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An alternating method based on the VNA solution for analysis of damaged solid containing arbitrarily distributed elliptical microcracks

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Abstract

This paper presents the development of an alternating method for the interaction analysis of arbitrary distributed numerous elliptical microcracks. The complete analytical solutions (VNA solutions) for a single elliptical crack in an infinite solid, subject to arbitrary crack-face tractions, are implemented in the present alternating method, together with the coordinate transformations for stress tensors. First, the present method is verified by solving the problems of two interacting cracks for which accurate numerical solutions have been obtained previously. Next, the present method demonstrates obtaining efficient and accurate solutions for the problems of many interacting elliptical cracks, which cannot be solved in a practical sense by the ordinary numerical methods such as the finite element method. Furthermore, damaged solids containing periodically distributed elliptical microcracks are analyzed by the present alternating method. The effective elastic moduli are evaluated for varying microcrack density. Detailed structures of the interactions in the damaged solids are visualized and clarified.

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Authors and Affiliations

  1. Department of Ocean Mechanical Engineering, Kobe University of Mercantile Marine, 5-1-1 Fukae Minamimachi, Higashinada-ku, Kobe, 658, Japan. e-mail

    Toshihisa Nishioka & Tetsuji Kato

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  1. Toshihisa Nishioka
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  2. Tetsuji Kato
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Nishioka, T., Kato, T. An alternating method based on the VNA solution for analysis of damaged solid containing arbitrarily distributed elliptical microcracks. International Journal of Fracture 97, 137–170 (1999). https://doi.org/10.1023/A:1018745005441

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