A Metric Theory of Rate Independent and Rate Dependent Plasticity: Theoretical and Computational Aspects

Abstract eng:
A new internal variable theory for the description of solid materials having mechanisms with different characteristic times, is developed within a finite deformation framework. The theory relies crucially on the consistent combination of a general viscoplastic theory and a new version of rate – independent generalized plasticity theory. In this new version of rate – independent generalized plasticity the concepts of viscous range and viscous process have been introduced, while, as in classical generalized plasticity, the notion of yield surface, as a basic ingredient, is not involved. The formulation is developed initially in a material setting and then is extended to a covariant one by applying some basic elements and results from the tensor analysis on manifolds. By introducing the material (intrinsic) metric as a primary internal variable, accounting for both rate dependent and rate independent phenomena within the body, a constitutive model is proposed. The ability of the model in simulating several patterns of the complex response of metals under quasi – static and dynamic loadings is assessed by representative numerical examples, after appropriate approximations of the Lie derivatives of tensorial quantities have been derived.

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