We study the effective behaviour of a periodic array of microscopic cracks inside a homogeneous conductor. Special emphasis is placed on a rigorous study of the case in which the corresponding effective conductivity becomes nearly singular, due to the fact that adjacent cracks nearly touch. It is heuristically shown how thin clusters of such extremely close cracks may macroscopically appear as a single crack. The results have implications for our earlier work on impedance imaging.
Bryan, Kurt M. and Vogelius, Michael, "Effective Behavior of Clusters of Microscopic Cracks Inside a Homogeneous Conductor" (1996). Mathematical Sciences Technical Reports (MSTR). 115.