Generalized eshelby integral formula for multiple inclusion composite materials

Abstract

Eshelby integral formula, which was initially derived for a single inclusion embedded in all matrix system, plays a fundamental role in the micromechanics of composite or heterogeneous materials. The integral formula is remarked to be readily generalized to the case of multiple inclusions. However, the proof for such case has never been established. Herein, the integral formula is reformulated within the frameworks of generalized self-consistent method for the case of multiple inclusion composite system and thus, establishing the proof of its generalized version. © Springer Nature Singapore Pte Ltd 2020.