Improved micromechanical prediction of short fibre reinforced composites using differential Mori-Tanaka homogenization

Abstract

Due to the spatial distribution of inclusions in random heterogeneous media, individual inclusions are stressed differently. Mean field homogenization (MFH) methods, a popular homogenization method, cannot account for this variability, instead predicting the same mean value of stress for a particular phase. In this paper, a differential scheme is expanded to calculate the stresses in the individual inclusions, including the scatter and variation of local stresses. The accurate prediction of stress variability of stresses within a particular phase has led to more accurate and realistic modelling of inclusion matrix debonding and inclusion breakage.Extensive benchmarking of the proposed models against finite element (FE) results confirms excellent predictive abilities of scatter at three length scales (effective property, individual inclusions, and matrix-inclusion interface). The potential of modelling stress variability post-onset of damage is also demonstrated.Different realisations of the differential Mori Tanaka (MT) lead to varying predictions of scatter in the individual inclusion stresses. However, the effective properties predictions remain consistent.The prediction of individual inclusion stresses, and their scatter constitutes a significant gap in the literature and has been addressed in this paper. This new scheme could lead to the development of several intricate models of damage in various composites without the need for extensive FE modelling.