Transition between the models in multiscale simulations: Continua and granular materials

Abstract

We consider two‐scale problems: the fine‐scale and the coarse‐scale. The coarse model is taken to be a continuum. The key question in this class of problems is related to the simulation of the fine‐scale cell: How are the coarse‐scale fields to be passed onto the fine scale? Often used periodic boundary conditions, have important drawbacks. The mathematical conditions that answer this question are called minimal boundary conditions (MBC). MBC are imposed on a fine‐scale computational cell as a constraint derived from the coarse‐scale model. They are minimal in the sense that nothing but the desired constraint is imposed—in contrast to periodic boundary conditions. Owing to their integral nature, the MBC can be applied to any shape of the fine‐scale computational cell. The application to fine‐scale continuum models has been discussed earlier, Mesarovic and Padbidri [1]. In this paper, we discuss application of MBC to fine‐scale discrete models with local interactions—granular materials. The key to this application is the equivalent representation of kinematics of granular flow using the Delaunay network.