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Two rigid non-circular inhomogeneities in an elastic matrix
Arch. Mech. 77 (3), 289-304, 2025, DOI: 10.24423/aom.4663
Keywords: two rigid non-circular rigid inhomogeneities; quadrature domain; conformal mapping; analytic continuation; rigid body rotation; analytical solution
Abstract
We derive analytical solutions to the plane elasticity problem of two interacting identical rigid non-circular inhomogeneities embedded in an infinite isotropic elastic matrix subjected to uniform remote in-plane normal and shear stresses. Explicit expressions for the pair of analytic functions due to remote normal and shear stresses are obtained with the aid of analytic continuation and a conformal mapping function for the doubly connected quadrature domain occupied by the matrix. The rigid body rotation of each rigid inhomogeneity induced by a uniform remote shear stress is determined once three corresponding regular integrals are evaluated. The remote asymptotic behaviors of the pair of analytic functions are determined once five associated regular integrals are evaluated.