On the Application of the Mean-Field Homogenization for Non-isotropic Matrix

Mean field homogenization methods like the Mori–Tanaka formulation are used to determine the effective response of heterogeneous materials. Typically, these methods are deployed for inclusions within the isotropic matrix. This is due to the availability of closed-form solutions for Eshelby’s tensor when the surrounding medium is isotropic. However, in real life, the matrix can often be transversely isotropic or even orthotropic. This paper proposes a model for the implementation of the Mori–Tanaka formulation for all types of matrices. The proposed method is implemented and validated against full finite element models for three length scales: effective properties (RVE level), phase average stresses (constituent level) and interface stresses. The proposed models are seen to deliver reasonable results at the different length scales for transversely isotropic as well as orthotropic matrices.