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In this paper, a multi-scale molecular dynamics-finite element coupling is presented to study the mechanical behavior of heterogeneous nano-crystalline structures. The stiffness and mass matrices of the continuum sub-domain are generated by applying a linear transformation on the matrices obtained via the atomic structure underlying the FE mesh. A Lagrange multiplier method is employed to the transition zone imposing velocity resemblance of the coupling regions. The constraint equations of motion are solved by the multi-time-step decomposition thus giving the opportunity to ascribe different time steps to each individual zone. The molecular dynamics is performed by employing the...