Development of the hybrid finite element method for applications to heterogeneous materials

In this study, a hybrid finite element method (HFEM) is developed for accurate prediction of the mechanical behavior of heterogeneous materials. A series of physical phenomena arising in heterogeneous materials are investigated based on the developed HFEM. These include the analysis of fluid-filled porous materials, thermal expansion mismatch, microcracking and transformation toughening in heterogeneous materials.; To solve these problems, several special elements are constructed based on the Hellinger-Reissner variational principle. Special approximating functions are generated in Muskhelishvili's complex variable method. This combination of the finite element method with the analytical approach results in a computationally-efficient method that can easily model the medium with random distribution of inclusions and/or microcracks.; In the effort to model the problem of fluid-filled porous materials with randomly distributed pores and pore pressure at the pore surfaces, a special element with an n-sided pore-embedded polygon is constructed. The effect of the pores and pore pressure on the local elastic field is well represented in the resulting element formulation. For a thermal expansion mismatch problem, the then-no-mechanical coupled problem is first transformed to a purely mechanical problem with prescribed thermal body-force and surface traction at the interface between particles and matrix based on the Duhamel-Newmann analogy. Then, a special element with surface traction at the interface is constructed. Residual stress due to the thermal expansion mismatch is then obtained by the developed HFEM. To investigate the cracking phenomena in heterogeneous materials, a special crack-tip element with traction acting on the crack surfaces is constructed. For transformation toughening, a special element which can represent the transformation response is constructed. An iterative procedure is presented to investigate the crack growth in the transformation toughening materials. The developed procedure can be applied to the problems of stress-induced transformation toughening to predict the increase of the fracture toughness and transformation zone size for the materials.; The proposed method is verified by comparing the results from this study with the traditional FEM simulation results, experimental results, and/or analytical solutions. From the provided examples, the efficiency of the proposed method as well as its accuracy is demonstrated in capturing the local stress distribution at the interface of inclusions and matrix. Such predictions will be very useful towards improving the mechanical behavior of the materials and/or designing of new materials.