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Molecular dynamics simulations have been used for decades to investigate continuum mechanics failure to give the correct distribution of stress near discontinuities, such as holes and crack tips. In this paper, stress distribution around elliptical holes in a sheet material has been examined in an atomistic and a continuum model. Atomistic interactions are described by the Tersoff potential tuned for carbon. Calculations were conducted for the problem of stress distribution around the elliptic hole in a 2D graphene sheet subjected to the gradually increasing uniaxial tension load. The atomistic stress is calculated as spatial average utilizing Hardy’s formulation. The results have been compared with the Kirsch solution for stress concentration at the edge of the circular hole. A quantitative measure for switching from atomistic to continuum model and vice versa has been proposed. Routes toward the effective data-driven coupling of macroand micromechanical models where continuum mechanics approach fails are pointed out.

Atomistic Modelling of 2D Stress Distribution Around Discontinuities