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TECHNICAL PAPERS

The Interaction of Two Spherical Gas Bubbles in an Infinite Elastic Solid

[+] Author and Article Information
F. Chalon, F. Montheillet

Division for Materials and Structures Sciences, URA CNRS 1884, Ecole Nationale Supérieure des Mines de Saint-Etienne, 158 cours Fauriel, 42000 Saint-Etienne, France

J. Appl. Mech 70(6), 789-798 (Jan 05, 2004) (10 pages) doi:10.1115/1.1629110 History: Received February 26, 2002; Revised June 10, 2003; Online January 05, 2004
Copyright © 2003 by ASME
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References

Lasser, R., 1989, Tritium and Helium-3 in Metals, Springer-Verlag, Berlin.
Sternberg,  E., and Sadowsky,  M. A., 1952, “On the Axisymmetric Problem of the Theory of Elasticity for an Infinite Region Containing Two Spherical Cavities,” ASME J. Appl. Mech., 19, pp. 19–27.
Boussinesq, J., 1885, Applications des Potentiels, Gauthier-Villars, Paris.
Miyamoto,  H., 1958, “On the Problem of Theory of Elasticity for a Region Containing More Than Two Spherical Cavities,” Bull. JSME, 1(2), pp. 103–108.
Tsuchida,  E., Nakahara,  I., and Kodama,  M., 1976, “On the Asymmetric Problem of Elasticity Theory for Infinite Elastic Solid Containing Some Spherical Cavities,” Bull. JSME, 19(135), pp. 993–1000.
Shelley,  J. F., and Yu,  Y. Y., 1966, “The Effect of Two Rigid Spherical Inclusions on the Stresses in an Infinite Elastic Solid,” ASME J. Appl. Mech., 33, pp. 68–74.
Chen,  H. S., and Acrivos,  A., 1978, “The Solution of the Equations of Linear Elasticity for an Infinite Region Containing Spherical Inclusions,” Int. J. Solids Struct., 14, pp. 331–348.
Willis,  J. R., and Bullough,  R., 1969, “The Interaction of Finite Gas Bubbles in a Solid,” J. Nucl. Mater., 32, pp. 76–87.
Papkovitch,  P. F., 1932, “Solution générale des équations différentielles fondamentales d’élasticité, exprimées par trois fonctions harmoniques,” C. R. Acad. Sci. Paris, 195, pp. 513–515.
Neuber, H., 1944, Kerbspannungslehre, J. W. Edwards, Ann Arbor, MI.
Eshelby,  J. D., 1957, “The Determination of the Elastic Field of an Ellipsoidal Inclusion and Related Problems,” Proc. R. Soc. London, Ser. A, A241, pp. 376–396.
Mura, T., 1982, Micromechanics of Defects in Solids, Martinus Nijhoff, Dordrecht, The Netherlands.

Figures

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Decomposition of the problem
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The two cavities and the set of Cartesian coordinates
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The finite element mesh: (a) general view; (b) the area close to the cavities
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(a) Mean stress along axis x3 for two bubbles of same size with same pressure; (b) mean stress along axis x3 for two bubbles of different sizes with same pressure; (c) von Mises equivalent stress along axis x3 for two bubbles of same size with same pressure, and (d) von Mises equivalent stress along axis x3 for two bubbles of different sizes with same pressure
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Mean stress and von Mises equivalent stress maps for two bubbles of same size with same pressure
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Mean stress and von Mises equivalent stress maps for two bubbles of different sizes with same pressure  
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Von Mises equivalent stress along axis x3 and von Mises equivalent stress maps for two bubbles of same size with different pressures

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