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Research Papers

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

[+] Author and Article Information
Chun-Jen Hsueh

Department of Mechanical and Civil Engineering,
California Institute of Technology,
Pasadena, CA 91125
e-mail: chhsueh@caltech.edu

Kaushik Bhattacharya

Department of Mechanical and Civil Engineering,
California Institute of Technology,
Pasadena, CA 91125
e-mail: bhatta@caltech.edu

Contributed by the Applied Mechanics Division of ASME for publication in the JOURNAL OF APPLIED MECHANICS. Manuscript received July 13, 2016; final manuscript received July 20, 2016; published online August 22, 2016. Editor: Yonggang Huang.

J. Appl. Mech 83(10), 101012 (Aug 22, 2016) (3 pages) Paper No: JAM-16-1355; doi: 10.1115/1.4034294 History: Received July 13, 2016; Revised July 20, 2016

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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Grahic Jump Location
Fig. 1

A macroscopic crack in a quasi-periodic heterogeneous medium

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