Vol. 8, No. 3, 2020

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On classical continuum mechanics, two-scale continua, and plasticity

Gianpietro Del Piero

Vol. 8 (2020), No. 3, 201–231
Abstract

The paper starts with a careful analysis of the kinematics of two-scale continua. The subsequent developments are based on a single additional concept, the concept of energy. Two basic axioms are formulated in energetic terms, and the stress tensors, the constitutive equations, and all other elements required for the formulation of the initial/boundary-value problem are regarded as derived quantities. A comparison with the theory of gradient plasticity shows the innovative aspects of the proposed theory.

Keywords
foundations of mechanics, two-scale continua, reference frames, gradient plasticity, nonlocal flow rules
Mathematical Subject Classification 2010
Primary: 74AXX, 74A05
Secondary: 74A60, 74C15, 74C20
Milestones
Received: 27 January 2020
Revised: 31 May 2020
Accepted: 8 July 2020
Published: 2 September 2020

Communicated by Miroslav Šilhavý
Authors
Gianpietro Del Piero
Dipartimento di Ingegneria
Università di Ferrara
Ferrara
Italy