A truly generalized plane strain meshless method for combined normal and shear loading of fibrous composites

Abstract

A truly meshless method based on the integral form of equilibrium equations is developed and formulated to study the micro-stresses in the unidirectional fiber reinforced composite material which is subjected to the normal and shear load. The presented meshless method is formulated for a special form of generalized plane strain assumption and is employed for micromechanical modeling of the composite. A small repeating area of the composite including a fiber surrounded by matrix, which is called representative volume element (RVE) is considered as the solution domain. A direct method is proposed for the enforcement of the appropriate periodic boundary conditions to the representative volume element (RVE) in shear and normal loading conditions. The computational efforts of the method are reduced because the domain integration has been eliminated from the formulation. The fully bonded interface condition is investigated and the continuity of displacements and traction is directly imposed to the fiber–matrix interface. Comparison of the predicted results shows excellent agreement with the results in the available literature. Results of this study also revealed that the presented model can provide highly accurate predictions with relatively small number of nodes and small computational time.