LAUSR

In this paper, a finite element method is proposed to analyze the microscopic and macroscopic mechanical behaviors of heterogeneous media with randomly distributed inclusions. A simple mesh partitioned the domain into regular quadrilateral or triangular elements, where one element may contain two phases. An assumed stress hybrid formulation is implemented in the finite element model and the functional is derived for an element containing two phases. Numerical examples were used to study the microscopic and macroscopic properties of the composites, such as the effective modulus, to validate of the proposed model. The results show that the proposed multiphase hybrid stress finite element model can accurately measure the stress fields of materials with arbitrary microstructural distributions and improve computational efficiency by about 30 to 1500 times in comparison with the traditional displacement based finite element method.