Quasicontinuum method using variable-node elements and its applications for simulations of nanostructures

Abstract

A new three-dimensional adaptive quasicintinuum (QC) method is studied to improve the conventional QC that utilizes tetrahedral elements. The linear tetrahedral elements of the conventional QC are replaced by hexahedral elements, and the adaptive refinement is achieved by utilizing what is known as variable-node elements. This leads to a substantial improvement in the solution convergence in the adaptive QC method, and removes the need of an extra code for the constrained Delaunay triangulation, which is required in the course of adaptive mesh refinement in the conventional QC with tetrahedral elements. The new QC scheme is firstly applied for simulations of Al (111) nanoindentation to explore the load-displacement behavior, and the effect of a void on the response to indentation. Secondly, the method is extended for application to the case of a curved crystalline structure like a carbon nanotube (CNT) to study deformation behaviors of CNTs. Numerical examples demonstrate the effectiveness and the accuracy of the new QC with the proposed hexahedral-type or variable-node elements.