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

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.