Techno Press
Tp_Editing System.E (TES.E)
Login Search

Volume 7, Number 1, April 2014

We present a full energy and force formulation of the quasicontinuum method with non-local and local transition elements. Non-local transition elements are developed to transmit inhomogeneity from the atomistic to the continuum regions. Local transition elements are developed to resolve the mathematical mismatch between non-local atoms and the local continuum. The rationale behind these transition elements is provided by analyzing the energy and force transitions between atoms and continuum under the Cauchy-Born rule. We show that breakdown of the Cauchy-Born rule occurs for slaved atoms of local elements within the cutoff of non-local atoms. The inadequacy of the Cauchy-Born rule at the transition region naturally leads to the need of atomistic treatment of transition slaved and transition representative atoms. Such an atomistic treatment together with a full or cutoff sampling allows non-local transition elements containing these transition entities to transmit inhomogeneity. Different force formulations for transition representative atoms and pure local representative atoms allow the local transition elements to resolve non-local and local mismatches. The method presented herein is validated by force calculations in an unstressed perfect crystal as well as an unrelaxed grain boundary model. A nanoindentation simulation in 3D is conducted to demonstrate the accuracy and efficiency of the proposed method.

Key Words
quasicontinuum; transition; atomistic model; finite elements

Shu-Wei Chang, Ying-Pao Liao and Chuin-Shan Chen: Department of Civil Engineering, National Taiwan University, Taiwan

Chang-Wei Huang: Department of Civil Engineering, Chung-Yuan Christian University, Taiwan

Techno-Press: Publishers of international journals and conference proceedings.       Copyright © 2021 Techno-Press
P.O. Box 33, Yuseong, Daejeon 34186 Korea, Tel: +82-2-736-6800 (GAE, EAS, WAS, ANR) +82-42-828-7995 (SEM, SCS, SSS) Fax : +82-2-736-6801, Email: