Pseudo-grain discretization and full Mori Tanaka formulation for random heterogeneous media: Predictive abilities for stresses in individual inclusions and the matrix

Both effective properties of composite and the stresses in the individual inclusions and in the matrix are necessary for modelling damage in short fibre composites. Mean field theorems are usually used to calculate the effective properties of composite materials, most common among them is the Mori-Tanaka formulation. Owing to occasional mathematical and physical admissibility problems with the Mori-Tanaka formulation, a pseudo-grain discretized Mori-Tanaka formulation (PGMT) was proposed in literature. This paper looks at the predictive capabilities for stresses in individual inclusions and matrix as well as the average stresses in inclusion phase for full Mori-Tanaka and PGMT formulation for 2D planar distribution of orientation of inclusions. The average stresses inside inclusions and the matrix are compared to solutions of full-scale finite element (FE) models for a wide range of configurations. It was seen that the Mori-Tanaka formulation gave excellent predictions of average stresses in individual inclusions, even when the basic assumptions of Mori-Tanaka were reported to be too simplistic, while the predictions of PGMT were off significantly in all the cases. The predictions of the matrix stresses by the two methods were found to be very similar to each other. The average value of stress averaged over the entire inclusion phase was also very close to each other. The Mori-Tanaka formulation must be used as the first choice homogenization scheme.