Composite materials are involving in engineering applications at a growing speed, due to their stiffer, stronger and lighter properties. This growth requires fast and powerful numerical methods like Boundary Element Method (BEM), and Finite Element Method (FEM). BEM has become popular especially in the last decade due to its advantage of requiring less computation time for the same accuracy. The objective of this study is, by using Boundary Element Method, to examine different shapes of reinforcement elements under unit traction and unit displacement boundary conditions in transversal direction and perfect interfacial bonding. The stress variations along the interface of the matrix and reinforcing material, effective elastic modulus of composites were studied due to different shapes and different volume fractions of reinforcement elements. These calculations were made for both the internal Representative Volume Element (RVE), and boundary RVE, which are the internal and boundary cells of composite material respectively. Finally, using an appropriate failure criterion, the failures of different shapes were examined and also the effective elastic modulus variations of the shapes during the progress of the failure for both internal and boundary RVE were studied.
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