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 macro-and micromechanical models where continuum mechanics approach fails are pointed out.
Utilizing molecular dynamics (MD) integration model we have investigated some of the relevant physical processes caused by different loading paths at the atomic level in Cu and Al monocrystal specimen. Interactions among the atoms in the bulk are modeled with the standard realistic Embedded Atom Method (EAM) potentials. MD simulation gives us the detailed information about non-equilibrium dynamics including crystal structure defects, vacancies and dislocations. In particular, we have obtained result that indicate increase in the total energy of the crystal during loading (especially cyclic) that provides us direct quantitative evidence of the metal weakening. For the basic response, we have deformed copper and aluminum single crystal according to the simple loading path and a series of multiaxial loading-paths including cyclic repetition. We compute equivalent stress-strain diagrams as well as dislocation total length vs time graphs to describe signatures of the anisotropic response of the crystal.
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