On multiple connectivity and reduction of constants for composites with body forces

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