Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Universal Theorems for Total Energy of the Dynamics of Linearly Elastic
  Heterogeneous Solids   In this paper we consider a sample of a linearly elastic heterogeneous
composite in elastodynamic equilibrium and present universal theorems which
provide lower bounds for the total elastic strain energy plus the kinetic
energy, and the total complementary elastic energy plus the kinetic energy. For
a general heterogeneous sample which undergoes harmonic motion at a single
frequency, we show that, among all consistent boundary data which produce the
same average strain, the uniform-stress boundary data render the total elastic
strain energy plus the kinetic energy an absolute minimum. We also show that,
among all consistent boundary data which produce the same average momentum in
the sample, the uniform velocity boundary data render the total complementary
elastic energy plus the kinetic energy an absolute minimum. We do not assume
statistical homogeneity or material isotropy in our treatment, although they
are not excluded. These universal theorems are the dynamic equivalent of the
universal theorems already known for the static case (Nemat-Nasser and Hori
1995). It is envisaged that the bounds on the total energy presented in this
paper will be used to formulate computable bounds on the overall dynamic
properties of linearly elastic heterogeneous composites with arbitrary
microstructures.

23
The categories of this paper are: solv-int
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The categories of this paper are: acc-phys
3
The categories of this paper are: physics
10
The categories of this paper are: q-bio
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The categories of this paper are: atom-ph
5
The categories of this paper are: gr-qc
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The categories of this paper are: econ
9
The categories of this paper are: nlin
31
The categories of this paper are: ao-sci
11
The categories of this paper are: hep-lat
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The categories of this paper are: patt-sol
1
The categories of this paper are: cs
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The categories of this paper are: supr-con
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The categories of this paper are: comp-gas
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The categories of this paper are: dg-ga
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The categories of this paper are: nucl-th