The elastic strain and stress fields between two bubbles of different sizes and different pressures were estimated by using the fundamental result of Eshelby. The equivalent inclusion method was extended to the case of two inclusions in an infinite elastic solid. This approach, which remains totally analytical, was compared successfully to finite element calculations. The mean stress provides information about gas diffusion between the bubbles: according to the results, the bubbles are likely to progressively equalize their sizes. Moreover, the derivation of the von Mises equivalent stress showed that its value, in the vicinity of the bubbles, is larger than the elasticity limit. Therefore, for a complete mechanical description of the problem, plasticity should be taken into account. In spite of its simplicity, this method nevertheless leads to results, which are very close to the prediction of numerical calculations.
The Interaction of Two Spherical Gas Bubbles in an Infinite Elastic Solid
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, February 26, 2002; final revision received, June 10, 2003. Associate Editor: A. Needleman. Discussion on the paper should be addressed to the Editor, Prof. Robert M. McMeeking, Department of Mechanical and Environmental Engineering, University of California—Santa Barbara, Santa Barbara, CA 93106-5070, and will be accepted until four months after final publication of the paper itself in the ASME JOURNAL OF APPLIED MECHANICS.
Chalon , F., and Montheillet, F. (January 5, 2004). "The Interaction of Two Spherical Gas Bubbles in an Infinite Elastic Solid ." ASME. J. Appl. Mech. November 2003; 70(6): 789–798. https://doi.org/10.1115/1.1629110
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