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Adaptive Model Selection Procedure for Concurrent Multiscale Problems

DOI: 10.1615/IntJMultCompEng.v5.i5.20
pages 369-386

Mohan A. Nuggehally
Scientific Computation Research Center, Rensselaer Polytechnic Institute, 110 8th St., Troy, NY 12180, USA

Mark S. Shephard
Department of Mechanical and Aerospace Engineering, Rensselaer Polytechnic Institute Troy, NY, 12180, USA

Catalin Picu
Department of Mechanical Engineering Rensselaer Polytechnic Institute Troy, NY, 12180, USA

Jacob Fish
Civil Engineering and Engineering Mechanics, Columbia University, New York, New York 10027, USA

Abstract

An adaptive method for the selection of models in a concurrent multiscale approach is presented. Different models from a hierarchy are chosen in different subdomains of the problem domain adaptively in an automated problem simulation. A concurrent atomistic to continuum (AtC) coupling method [27], based on a blend of the continuum stress and the atomistic force, is adopted for the problem formulation. Two error indicators are used for the hierarchy of models consisting of a linear elastic model, a nonlinear elastic model, and an embedded atom method (EAM) based atomistic model. A nonlinear indicator , which is based on the relative error in the energy between the nonlinear model and the linear model, is used to select or deselect the nonlinear model subdomain. An atomistic indicator is a stress-gradient-based criterion to predict dislocation nucleation, which was developed by Miller and Acharya [6]. A material-specific critical value associated with the dislocation nucleation criterion is used in selecting and deselecting the atomistic subdomain during an automated simulation. An adaptive strategy uses limit values of the two indicators to adaptively modify the subdomains of the three different models. Example results are illustrated to demonstrate the adaptive method.