Author(s)

W. J. Liu & X. J. Xin

Abstract

The elastic analysis for micromechanics of materials containing defects and inhomogeneities is of considerable significance in many engineering disciplines. In this study, the Multiscale Hybrid Method (MHM) based on a combined boundary integral and volume integral equation, is developed for the micromechanics of materials containing defects and inhomogeneities of different length scales. In MHM, only the macro boundary and the inhomogeneities need to be discretized. Interactions between the inhomogeneities and the boundary are explicit in the governing equations, while the inhomogeneity length scale is fully decoupled from the boundary scale, offering the capability to handle essentially different length scales. A displacement-based direct solution approach is used to lower the order of singularity in the governing integral equations and offers a high accuracy of displacement solution. Numerical techniques including the coordinate origin shift scheme, the subtraction technique, and Moving Least Squares Approximation are employed in numerical implementation. A 2D version of the method was implemented. Bodies containing multiple inclusions are simulated and compared with available closed form solutions or numerical solutions using FEM. Keywords: multiscale hybrid method, boundary integral equation, volume integral equation, subtraction technique, inclusion, numerical method. 1 Introduction Elastic analysis for micromechanics of materials containing defects and inhomogeneities is of considerable significance in many engineering disciplines. Existing computational techniques such as Finite Element Method (FEM) [1]

Keywords

multiscale hybrid method, boundary integral equation, volume integral equation, subtraction technique, inclusion, numerical method.