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Material Stability Conditions for a Class of Inhomogeneous Anisotropic Media

Department of Computational Mechanics, FEM, State University of Campinas, 13.083-970, Campinas - SP, Brazil

In this paper we analyze the hyperbolicity of a non-homogeneous differential operator of constant coefficients, which describes a class of inhomogeneous anisotropic media. This class of inhomogeneous media requires constraints on the types of material profiles. We identify two subclasses, Case A, which requires additional material constraints and Case B. We show that for Case A, the non-homogeneous differential operator is hyperbolic independent from the strictly or non-strictly hyperbolic behavior of its principal part. For Case B we have identified two regions of material instability when the operator's principal part ceases to be strictly hyperbolic. The analysis is exemplified for inhomogeneous transversely isotropic media.

Key Words: Inhomogeneous solids • anisotropy • non-homogeneus hyperbolic polynomial • material stability • transversely isotropic

This version was published on June 1, 2009

Mathematics and Mechanics of Solids, Vol. 14, No. 4, 377-389 (2009)
DOI: 10.1177/1081286507080143


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