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A class of universal relations for constrained, isotropic elastic materials

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Summary

A class of universal relations for all kinematically constrained, isotropic, elastic materials is described by the equationSB=BS relating the symmetric extra stress and the Cauchy-Green deformation tensors. This rule generates easily at most three universal relations for all kinematically admissible deformations of any constrained, isotropic body for which these tensors are nondiagonal. New universal formulae for homogeneous, compressible and incompressible materials reinforced by inextensible fibers in a variety of arrangements are presented for several kinds of homogeneous and nonhomogeneous, controllable universal deformations.

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Authors and Affiliations

  1. Department of Engineering Mechanics, University of Kentucky, 40506-0046, Lexington, KY, USA

    M. F. Beatty

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  1. M. F. Beatty
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Beatty, M.F. A class of universal relations for constrained, isotropic elastic materials. Acta Mechanica 80, 299–312 (1989). https://doi.org/10.1007/BF01176166

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  • DOI: https://doi.org/10.1007/BF01176166

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