On nonlinear universal relations in nonlinear elasticity

Bustamante, R. and Ogden, R.W. (2006) On nonlinear universal relations in nonlinear elasticity. Zeitschrift für Angewandte Mathematik und Physik, 57(4), pp. 708-721. (doi:10.1007/s00033-006-0068-3)

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Publisher's URL: http://dx.doi.org/10.1007/s00033-006-0068-3

Abstract

In the theory of nonlinear elasticity universal relations are relationships connecting the components of stress and deformation tensors that hold independently of the constitutive equation for the considered class (or sub-class) of materials. They are classified as linear or nonlinear according as the components of the stress appear linearly or nonlinearly in the relations. In this paper a general scheme is developed for the derivation of nonlinear universal relations and is applied to the constitutive law of an isotropic Cauchy elastic solid. In particular, we consider examples of quadratic and cubic universal relations. In respect of universal solutions our results confirm the general result of Pucci and Saccomandi [1] that nonlinear universal relations are necessarily generated by the linear ones. On the other hand, for non-universal solutions we develop a general method for generating nonlinear universal relations and illustrate the results in the case of cubic relations.

Item Type:Articles
Status:Published
Refereed:Yes
Glasgow Author(s) Enlighten ID:Ogden, Professor Raymond
Authors: Bustamante, R., and Ogden, R.W.
College/School:College of Science and Engineering > School of Mathematics and Statistics > Mathematics
Journal Name:Zeitschrift für Angewandte Mathematik und Physik
ISSN:0044-2275
ISSN (Online):1420-9039

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