Displacement field splitting of defective hexagonal lattices

Physical review. B./Physical review. B, vol. 106

Abstract

In this paper, we propose a methodology that allows disentangling the interaction of two Stone-Wales defects in a two-dimensional model material, which has the crystalline structure of a honeycomb lattice. The nonaffinity of the material response is represented as a linear superposition of nonaffine displacements caused by every individual defect and a residual nonaffine displacement field. The latter is then identified as the interaction field linked to a weakening or---as also shown---strengthening effect. We perform various numerical deformation tests in the athermal quasistatic limit on selected configurations. In doing so, we introduce a field variable to validate the contribution of the defect interaction field that indicates the mode of material failure, which also explains why some configurations with two Stone-Wales defects have a higher tensile strength than other configurations with only one defect.

Authors 5

1. Tobias Focks Aachen Institute of General Mechanics

   RWTH Aachen University

   Affiliation as printed

   Institute of General Mechanics, RWTH Aachen University, Aachen 52062, Germany

2. Franz Bamer Aachen Institute of General Mechanics

   RWTH Aachen University

   Affiliation as printed

   Institute of General Mechanics, RWTH Aachen University, Aachen 52062, Germany

3. Bernd A. Markert Aachen Institute of General Mechanics

   RWTH Aachen University

   Affiliation as printed

   Institute of General Mechanics, RWTH Aachen University, Aachen 52062, Germany

4. Zhao Wu Aachen Institute of General Mechanics Research Lab for Applied and Computational Mathematics

   RWTH Aachen University

   Affiliation as printed

   Institute of General Mechanics, RWTH Aachen University, Aachen 52062, Germany

   Research Lab for Applied and Computational Mathematics, RWTH Aachen University, Aachen 52062, Germany

5. Benjamin Stamm Aachen Institute of General Mechanics Research Lab for Applied and Computational Mathematics

   RWTH Aachen University

   Affiliation as printed

   Institute of General Mechanics, RWTH Aachen University, Aachen 52062, Germany

   Research Lab for Applied and Computational Mathematics, RWTH Aachen University, Aachen 52062, Germany