Checkerboard composites and the Motola-Steffe conjecture

Abstract: In this talk an overview of doubly periodic composite structures will be given and their relevance to real structures discussed. The explicit solution for a doubly periodic rectangular composite structure will be derived. From this many special cases descend and in particular a long-standing conjecture on the effective properties of a square four phase checkerboard composites (Mortola and Steffe 1985) is proved true. Other doubly periodic structures and patterns will be discussed, as will limitations in the current approach.