An iterative numerical scheme for the calculation of the effective moduli of heterogeneous materials with finite element method

摘要

An iterative numerical scheme to calculate the effective moduli of a heterogeneous material is presened based on the finite element method. The effect of the inclusions on the effective moduli of the heterogeneous material is embodied in a virtual local body force caused by eigenstrain within the equivalent homogeneous material in the scheme. The effective moduli of the original material are achieved by iteratively calculating the virtual local body force with the adoption of two systems of mesh in the scheme. The meshes in the first system discretize the whole domain and serve as the finite element meshes to obtain the solution, and the meshes in the second system discretize the inclusions. The difficulty of mesh generation due to inclusions is overcome by the complete independence between the two systems of mesh. Examples are presented to verify the validity of the scheme, and its convergence rate is also discussed. Application of the scheme is conducted to study the effect of inclusion shapes on the anisotropy of composite.