HYBRID MORI-TANAKA/FINITE ELEMENT METHOD IN HOMOGENIZATION OF COMPOSITE MATERIALS WITH VARIOUS REINFORCEMENT SHAPE AND ORIENTATION

This paper is devoted to application of hybrid Mori-Tanaka/finite element method for modeling of composite materials reinforced with inclusions of arbitrary shape and random orientation. The paper discusses numerical procedures connected with the hybrid homogenization both for linear and nonlinear composites. Homogenization in nonlinear regime is performed by coupling the Mori-Tanaka model with the finite element solution of the equivalent inclusion problem through an iterative procedure. Moreover, the paper introduces a novel approach of modified equivalent inclusion problem that allows one to analyze composites with misaligned inclusions. Composites containing an elastic-plastic matrix reinforced with linear-elastic spherical and cubic particles have been analyzed. Results obtained by using the hybrid homogenization method are compared to the pure numerical solution achieved by the finite element homogenization based on the representative volume element containing a substantial number of inclusions. In general, good agreement between results obtained by using the hybrid and the pure numerical homogenization has been noted.