A Stroh Formalism for Small-on-Large Problems in Spherical Polar Coordinates

Abstract

The governing equations for small-on-large analysis of an incompressible hyperelastic solid are reduced to a coupled system of six first-order ordinary differential equations with respect to the radial coordinate in spherical polar coordinates. This reduction to Stroh form does not assume a particular form for the strain-energy function.

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Acknowledgements

I thank Michel Destrade for advice and pointers to the literature, and an anonymous reviewer for constructive comments.

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Correspondence to P. A. Martin.

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Martin, P.A. A Stroh Formalism for Small-on-Large Problems in Spherical Polar Coordinates. J Elast 138, 125–144 (2020). https://doi.org/10.1007/s10659-019-09730-2

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Keywords

  • Nonlinear elasticity
  • Small-on-large
  • Incremental equations

Mathematics Subject Classification (2010)

  • 74B15
  • 74B20
  • 35A09
  • 35J57