Multiscale simulation using generalized interpolation material point (GIMP) method and molecular dynamics (MD)

J Ma and H Lu and B Wang and R Hornung and A Wissink and R Komanduri, CMES-COMPUTER MODELING IN ENGINEERING & SCIENCES, 14, 101-117 (2006).

A new method for multiscale simulation bridging two scales, namely, the continuum scale using the generalized interpolation material point (GIMP) method and the atomistic scale using the molecular dynamics (MD), is presented and verified in 2D. The atomistic strain from the molecular dynamics simulation is determined through interpolation of the displacement field into an Eulerian background grid using the same generalized interpolation functions as that in the GIMP method. The atomistic strain is consistent with that determined from the virial theorem for interior points but provides more accurate values at the boundary of the MD region and in the transition region between MD-GIMP A material point in the continuum is split into smaller material points using multi-level refinement until it has nearly reached the atom size to couple with atoms in the MD region. Consequently, coupling between GIMP and MD is achieved by using compatible deformation, force, and energy fields in the transition region between GIMP and MD. The coupling algorithm is implemented in the Structural Adaptive Mesh Refinement Application Infrastructure (SAMRAI) for parallel processing. Both mode I and mode II crack problems are simulated using the coupling algorithm. The stress field near the crack tip was verified by comparing the results from the coupled simulations with purely GIMP simulations of the same model. Coupled simulation results were also compared with pure MD simulation results. In both cases, a very good agreement was obtained.

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