An Atomistic-to-Continuum Framework for Nonlinear

Report No. ARL-RP-161
Authors: John D. Clayton; Peter W. Chung
Date/Pages: February 2007; 42 pages
Abstract: Presented is a multiscale methodology enabling description of the fundamental mechanical behavior of crystalline materials at the length scale of a macroscopic continuum (i.e., millimeter resolution) given a characterization of discrete atomic interactions at the nanoscale (i.e., angstrom resolution). Asymptotic homogenization methods permit the calculation of effective mechanical properties (e.g. strain energy, stress, and stiffness) of a representative crystalline volume element containing statistically periodic defect structures. From a numerical standpoint, the theoretical?computational method postulated and implemented here in the context of lattice statics enables prediction of minimum energy configurations of imperfect atomic-scale crystals deformed to finite strain levels. Numerical simulations demonstrate the utility of our framework for the particular case of bodycentered- cubic tungsten. Elastic stiffness and energetic properties of periodic unit cells containing vacancies, screw dislocations, and low-angle twist boundaries are computed. Nonlinear aspects of elastic behavior in the context of plastic flow are then modeled from the perspective of atomistic-to-continuum homogenization, following the introduction of a minimal set of kinetic assumptions required to account for the propagation of dislocations across the unit cell at finite deformations.
Distribution: Approved for public release
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Last Update / Reviewed: February 1, 2007