Bridging Methods for Atomistic-to-continuum Coupling and Their Implementation

Bridging Methods for Atomistic - to - Continuum 2 Coupling and Their Implementation

Bridging Methods for Coupling Atomistic and Continuum Models

We review some recent developments in the coupling of atomistic and continuum models based on the blending of the two models in a bridge region connecting the other two regions in which the models are separately applied. We define four such models and subject them to patch and consistency tests. We also discuss important implementation issues such as: the enforcement of displacement continuity ...

Blended Atomistic-to-Continuum coupling analyses and methods

This article considers the blending of atomistic and continuum problems on a bridging subdomain building upon the ideas introduced in [1, 2, 7]. The continuity of the atomistic and continuum solutions is imposed by a constraint operator using Lagrange multipliers. These methods are stated in an abstract form. The consistency of these methods is analyzed. A new blending model is designed using m...

Blending Methods for Coupling Atomistic and Continuum Models

In this paper we review recent developments in blending methods for atomistic-to-continuum (AtC) coupling in material statics problems. Such methods tie together atomistic and continuum models by using a bridge domain that connects the two models. There are several reasons why AtC coupling methods (of which blending methods are a subset) are important and have been subject to an increased inter...

A Mathematical Analysis of Atomistic to Continuum Coupling Methods

a. Mathematical upscaling: derivation of coarse-scale equations directly from atomistic equations using Generalized Mathematical Homogenization theory (Fish, Chen, Li, 2007). b. Computational upscaling: reducing the complexity of solving an atomistic problem to a manageable size that can be adapted based on available computational resources. Our model reduction approach is based on the space-ti...