On a discrete-to-continuum convergence result for a two dimensional brittle material in the small displacement regime

Manuel Friedrich; Bernd Schmidt

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arXiv · 1403.0443

On a discrete-to-continuum convergence result for a two dimensional brittle material in the small displacement regime

Manuel Friedrich·Bernd Schmidt

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Abstract

We consider a two-dimensional atomic mass spring system and show that in the small displacement regime the corresponding discrete energies can be related to a continuum Griffith energy functional in the sense of Gamma-convergence. We also analyze the continuum problem for a rectangular bar under tensile boundary conditions and find that depending on the boundary loading the minimizers are either homogeneous elastic deformations or configurations that are completely cracked generically along a crystallographic line. As applications we discuss cleavage properties of strained crystals and an effective continuum fracture energy for magnets.

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Manuel Friedrich, Bernd Schmidt. 2014-03-03. On a discrete-to-continuum convergence result for a two dimensional brittle material in the small displacement regime. https://arxiv.org/abs/1403.0443

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