The second Stekloff eigenvalue of an inclusion and new size effects for composites with interface thermal barriers

Abstract

Two‐phase particle reinforced composites are considered. We treat the case when there is an interfacial thermal barrier between phases. We obtain the geometric criterion that determines when the effects of the interfacial thermal barrier overcome the benefits of a highly conducting reinforcement. This criterion is general and applies to any reinforcement with Lipschitz continuous boundary. It is given in terms of the second Stekloff eigenvalue of the reinforcement. This result is used to predict size effects for a general class of inclusion shapes.