A Multiscale Hybrid Method For Materials
Containing Defects And Inhomogeneities
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.
Related Book
Other papers in this volume
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