Three dimensional micro/macro-mechanical analysis of the interfaces of composites by a differential quadrature hierarchical finite element method

The enhancement effects of nanosized particles have been widely investigated and applied in multifunctional composite materials. It is recognized that the particles and their interfaces play important roles in the mechanical characteristics of nanocomposites. In this paper, a differential quadrature hierarchical finite element method (DQHFEM) for hexahedral, triangular prism and tetrahedral domains were applied to three dimensional analyses of the interfaces of composites for the first time. A continuum-based analytical model for the representative volume element (RVE) was built. And the interface was considered as the continuous geometry part without any subjective displacement assumptions. The particle and its interface were treated as different types of material with different elastic constants and are of different scale compared with the matrix of composites in the DQHFEM model. The particle and its interface were simulated by only one DQHFEM element respectively, which is impossible for common finite element method (FEM). Comparing the numerical results of the RVE model with those from other methods, the effectiveness and high accuracy of the DQHFEM for two-scale analysis of the problem was validated.