Premium
Computational method for atomistic homogenization of nanopatterned point defect structures
Author(s) -
Chung Peter W.
Publication year - 2004
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.989
Subject(s) - homogenization (climate) , quasistatic process , statics , hyperelastic material , continuum mechanics , finite element method , classical mechanics , statistical physics , physics , mathematics , mathematical analysis , thermodynamics , biodiversity , ecology , biology
Abstract The development of an approximation method that rigorously averages small‐scale atomistic physics and embeds them in large‐scale mechanics is the principal aim of this work. This paper presents a general computational procedure based on homogenization to average frozen nanoscale atomistics and couple them to the equations of continuum hyperelasticity. The proposed application is to nanopatterned systems in which complex atomic configurations are organized in a repeating periodic array. The finite element method is used to solve the equations at the large scale, but the small‐scale equation is representative of lattice‐statics. The method is predicated on a quasistatic zero‐temperature assumption and, through homogenization, leads to a coupled set of variational equations. The numerical procedure is presented in detail, and 2‐D examples of ultra thin film layers of carbon one atom thick are shown to illustrate its applicability. Homogenization naturally gives rise to an inner displacement term with which point defects are explicitly modelled and their non‐linear interactions with global states of multiaxial strain are studied. Published in 2004 by John Wiley & Sons, Ltd.