Cauchy–Born strain energy density for coupled incommensurate elastic chains

Abstract

The recent fabrication of weakly interacting incommensurate two-dimensional layer stacks (A. Geim and I. Grigorieva, Nature 499 (2013) 419–425) requires an extension of the classical notion of the Cauchy–Born strain energy density since these atomistic systems are typically not periodic. In this paper, we rigorously formulate and analyze a Cauchy–Born strain energy density for weakly interacting incommensurate one-dimensional lattices (chains) as a large body limit and we give error estimates for its approximation by finite samples as well as the popular supercell method.

Document Details

Document Type
Pub Defense Publication
Publication Date
Mar 01, 2018
Source ID
10.1051/m2an/2017057

Entities

People

  • Mitchell Barry Luskin
  • Paul Cazeaux

Organizations

  • Army Research Office

Tags

Fields of Study

  • Physics

Readers

  • Approximation Theory.
  • Computational Fluid Dynamics (CFD)
  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)