Interaction of a Row of Ellipsoidal Inclusions in an Infinite Body under Asymmetric Uniaxial Tension

• Published in: Transactions of the Japan Society of Mechanical Engineers Series A Vol. 65; no. 633; pp. 1032 - 1037
• Main Authors: NODA, NaoAki, HAYASHIDA, Hitoshi, TOMARI, Kenji
• Format: Journal Article
• Language: English; Japanese
• Published: The Japan Society of Mechanical Engineers 1999
• Subjects: Body Force Method; Elasticity; Ellipsoidal Inclusion; Numerical Analysis; Stress Concentration Factor
• ISSN: 0387-5008; 1884-8338
• DOI: 10.1299/kikaia.65.1032

This paper deals with an interaction problem of a row of ellipsoidal inclusions under asymmetric uniaxial tension using singular integral equations of the body force method. The problem is solved on the superposition of two auxiliary loads ; (i) biaxial tension and (ii) plane state of pure shear. These problems are formulated as a system of singular integral equations with Cauchy-type or logarithmic-type singularities, where unknown functions are densities of body forces distributed in the γ, θ, z directions in infinite bodies having the same elastic constants as those of the matrix and inclusions. In order to satisfy the boundary conditions along the ellipsoidal boundaries, the unknown functions are approximated by a linear combination of fundamental density functions and polynominals. The present method is found to yield rapidly converging numerical results for stress distributions along the boundaries. For any fixed shape and spacing of inclusions, the maximum stress is shown to be linear with the reciprocal of the squared number of inclusions.