Friedrich M, Schmidt B (2015)
Publication Type: Journal article
Publication year: 2015
Book Volume: 10
Pages Range: 321-342
Journal Issue: 2
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.
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://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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