Prevalent mean-field homogenization techniques excel in approximating effective stiffness, they fall short in predicting the stress states of individual inclusions within the same phase. Differential Mori-Tanaka (DMT) method presents possibilities for estimating stresses/strains in individual inclusions, which can be used for improved micromechanics of short fibre composites. This paper showcases inherent physical admissibility problems associated with DMT and proposes a novel modification to address them. The two schemes viz. DMT and modified-DMT are benchmarked using full-FE results. The modified-DMT effectively circumvents the physical admissibility problems with the DMT and is shown to results in qualitatively superior predictions of stresses in individual inclusions. 

Click the below link to read the full article: https://doi.org/10.1016/j.mechmat.2024.105125 

Mean field homogenization (MFH) methods are widely employed for homogenizing heterogeneous materials. However, they are limited to predicting effective properties and phase-averaged stresses, failing to capture stresses within individual inclusions. This paper introduces a novel homogenization approach, termed MDMT-Voigt, aimed at addressing this lacuna. The proposed model is validated extensively using finite element analysis (FEA), encompassing virtual Representative Volume Elements (RVEs) with a range of aspect ratios, volume fractions, and orientation distributions. Furthermore, validation is conducted using RVEs derived from experimentally determined microstructures via micro-computed tomography. Across all models considered, the FEA results yield a range of stresses for inclusions with same orientation and aspect ratio which is captured well by the proposed MDMT-Voigt model. Prediction of stresses in individual inclusions represents a significant advancement over conventional MFH methods, offering substantial potential for enhanced micromechanics modelling comparable to full finite element approaches, but at a computational efficiency order of magnitude lower. The paper ends with a demonstration confirming improved micromechanics using the Modified Coulomb criteria.

Click the below link to read the full article:

https://doi.org/10.1016/j.ijsolstr.2024.113152 

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 realizations 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.

Click the below link to read the full article:

https://doi.org/10.1016/j.mechmat.2023.104768