On nonlinear universal relations in nonlinear elasticity

@article{citeulike:1319527, abstract = {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.}, author = {Bustamante, R. and Ogden, R. }, citeulike-article-id = {1319527}, doi = {10.1007/s00033-006-0068-3}, journal = {Zeitschrift f\"{u}r Angewandte Mathematik und Physik (ZAMP)}, keywords = {eap}, month = {July}, number = {4}, pages = {708--721}, posted-at = {2007-05-22 17:05:41}, priority = {2}, title = {On nonlinear universal relations in nonlinear elasticity}, url = {http://dx.doi.org/10.1007/s00033-006-0068-3}, volume = {57}, year = {2006} }

TY - JOUR ID - citeulike:1319527 L3 - citeulike-article-id:1319527 TI - On nonlinear universal relations in nonlinear elasticity JF - Zeitschrift für Angewandte Mathematik und Physik (ZAMP) VL - 57 IS - 4 SP - 708 EP - 721 N2 - 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. KW - eap AU - Bustamante, R AU - Ogden, R PY - 2006/07/23/ UR - http://dx.doi.org/10.1007/s00033-006-0068-3 ER -