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From Saturated Elasticity to Finite Evolution, Plasticity and Growth

Department of Mechanical and Manufacturing Engineering, The University of Calgary, Calgary, Alberta T2N 1N4, Canada, epstein{at}enme.ucalgary.ca

A complete theory of saturated nonlinear elasticity is formulated in terms of a relaxed energy function, whose existence and uniqueness are proved. Within this reversible context, it is shown that a normality rule for the post-saturated strains emerges naturally. Special consideration is given to saturation conditions expressed in terms of the logarithmic stress. Introducing the concept of material evolution, the passage to irreversible theories, such as plasticity and growth, is effected by means of a criterion of instantaneous healing imposed on any given underlying saturation scheme.

Key Words: Saturated elasticity • wrinkling • logarithmic strain • damage • Eshelby tensor • plasticity • growth

Mathematics and Mechanics of Solids, Vol. 7, No. 3, 255-283 (2002)
DOI: 10.1177/108128602027734


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