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Published November 2014 | public
Journal Article

Effective toughness of heterogeneous media


We propose a versatile approach to computing the effective toughness of heterogeneous media. This approach focusses on the material property independent of the details of the boundary condition. The key idea is what we call a surfing boundary condition, where a steadily propagating crack opening displacement is applied as a boundary condition to a large domain while the crack set is allowed to evolve as it chooses. The approach is verified and used to study examples in brittle fracture. We demonstrate that effective toughness is different from effective or weighted surface area of the crack set. Furthermore, we demonstrate that elastic heterogeneity can have a profound effect on fracture toughness: it can be a significant toughening mechanism and it can lead to toughness asymmetry wherein the toughness depends not only on the direction but also on the sense of propagation. The role of length-scale is also discussed.

Additional Information

© 2014 Elsevier Ltd. Received 24 December 2013; Received in revised form 15 May 2014; Accepted 11 June 2014; Available online 20 June 2014. We have greatly benefited from many discussions with Chris J. Larsen and G. "Ravi" Ravichandran, and are grateful for their insights, criticism and encouragement. We are also grateful for the insightful comments of the reviewers. MZH, C-JH and KB gratefully acknowledge the financial support of the U.S. National Science Foundation (Grant No. CMMI-1201102). BB׳s work was supported in part by the National Science Foundation Grant No. DMS-0909267. Some numerical experiments were performed using resources of the Extreme Science and Engineering Discovery Environment (XSEDE), which is supported by National Science Foundation grant number OCI-1053575 under the Resource Allocation TG- DMS060014, and some using the Garuda Computational Cluster which are partially funding through a DURIP grant from the US Army Research Office.

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