Mechanical modeling of arbitrarily perforated orthotropic composites with the numerical manifold method

Abstract

With the widespread use of composites, analysis of their responses under various loadings is of significant importance. In this work, the mechanical behaviors of 2-D orthotropic composites with arbitrary holes are investigated by the numerical manifold method (NMM). Profiting from its unique dual cover systems, namely, the mathematical cover (MC) and the physical cover (PC), the NMM is able to model problems in arbitrarily-shaped physical domains with nonconforming MCs. The NMM global discrete equations are derived by the Galerkin method based on the governing equations, boundary conditions and also the NMM displacement approximations. To verify the convergence and also the accuracy of the proposed method, several numerical experiments are conducted through uniform MCs composed of square mathematical elements, and the results are in excellent agreement with the reference ones; besides, the effects of material principal direction and hole configurations on the mechanical behaviors of the orthotropic composites are also revealed.