Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Bounds on Effective Dynamic Properties of Elastic Composites   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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The categories of this paper are: astro-ph
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The categories of this paper are: cmp-lg
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The categories of this paper are: q-bio
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The categories of this paper are: acc-phys
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The categories of this paper are: funct-an
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The categories of this paper are: mtrl-th
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The categories of this paper are: math
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The categories of this paper are: hep-ex
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The categories of this paper are: nucl-th
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The categories of this paper are: cs
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The categories of this paper are: nucl-ex
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The categories of this paper are: physics
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The categories of this paper are: quant-ph
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The categories of this paper are: q-alg
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The categories of this paper are: comp-gas
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The categories of this paper are: q-fin