FINITE-ELEMENT SOLUTION OF THE PROBLEM OF A SPHERICAL INHOMOGENEITY IN AN INFINITE POWER-LAW VISCOUS MATRIX

The problem of a spherical inclusion surrounded by an unbounded matrix loaded at infinity plays a prominent role in the mechanics of materia ls, and is addressed in this paper for power-law viscous materials via the finite element method. With respect to a previous analysis, the r esults of which are further developed, the influence of the necessaril y finite size of the mesh is carefully analyzed (by using two types of boundary conditions, among other tests) and two finite element codes are compared. In addition to the localization rules for the strain rat e and stress deviator in the inclusion, the analysis also covers the i nfluence of a dilute concentration of deformable spheres in a power-la w matrix, which generalizes previous studies on cavities or rigid incl usions. All the results are fitted by curves, and this is expected to assist in further practical applications. (C) Elsevier, Paris.