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arXiv · 1202.0328

Bounds on Effective Dynamic Properties of Elastic Composites

Sia Nemat-Nasser·Ankit Srivastava
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Abstract

We present general, computable, improvable, and rigorous bounds for the total energy of a finite heterogeneous volume element or a periodically distributed unit cell of an elastic composite of any known distribution of inhomogeneities of any geometry and elasticity, undergoing a harmonic motion at a fixed frequency or supporting a single-frequency Bloch-form elastic wave of a given wave-vector. These bounds are rigorously valid for \emph{any consistent boundary conditions} that produce in the finite sample or in the unit cell, either a common average strain or a common average momentum. No other restrictions are imposed. We do not assume statistical homogeneity or isotropy. Our approach is based on the Hashin-Shtrikman (1962) bounds in elastostatics, which have been shown to provide strict bounds for the overall elastic moduli commonly defined (or actually measured) using uniform boundary tractions and/or linear boundary displacements; i.e., boundary data corresponding to the overall uniform stress and/or uniform strain conditions. Here we present strict bounds for the dynamic frequency-dependent constitutive parameters of the composite and give explicit expressions for a direct calculation of these bounds.

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Sia Nemat-Nasser, Ankit Srivastava. 2012-02-02. Bounds on Effective Dynamic Properties of Elastic Composites. https://doi.org/10.1016/j.jmps.2012.07.003

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