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cauchy–born model

ESAIM: Mathematical Modelling and Numerical Analysis (1)

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On the stability of Bravais lattices and their Cauchy–Born approximations *
Thomas Hudson, Christoph Ortner
Journal:

ESAIM: Mathematical Modelling and Numerical Analysis / Volume 46 / Issue 1 / January 2012

Published online by Cambridge University Press:

26 July 2011, pp. 81-110

Print publication:

January 2012
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We investigate the stability of Bravais lattices and their Cauchy–Born approximations under periodic perturbations. We formulate a general interaction law and derive its Cauchy–Born continuum limit. We then analyze the atomistic and Cauchy–Born stability regions, that is, the sets of all matrices that describe a stable Bravais lattice in the atomistic and Cauchy–Born models respectively. Motivated by recent results in one dimension on the stability of atomistic/continuum coupling methods, we analyze the relationship between atomistic and Cauchy–Born stability regions, and the convergence of atomistic stability regions as the cell size tends to infinity.