An Analysis of Crystal Cleavage in the Passage from Atomistic Models to Continuum Theory
Friedrich M, Schmidt B (2015)
Publication Type: Journal article
Publication year: 2015
Journal
Book Volume: 217
Pages Range: 263-308
Journal Issue: 1
DOI: 10.1007/s00205-014-0833-y
Abstract
We study the behavior of brittle atomistic models in general dimensions under uniaxial tension and investigate the system for critical fracture loads. We rigorously prove that in the discrete-to-continuum limit the minimal energy satisfies a particular cleavage law with quadratic response to small boundary displacements followed by a sharp constant cut-off beyond some critical value. Moreover, we show that the minimal energy is attained by homogeneous elastic configurations in the subcritical case and that beyond critical loading cleavage along specific crystallographic hyperplanes is energetically favorable. In particular, our results apply to mass spring models with full nearest and next-to-nearest pair interactions and provide the limiting minimal energy and minimal configurations.
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APA:
Friedrich, M., & Schmidt, B. (2015). An Analysis of Crystal Cleavage in the Passage from Atomistic Models to Continuum Theory. Archive for Rational Mechanics and Analysis, 217(1), 263-308. https://doi.org/10.1007/s00205-014-0833-y
MLA:
Friedrich, Manuel, and Bernd Schmidt. "An Analysis of Crystal Cleavage in the Passage from Atomistic Models to Continuum Theory." Archive for Rational Mechanics and Analysis 217.1 (2015): 263-308.
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