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A variational approach to gradient plasticity

Banff International Research Station for Mathematical Innovation and Discovery

In this talk, a variational model for gradient plasticity is proposed, which is based on an energy functional sum of a stored elastic bulk energy, a non-convex dissipative plastic energy, and a quadratic non-local term, depending on the gradient of the plastic strain. The basic modelling ingredients are presented in a simple one-dimensional setting, where the key physical aspects of the phenomena can easily be extracted. The evolution laws are deduced by using the mathematical tool of incremental energy minimization, and they are commented, highlighting the main differences and similarities with variational damage models. The typical assumptions of classical plasticity, such as yield condition, hardening rule, consistency condition, and elastic unloading, are obtained as necessary conditions for a minimum. Then, analytical solutions are determined, and attention is focused on the correlations between the convex-concave properties of the plastic energy and the distribution of the deformation field. The issue of solution stability is also addressed. Finally, some numerical results are discussed. First, tensile tests on steel bars and concrete samples are reproduced, and, then, a more complex two-dimensional crystal plasticity is proposed, and the process of microstructures evolution in metals is described by assuming a double-well plastic potential.

Mathematics; Mechanics of deformable solids; Calculus of variations and optimal control; optimization; Material science

video/mp4

Author affiliation: Polytechnic University of Marche

2017-02-09

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/59682

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/4.0/