engleski

Ghost forces in concurrent atomistic-to-continuum coupling based on Bridging domain method

The main objective of this work is to propose an efficient corrective method for suppressing spurious effects (called ghost forces) that may arise in the atomistic-to-continuum coupling used for concurrent multi-scale modeling based on the minimization of a global energy functional. The coupling approach is related to the so-called Arlequin method, which is a general approach to couple different models by means of blending energy functional. Particularly the coupling is related to the bridging domain method developed by T. Belytschko et. al. The formulation refers to the partitioned domain problem with overlapping domains (handshake zone) where the displacement coupling is enforced by Lagrange multipliers. An approach using penalty method is also considered. The atomistic domain is treated with molecular mechanics to describe non-local atomic interactions by the pairwise harmonic and Lennard-Jones potentials, and continuum is discretized with finite elements. A Homogenized continuum model is obtained by calculating the strain energy density from underlaying atomistic structure via Cauchy-Born rule and representative volume element. The focus is currently on the static limit and 1D case.

atomistic-to-continuum coupling; bridging domain method; molecular mechanics; ghost forces; multi-scale method

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