Elastic coefficients of composites containing spherical inclusions in a periodic array (Q1079974)

The effective elasticity tensor of a composite medium consisting of spherical elastic particles firmly embedded in a periodic cubic arrangement into another elastic medium is characterized by three scalars \(\alpha\), \(\beta\) and \(\gamma\). We employ a method of singularity distribution and determine these scalars for various values of volume fraction of the spheres and the Lamé constants of the particles and the matrix. The results, which are presented for the simple, body-centered and face-centered cubic arrays, are in agreement with the previously known results of \textit{K. C. Nunan} and \textit{J. B. Keller} [ibid. 32, 259- 280 (1984; Zbl 0549.73003)] for the rigid particles and of \textit{T. Iwakuma} and \textit{S. Nemat-Nasser} [Computers and Structures 16, 13-19 (1983; Zbl 0498.73116)] for the non-rigid particles.