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

Friedrich M, Schmidt B (2015)

Publication Type: Journal article

Publication year: 2015

Journal

Networks and Heterogeneous Media American Institute of Mathematical Sciences (AIMS)

Book Volume: 10

Pages Range: 321-342

Journal Issue: 2

DOI: 10.3934/nhm.2015.10.321

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 G-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.

Authors with CRIS profile

Manuel Friedrich

Involved external institutions

Universität Augsburg DE Germany (DE)

How to cite

APA:

Friedrich, M., & Schmidt, B. (2015). On a discrete-to-continuum convergence result for a two dimensional brittle material in the small displacement regime. Networks and Heterogeneous Media, 10(2), 321-342. https://dx.doi.org/10.3934/nhm.2015.10.321

MLA:

Friedrich, Manuel, and Bernd Schmidt. "On a discrete-to-continuum convergence result for a two dimensional brittle material in the small displacement regime." Networks and Heterogeneous Media 10.2 (2015): 321-342.

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