Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Nonlinear elastic moduli of composite materials with nonlinear spherical
  inclusions dispersed in a nonlinear matrix   A theory is developed for evaluation of nonlinear elastic moduli of composite
materials with nonlinear inclusions dispersed in another nonlinear material
(matrix). We elaborate a method aimed for determination of elastic parameters
of a composite: its linear elastic moduli (second-order elastic constants) and
nonlinear elastic moduli, which are known as the Murnaghan moduli (third-order
elastic constants). We find an analytical form for the effective Murnaghan
moduli of a composite with spherical inclusions. The effective moduli depend
linearly on Murnaghan moduli of constituents. The results obtained have been
verified through numerical modeling using the finite element method.

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The categories of this paper are: alg-geom
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The categories of this paper are: nlin
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The categories of this paper are: adap-org
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The categories of this paper are: q-fin
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The categories of this paper are: patt-sol
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The categories of this paper are: atom-ph
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The categories of this paper are: cmp-lg
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The categories of this paper are: supr-con
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The categories of this paper are: bayes-an
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The categories of this paper are: q-bio
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The categories of this paper are: econ
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The categories of this paper are: gr-qc
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The categories of this paper are: eess
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The categories of this paper are: quant-ph
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The categories of this paper are: math
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The categories of this paper are: cs