On the method of virtual power in continuum mechanics

Del Piero, Gianpietro

doi:10.2140/jomms.2009.4.281

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On the method of virtual power in continuum mechanics

Gianpietro Del Piero

Vol. 4 (2009), No. 2, 281–292

DOI: 10.2140/jomms.2009.4.281

Abstract

The method of virtual power is generally used to produce balance equations for nontraditional continua such as continua with various types of microstructure. Here I show that the expression of the internal power can be deduced from that of the external power using a general invariance requirement due to Noll and a generalized version of Cauchy’s tetrahedron theorem. In other words, the measures of deformation and stress, as well as the balance equations, are determined by the expression chosen for the external power and by the invariance assumptions. A pair of examples taken from the literature shows that both ingredients are essential for defining a specific class of continua.

Dedicated to the memory of Paul Germain

Keywords

foundations of continuum mechanics, virtual power, continua with microstructure, materials with microstructure

Milestones

Received: 20 December 2007

Accepted: 7 March 2008

Published: 12 April 2009

Authors

Gianpietro Del Piero
Dipartimento di Ingegneria Università di Ferrara Via Saragat 1 44100 Ferrara Italy

Vol. 4, No. 2, 2009

Gianpietro Del Piero

Abstract

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Authors