Calculus of Variations and Geometric Measure Theory
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J. Matias - M. Morandotti - D. R. Owen - E. Zappale

Relaxation of non-local energies for structured deformations with applications to plasticity

created by morandott on 05 Jul 2019
modified on 06 Jul 2019



Inserted: 5 jul 2019
Last Updated: 6 jul 2019

Pages: 29
Year: 2019


An integral representation result is obtained for the asymptotics of energies including both local and non-local terms, in the context of structured deformations. Starting from an initial energy featuring a local bulk and interfacial contribution and a non-local measure of the jump discontinuities, an iterated limiting procedure is performed. First, the initial energy is relaxed to structured deformation, and then the measure of non-locality is sent to zero, with the effect of obtaining an explicit local energy in which the non-linear contribution of submacroscopic slips and separations is accounted for. Two terms, different in nature, emerge in the bulk part of the final energy: one coming from the initial bulk energy and one arising from the non-local contribution to the initial energy. This structure turns out to be particularly useful for studying mechanical phenomena such as yielding and hysteresis. Moreover, in the class of invertible structured deformations, applications to crystal plasticity are presented.

Keywords: relaxation, Non-local energies, Structured deformations, crystal plasticity


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