A micromechanics-based analysis of effects of square and hexagonal fiber arrays in fibrous composites using DQEM

A micromechanics-based model is presented to predict stress and strain fields and overall elastic properties of a unidirectional (UD) fiber reinforced composite. The differential quadrature element method (DQEM) is formulated for the generalized plane strain assumption and used to obtain solution of the governing partial differential equations of the problem. The cubic serendipity shape functions are used to convert the solution domain to a proper rectangular domain and the new version of the governing equations and boundary conditions are also derived. Two types of representative volume elements (RVEs), e.g. square and hexagonal fiber array packing are considered to represent the real composite. Fully bonded fiber–matrix interface condition is considered and the displacement continuity and traction reciprocity are properly imposed to the interface. Application of the DQEM to the problem leads to an over-determined system of linear equations mainly due to the particular periodic boundary conditions of the RVEs. The Least-squares technique is then employed to obtain solutions for the resulted over-determined system of equations. Numerical results are in excellent agreement with the available analytical and finite element studies. However discrepancies are found between results of the two RVEs. The presented model can provide highly accurate results with very small number of elements and grid points within each element. In addition, the model shows advantages over conventional analytical models for less simplifying assumptions related to the geometry of the RVE.

► The stress/strain fields and overall properties of a UD composite are predicted.
► Square and hexagonal RVEs together with GPS condition are solved using DQEM.
► Numerical results are in excellent agreement with the other available predictions.
► The Tsai-Wu and Tsai-Hill failure criteria well agree with the presented DQEM.
► The DQEM associated with the least-squares approximation is an efficient approach.