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Reliability of Atomistic-Continuum Modeling Simulations for Problems in Molecular Statics

S. Prudhomme, JP. Bauman and .T. Oden
The University of Texas at Austin, US

error estimation, adaptivity, nanoindentation

Multi-scale computational modeling aims at developing systematic techniques for bridging scales between atomistic models and continuum models in order to increase the speed of dynamical calculations. Continuum level models can simulate large volumes of material, at the expense of accuracy. Conversely, nanoscale models can accurately capture small-scale features, but are computationally too slow to simulate large (useful) volumes of material. The goal of multi-scale modeling is to take advantage of the fact that in many systems, only a small percentage of the total region is of interest. However, the main challenge in implementing multi-scale approaches lies in determining which regions are simulated with a continuum model or a nanoscale model, and to adequately model the transition region. Here, we apply the Goal-Oriented Adaptive Modeling method to problems in molecular statics. This method has been recently developed to control modeling errors in computational simulations with the purpose of providing accurate solutions with respect to user-defined quantities of interest and has been successfully employed in a variety of problems in mechanics. Goal Oriented Adaptive Modeling is a general framework based on an error estimation module that estimates the error between two different models, and an adaptive algorithm module that automatically selects the models to be used in the various regions of the computational domain. The method involves solving a dual problem whose solution indicates how the sources of errors influence the error in the targeted quantity of interest. We show here how the algorithm can be applied to a nanoindentation problem using the quasicontinuum method.

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