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Published October 2016 | Published
Journal Article Open

Homogenization and Path Independence of the J-Integral in Heterogeneous Materials


The J-integral that determines the driving force on a crack tip is a central concept of fracture mechanics. It is particularly useful since it is path independent in homogeneous materials. However, most materials are heterogeneous at a microscopic scale, and the J-integral is not necessarily path independent in heterogeneous media. In this paper, we prove the existence of an effective J-integral in heterogeneous media, show that it can be computed from the knowledge of the macroscopic or homogenized displacement fields and that it is path independent in macroscopically homogeneous media as long as the contours are large compared to the length scale of the heterogeneities. This result justifies the common engineering use of the J-integral.

Additional Information

© 2016 by ASME. Paper No: JAM-16-1355; doi: 10.1115/1.4034294. Received July 13, 2016; Revised July 20, 2016. We gratefully acknowledge the financial support of the U.S. National Science Foundation Award No. DMS-1535083 under the Designing Materials to Revolutionize and Engineer our Future (DMREF) Program.

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August 20, 2023
October 23, 2023