Renormalized Energy for Dislocations in Quasi-Crystals

Lei Wu

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arXiv · 1612.02704

Renormalized Energy for Dislocations in Quasi-Crystals

Lei Wu

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Abstract

Anti-plane shear deformations of a hexagonal quasi-crystal with multiple screw dislocations are considered. Using a variational formulation, the elastic equilibrium is characterized via limit of minimizers of a core-regularized energy functional. A sharp estimate of the asymptotic energy when the core radius tends to zero is obtained using higher-order $\Gamma$-convergence. Also, the interaction between dislocations and the Peach-K\"{o}hler force at each dislocation are analyzed.

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Lei Wu. 2016-12-08. Renormalized Energy for Dislocations in Quasi-Crystals. https://arxiv.org/abs/1612.02704

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