In this paper, a three-dimensional penny-shaped isotropic inhomogeneity surrounded by unbounded isotropic matrix in a uniform stress field is studied based on Eshelby’s equivalent inclusion method. The solution including the deduced equivalent eigenstrain and its asymptotic expressions is presented in tensorial form. The so-called energy-based equivalent inclusion method is introduced to remove the singularities of the size and eigenstrain of the Eshelby’s equivalent inclusion of the penny-shaped inhomogeneity, and yield the same energy disturbance. The size of the energy-based equivalent inclusion can be used as a generic damage measurement.
Asymptotic Solutions of Penny-Shaped Inhomogeneities in Global Eshelby’s Tensor
Contributed by the Applied Mechanics Division of THE AMERICAN SOCIETY OF MECHANICAL ENGINEERS for publication in the ASME JOURNAL OF APPLIED MECHANICS. Manuscript received by the ASME Applied Mechanics Division, April 18, 2000; final revision, Jan. 8, 2001. Associate Editor: D. Kouris. Discussion on the paper should be addressed to the Editor, Professor Lewis T. Wheeler, Department of Mechanical Engineering, University of Houston, Houston, TX 77204-4792, and will be accepted until four months after final publication of the paper itself in the ASME JOURNAL OF APPLIED MECHANICS.
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Yang, Q., Zhou, W. Y., and Swoboda, G. (January 8, 2001). "Asymptotic Solutions of Penny-Shaped Inhomogeneities in Global Eshelby’s Tensor ." ASME. J. Appl. Mech. September 2001; 68(5): 740–750. https://doi.org/10.1115/1.1380676
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