An Energy Estimate for Dislocation Configurations and the Emergence of Cosserat-Type Structures in Metal Plasticity

2016/08/22 by Lauteri, Gianluca, Luckhaus, Stephan · 1 citation
#FOS: Mathematics #FOS: Physical sciences #Functional Analysis (math.FA) #Mathematical Physics (math-ph)

paper · doi:10.48550/arxiv.1608.06155

Abstract

We investigate low energy structures of a lattice with dislocations in the context of nonlinear elasticity. We show that these low energy configurations exhibit in the limit a Cosserat-like behavior. Moreover, we give bounds from above and below to the energy of such configurations.

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• Leading order asymptotics for non-local energies and the Read-Shockley law

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