Vol. 4, No. 4, 2009

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On inhomogeneity, growth, ageing and the dynamics of materials

Gerard A. Maugin

Vol. 4 (2009), No. 4, 731–741

The explicit dependence of material properties on the basic space-time parametrization of continuum mechanics is a most interesting departure from standard behavior. The best framework to formally place these effects in evidence is the so-called material mechanics of materials advocated by the late G.Herrmann. Among the manifestations of these dependencies, material inhomogeneity is the most obvious and frequent one, but others such as volumetric growth or ageing also occur naturally, not to speak of artificial situations where one tries to build dynamic materials whose parts purposefully react differently in space and time at the will of the designer. These different cases are briefly sketched out first on the basis of a Lagrangian formulation and then in the general framework of thermomechanics.

inhomogeneity, growth, ageing, continuum, dynamics
Received: 28 November 2007
Revised: 14 February 2008
Accepted: 14 February 2008
Published: 7 August 2009
Gerard A. Maugin
Université Pierre et Marie Curie (Paris 6)
Institut Jean Le Rond d’Alembert
Case 162,  4 place Jussieu,
75252 Paris Cedex 05, France