Fibrous nanocomposites with interface stress: Hill's and Levin's connections for effective moduli

摘要

We study the macroscopic behavior of solids containing circular cylindrical nanoinclusions of the same size with surface effects prevailing at interfaces. The overall thermomechanical properties of these solids are shown to comply with two sets of exact connections. The first set, similar to Hill's universal connections, provides two constraints among the three axisymmetric overall elastic moduli. The second set relates the effective coefficients of thermal expansion to the effective moduli, in analogy with Levin's formula. In contrast to the classical results, the presence of surface effects makes both sets of connections dependent on the absolute size of the nanoinclusions.