On the Stability of Bravais Lattices and their Cauchy-Born Approximations
نویسندگان
چکیده
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.
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