An Evaluation Method of Macroscopic Shape of Defects in Microscopically Inhomogeneous Materials

摘要

A method of evaluating the macroscopic shape of defects in microscopically inhomogeneous material such as inclusion-reinforced composites is proposed by considering the order of scales that describes the mechanical behaviors (or physical phenomena). By using the method of multi-scale asymptotic expansions for field variables, the averaging technique with representative volume elements for inhomogeneous media becomes a reasonable tool to deal with the medium as a homoge- neous one in macroscale. Therefore the linearized inverse scattering method along with Kirchhoff approximations can be applied to identify the shape of defects in macroscopically homogeneous media since the homogenization procedure replaces the media by homogeneous ones. Numerical examples show the capability of the proposed method to determine the shape of cracks whose sizes are much larger than the microscopic heterogeneities, which are invisible for ultrasonic waves.