Engineering Transactions, 39, 3-4, pp. 461-538, 1991

Generalized Strain and Stress Measures: Critical Survey and New Results

A. Curnier
Ecole Polytechnique Federale de Lauisanne, Lausanne
Switzerland

L. Rakotomanana
Ecole Polytechnique Federale de Lauisanne, Lausanne
Switzerland

Four basic principles: objectivity, isotropy, consistency and regularity are proposed to res tri.et the concepts of generalized strain and (more originally) of generalized stress. These principles are used to derive two general representations of the corresponding strain and stress functions. Based on a materiaI definition of conjugacy, each candidate strain is then placed in one-to-one correspondence with a certain conjugate stress and vice versa. Besides the classical strain-stress pairs already current in the literature, an interesting family of new strains and conjugate stresses is disclosed in the process. The main contributions of this paper, however, are to demonstrate the superiority of a particular class of strain and stress measures, herein called "congruent", and to reveal the coexistence of different definitions of conjugacy, which is a source of confusion.

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