A hybrid finite element method for heterogeneous materials with randomly dispersed elastic inclusions

Abstract A new hybrid finite element method is presented for the mechanical analysis of heterogeneous materials with randomly dispersed inclusions. A special n-sided polygonal element with an elastic inclusion is developed on the basis of the Hellinger-Reissner principle. The element formulations are derived by decomposing the original problem into inclusion and matrix problems and relating each other through consistency conditions at their interface. For circular inclusions, the proposed method is verified against simple analytical solutions and shown to be suitable even for extreme cases such as porous materials and materials with rigid inclusions. It is also demonstrated that the effect of random packing of inclusions on stress concentration factors can be easily evaluated using the proposed method.