Multiscale Methods for Fracture: A Review

Abstract

The global response of a system is often governed by the
material behaviour at smaller length scales. Investigating the system
mechanics at the smallest scale does not always provide the complete
picture. Therefore, in the ambitious objective to derive the overall fullscale
global response using a bottom-up approach, multiscale methods
coupling disparate length and time scales have been evolved in the past
two decades. The major objective of the multiscale methods is to reduce
the computational costs by coupling the inexpensive coarse-scale/continuum
based models with expensive fine-scale models. The fine-scale
region is employed in the critical areas, such as crack tips or core of the
dislocation. To improve the efficiency the fine-scale domain is adaptively
adjusted as the defects propagate. As a result, the accuracy of the finescale
model is combined with the efficiency of the coarse-scale model,
arriving at a computationally efficient and accurate multiscale model.
Currently, multiscale methods are applied to study problems in numerous
fields, involving multiphysics. In this article, we present an overview
of the multiscale methods for fracture applications. We discussed the
techniques to model the coarse- and fine-scale domains, details of the
coupling methods, adaptivity, and efficient coarse-graining techniques.
The article is concluded with comments on recent trends and future
scope.