Multiscale Methods for Fracture: A Review

PR Budarapu and T Rabczuk, JOURNAL OF THE INDIAN INSTITUTE OF SCIENCE, 97, 339-376 (2017).

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 full-scale 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 fine-scale 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.

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