On the admissibility of an isotropic, smooth elastic continuum

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Abstract

Many studies of elasticity of inhomogeneous materials - in both elastostatics and elastodynamics - assume the existence of locally isotropic, smooth stiffness tensor fields. We investigate the correctness of such a model in the simplest setup of antiplane classical elasticity. We work with the concept of mesoscale (or apparent) moduli for a finite-size window placed in such a material, in accordance with the Hill condition for the Hooke law. The limit from mesoscale down to infinitesimal windows is admissible within the model of an assumed smooth, locally isotropic continuum. However, this limit is not admissible from the standpoint of a microstructure, and, in order to set up an inhomogeneous elastic medium, one must introduce its anisotropy. A separate argument against the local isotropy stems from the representation of a correlation function of a wide-sense stationary and isotropic random field, whose realizations are smooth stiffness tensor fields.

Original languageEnglish (US)
Pages (from-to)345-355
Number of pages11
JournalArchives of Mechanics
Volume57
Issue number4
StatePublished - Sep 23 2005
Externally publishedYes

ASJC Scopus subject areas

  • Condensed Matter Physics
  • Mechanical Engineering

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