Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: An analytic derivation of the bifurcation conditions for localization in
  hyperelastic tubes and sheets   We provide an analytic derivation of the bifurcation conditions for localized
bulging in an inflated hyperelastic tube of arbitrary wall thickness and
axisymmetric necking in a hyperelastic sheet under equibiaxial stretching. It
has previously been shown numerically that the bifurcation condition for the
former problem is equivalent to the vanishing of the Jacobian determinant of
the internal pressure $P$ and resultant axial force $N$, with each of them
viewed as a function of the azimuthal stretch on the inner surface and the
axial stretch. This equivalence is established here analytically. For the
latter problem for which it has recently been shown that the bifurcation
condition is not given by a Jacobian determinant equal to zero, we explain why
this is the case and provide an alternative interpretation.

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The categories of this paper are: math-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: ao-sci
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The categories of this paper are: quant-ph
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The categories of this paper are: astro-ph
1
The categories of this paper are: cs
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The categories of this paper are: mtrl-th
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The categories of this paper are: adap-org
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The categories of this paper are: solv-int
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The categories of this paper are: acc-phys
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The categories of this paper are: plasm-ph
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The categories of this paper are: hep-ex
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The categories of this paper are: cmp-lg
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The categories of this paper are: patt-sol
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The categories of this paper are: chao-dyn
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The categories of this paper are: hep-th