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Quasistatic evolution for Cam-Clay plasticity: a weak formulation via viscoplastic regularization and time rescaling

TitleQuasistatic evolution for Cam-Clay plasticity: a weak formulation via viscoplastic regularization and time rescaling
Publication TypeJournal Article
Year of Publication2011
AuthorsDal Maso, G, DeSimone, A, Solombrino, F
JournalCalculus of Variations and Partial Differential Equations 40 (2011) 125-181
KeywordsCam-Clay plasticity
Abstract

Cam-Clay nonassociative plasticity exhibits both hardening and softening behaviour, depending on the loading. For many initial data the classical formulation of the quasistatic evolution problem has no smooth solution. We propose here a notion of generalized solution, based on a viscoplastic approximation. To study the limit of the viscoplastic evolutions we rescale time, in such a way that the plastic strain is uniformly Lipschitz with respect to the rescaled time. The limit of these rescaled solutions, as the viscosity parameter tends to zero, is characterized through an energy-dissipation balance, that can be written in a natural way using the rescaled time. As shown in [4] and [6], the proposed solution may be discontinuous with respect to the original time. Our formulation allows to compute the amount of viscous dissipation occurring instantaneously at each discontinuity time.

URLhttp://hdl.handle.net/1963/3670
DOI10.1007/s00526-010-0336-0

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