Vol. 2, No. 1, 2014

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Nonclassical continua, pseudobalance, and the law of action and reaction

Gianpietro Del Piero

Vol. 2 (2014), No. 1, 71–107
Abstract

The procedure followed in constructing models for generalized continua is revisited. It is shown that the microforce balance equations required for the description of generalized continua are not in fact expressions of the balance of physical quantities, but consequences of the regularity assumed for the systems of contact actions. In the proposed approach the law of action and reaction, which in classical continuum mechanics is a consequence of Euler’s balance laws, recovers the status of a basic principle as held in Newtonian mechanics. Some examples of generalized continua taken from the literature are discussed.

Dedicated to the memory of Luiz-Carlos Martins.

Keywords
foundations of continuum mechanics, virtual power, generalized continua, microstructure
Mathematical Subject Classification 2010
Primary: 74-XX
Milestones
Received: 16 November 2012
Revised: 1 April 2013
Accepted: 21 May 2013
Published: 4 December 2013

Communicated by Pierre Seppecher
Authors
Gianpietro Del Piero
Dipartimento di Ingegneria
Università di Ferrara
via Saragat 1
 44100 Ferrara
Italy