Micromechanical analysis of unidirectional composites using a least-squares-based differential quadrature element method

Abstract

A generalized plane strain micromechanical model is developed to predict the stress and strain fields and overall elastic properties of a unidirectional fiber-reinforced composite subjected to various axial and transverse normal loading conditions using a least-squares-based differential quadrature element method (DQEM). The representative volume element (RVE) of the composite consists of a quarter of the fiber surrounded by matrix to represent the real composite with a repeating square array of fibers. The cubic serendipity shape functions are used to convert the solution domain to a proper rectangular domain and the new versions of the governing equations and boundary conditions are also derived. The fully bonded fiber-matrix interface condition is considered and the displacement continuity and traction reciprocity are imposed on the fiber-matrix interface. Application of DQEM to the problem leads to an overdetermined system of linear equations mainly due to the particular periodic boundary conditions of the RVE. A least-squares differential quadrature element method is used to obtain solutions for the governing partial differential equations of the problem. The numerical results are in excellent agreement with the available analytical and finite element studies. Moreover, the results of this study reveal that the presented model can provide highly accurate results with a very small number of elements and grid points within each element. In addition, the model shows advantages over conventional analytical models for fewer simplifying assumptions related to the geometry of the RVE.