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

Hsueh, Chun-Jen and Bhattacharya, Kaushik (2016) Homogenization and Path Independence of the J-Integral in Heterogeneous Materials. Journal of Applied Mechanics, 83 (10). Art. No. 101012. ISSN 0021-8936.

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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.

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Bhattacharya, Kaushik0000-0003-2908-5469
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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Issue or Number:10
Record Number:CaltechAUTHORS:20161017-154928755
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Official Citation:Hsueh C, Bhattacharya K. Homogenization and Path Independence of the J-Integral in Heterogeneous Materials. ASME. J. Appl. Mech. 2016;83(10):101012-101012-3. doi:10.1115/1.4034294
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:71195
Deposited By: Tony Diaz
Deposited On:17 Oct 2016 22:53
Last Modified:03 Oct 2019 16:04

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