ON MULTIPLE CONNECTIVITY AND REDUCTION OF CONSTANTS FOR COMPOSITES WITH BODY FORCES

In this paper we discuss the problem of reduction of constants in plan e elasticity when a two-phase material is subjected to body forces, an d we focus on multiply connected materials with either perfectly bonde d or slipping interfaces. We derive the generalized Michell conditions for a multiply connected single-phase material with body forces, as w ell as the conditions under which constant shift in the compliances (l eading to the reduction of elastic parameters) is possible for two-pha se multiply connected composites with bonded and slipping interfaces. Also, we present several examples including the concentrated force pro blem, which depends on Poisson's ratio, and the concentrated moment pr oblem, which does not.