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Double Inclusion Analysis



The stress field is derived analytically for a three-phase elastic material in which a spherical inclusion is surrounded by another inclusion with different material properties outside which lies an unbounded medium subject to a uniform strain at infinity. The derived stress expressions are novel and in closed form which can supersede the work by Christenson and Lo. A computer algebra system is essential for the analysis without which it is not possible to handle the amount of algebra involved. The stress field inside the innermost inclusion can be used for calculating the effective elastic stiffness of composites. It is also possible to extend the analysis to n-phase (layered) materials.


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