Vol. 6, No. 3, 2018

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ISSN: 2325-3444 (e-only)
ISSN: 2326-7186 (print)
The variational structure of classical plasticity

Gianpietro Del Piero

Vol. 6 (2018), No. 3, 137–180

A unified approach to classical plasticity, including metal plasticity, geomaterials, and crystal plasticity, is presented. A distinctive feature of this approach is that the basic constitutive elements (yield criterion, flow rule, consistency condition, and hardening rule), instead of being assumed on a phenomenological basis or deduced from ad hoc principles, are obtained directly from the stationarity of the energy. The plastic continuum is regarded as a particular micromorphic continuum, and its energy has the form resulting from a homogenization procedure introduced in the theory of structured deformations. This form of the energy requires an additive decomposition of the deformation gradient, in place of the multiplicative decomposition usually adopted in finite plasticity. It is shown by examples that many of the models adopted in classical plasticity can be obtained from ad hoc specifications of the energy.

classical plasticity, quasistatic evolution, incremental energy minimization, plastic stationarity condition, nonassociated flow rules
Mathematical Subject Classification 2010
Primary: 74C15, 74G65, 74A20
Secondary: 74E15, 74L10
Received: 22 August 2017
Revised: 27 February 2018
Accepted: 11 April 2018
Published: 26 July 2018

Communicated by Miroslav Šilhavý
Gianpietro Del Piero
Dipartimento di Ingegneria
Università di Ferrara
Centro Internazionale di Ricerca per la Matematica & Meccanica dei Sistemi Complessi
Università dell’Aquila