Paris, F-75005, France
Email: jean-francois.babadjian@upmc.fr

Maria Giovanna Mora
Affiliation: Dipartimento di Matematica, Università di Pavia, via Ferrata 1, 27100 Pavia, Italy
Email: mariagiovanna.mora@unipv.it

DOI: https://doi.org/10.1090/S0033-569X-2015-01376-8
Keywords: Elasto-plasticity, Functions of bounded deformation, Calculus of variations, Dynamic evolution, Quasi-static evolution, Convex analysis
Received by editor(s): March 8, 2013
Received by editor(s) in revised form: July 23, 2013
Published electronically: February 3, 2015
Article copyright: © Copyright 2015 Brown University

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