Stresses in an infinite medium with two similar circular cylindrical inclusions

SummaryStresses around two similar circular cylindrical inclusions in an infinite medium under the generalised plane strain conditions subjected to uniform far-field stresses are investigated in this paper. The analysis is based on the complex stress potentials of Muskhelishvili [1]. Stresses can be found with any clearance between the two inclusions. Special treatment has been made for the case in which the two inclusions are in contact with each other, leading to a closed form solution to the local stresses at the contact point. Stress singularities are established in two extreme cases of either rigid or void inclusions, complementing the results for the anti-plane problem [2]. It has been shown that for inclusions of finite modulus no stress singularity arises but different degrees of stress concentration around the contact point can be found instead depending on the Young's modulus ratio between the inclusion and the medium and the loading condition. Other effects, such as the clearance between the inclusions and the Young's modulus ratio between the inclusion and the medium on the distribution of the interfacial stresses, are also examined when the two inclusions are in contact or separate. Numerical results are shown and discussed and they tend to imply a wider applicability of the conclusions obtained in this paper than the idealised case as analysed.