Multiple elastic or rigid line inclusions in a multilayered orthotropic solid

Abstract

This paper studies the problem of multiple line inclusions in a non-homogeneous medium. The formulation and solutions for rigid line inclusions and homogeneous medium are special cases when the stiffness values of the inclusions are infinite and the non-homogeneity of the material vanishes. The model built in this study is capable of dealing with any material non-homogeneity (material properties vary continuously or in step-wise form), orthotropic mechanical properties, isotropic mechanical properties, and any number of parallel or collinear inclusions. More importantly, the inclusions are not limited to rigid (they can be elastic). Dependence of the inclusion tip fields on the strain intensity factor is given in closed form. Numerical results are given for the situations of mechanical load as well as thermal load applied in the medium.