Energy-based definition of equivalent inhomogeneity for various interphase models and analysis of effective properties of particulate composites

A new concept of equivalent inhomogeneity is proposed to facilitate analysis of effective properties of composites with interphases using techniques devised for problems without interphases. The basic idea to replace the inhomogeneity and its interphase by a single equivalent inhomogeneity (combining properties of both) is akin to previously proposed developments but the criterion of equivalency is entirely different. It is based on Hill's energy equivalence principle, and is illustrated considering spherical inhomogeneity with Gurtin–Murdoch surface model and spring layer model of interphases. The validity of the suggested technique is documented by remarkably good agreement with the best available solutions for composites containing spherical inhomogeneities with spring layer model of interphase.