On the stability of Bravais lattices and their Cauchy–Born approximations
Hudson, Thomas and Ortner, Christoph. (2012) On the stability of Bravais lattices and their Cauchy–Born approximations. ESAIM: Mathematical Modelling and Numerical Analysis, Vol.46 (No.1). pp. 81-110. ISSN 0764-583XFull text not available from this repository.
Official URL: http://dx.doi.org/10.1051/m2an/2011014
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.
|Item Type:||Journal Article|
|Subjects:||Q Science > QA Mathematics|
|Divisions:||Faculty of Science > Mathematics|
|Journal or Publication Title:||ESAIM: Mathematical Modelling and Numerical Analysis|
|Page Range:||pp. 81-110|
|Access rights to Published version:||Restricted or Subscription Access|
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