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arXiv · 2006.15073

From the Peierls-Nabarro model to the equation of motion of the dislocation continuum

Stefania Patrizi·Tharathep Sangsawang
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Abstract

We consider a semi-linear integro-differential equation in dimension one associated to the half Laplacian %This model describes the evolution of phase transitions associated to dislocations. whose solution represents the atom dislocation in a crystal. The equation comprises the evolutive version of the classical Peierls-Nabarro model. We show that for a large number of dislocations, the solution, properly rescaled, converges to the solution of a well known equation called by Head \cite{H} "the equation of motion of the dislocation continuum". The limit equation is a model for the macroscopic crystal plasticity with density of dislocations. In particular, we recover the so called Orowan's law which states that dislocations move at a velocity proportional to the effective stress.

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Stefania Patrizi, Tharathep Sangsawang. 2020-08-15. From the Peierls-Nabarro model to the equation of motion of the dislocation continuum. https://arxiv.org/abs/2006.15073

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