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A method for coupling atomistic and continuum models across a subdomain, or bridge region, is presented. Coupling is effected through a force-based blending model. The method properly accounts for the the atomistic and continuum contributions to the force balance at points in the bridge region. Simple patch tests and computational experiments are used to study the method and its properties in one dimension. A discussion of implementation issues in higher dimensions is provided.

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 η N L−L , 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.

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Building on a general abstraction of the steps and transformations of a multiscale analysis, this chapter considers an approach to the development of multiscale simulation in which interoperable components can be effectively combined to address a wide range of multiscale simulations. Key concerns in the development of these interoperable components are maximizing the ability to use existing single simulation tools and supporting adaptive simulation control methods. In addition to indicating specific tools that have been developed to support multiscale simulations, an example adaptive atomistic/continuum simulation procedure is demonstrated.