On nonlinear universal relations in nonlinear elasticity

Bustamante, R.; Ogden, R. W.

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.

Más información

Título según WOS: ID WOS:000239429100011 Not found in local WOS DB
Título de la Revista: ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK
Volumen: 57
Número: 4
Editorial: SPRINGER BASEL AG
Fecha de publicación: 2006
Página de inicio: 708
Página final: 721
DOI:

10.1007/s00033-006-0068-3

Notas: ISI