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Estimation of crack density due to fragmentation of brittle ellipsoidal inhomogeneities embedded in a ductile matrix

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Abstract

An estimation is found for the energy release due to fragmentation of a brittle inhomogeneity of ellipsoidal shape embedded in a ductile matrix under remote static loading. In the state of completed fragmentation the inhomogeneity is replaced by a void with zero stiffness. Thus, the problem of estimating the energy release reduces to the eigenstrain problem solved by Eshelby. The energy release calculated for prolate spheroidal inhomogeneities is used in the balance of energy to determine the crack density. The application to the geological system of garnet inhomogeneities embedded in a quartz matrix is considered.

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Authors and Affiliations

  1. Lehrstuhl für Allgemeine Mechanik, Ruhr-Universität Bochum, 44780, Bochum, Germany

    K. C. Le, M. Korobeinik & K. Hackl

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  1. K. C. Le
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  2. M. Korobeinik
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  3. K. Hackl
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Correspondence to K. C. Le.

Additional information

The authors thank C. Trepmann and B. Stöckhert for helpful discussions and for providing Fig. 1. They also thank the reviewers for their constructive suggestions. The financial support by the DFG (German Science Foundation) within the Collaborative Research Center 526 (project D9) is gratefully acknowledged.

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Le, K., Korobeinik, M. & Hackl, K. Estimation of crack density due to fragmentation of brittle ellipsoidal inhomogeneities embedded in a ductile matrix. Arch Appl Mech 74, 439–448 (2005). https://doi.org/10.1007/s00419-004-0367-0

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  • DOI: https://doi.org/10.1007/s00419-004-0367-0

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