Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Localised bifurcation in soft cylindrical tubes under axial stretching
  and surface tension   We investigate localised bulging or necking in an incompressible,
hyperelastic cylindrical tube under axial stretching and surface tension. Three
cases are considered in which the tube is subjected to different constraints.
In case 1 the inner and outer surfaces are traction-free and under surface
tension, whilst in cases 2 and 3 the inner and outer surfaces (respectively)
are fixed to prevent radial displacement and surface tension. However, each
free surface in these latter two cases is still under surface tension. We first
state the analytical bifurcation conditions for localisation and then validate
them numerically whilst determining whether localisation is preferred over
bifurcation into periodic modes. It is shown that bifurcation into a localised
solution is unattainable in case 1 but possible and favourable in cases 2 and
3. In contrast, in case 1 any bifurcation must necessarily take the form of a
periodic mode with a non-zero wave number. Our results are validated using
Finite Element Method (FEM) simulations.

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The categories of this paper are: bayes-an
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The categories of this paper are: adap-org
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The categories of this paper are: math-ph
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The categories of this paper are: q-fin
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The categories of this paper are: hep-ex
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The categories of this paper are: hep-ph
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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: quant-ph
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The categories of this paper are: atom-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: chao-dyn
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The categories of this paper are: funct-an
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The categories of this paper are: alg-geom
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The categories of this paper are: mtrl-th
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The categories of this paper are: patt-sol