Abstract
We prove that it is possible to maintain an internal uniform hydrostatic stress field within a non-elliptical inhomogeneity in the neighborhood of a non-circular inhomogeneity when the surrounding matrix is subjected to uniform remote in-plane stresses. The non-circular inhomogeneity and the matrix have a common shear modulus but distinct Poisson's ratios. The given non-circular shapes of the inhomogeneity include a Booth's lemniscate, a generalized Booth's lemniscate and a cardioid. Our analysis indicates that the uniform hydrostatic field inside the non-elliptical inhomogeneity is unaffected by the existence of the nearby non-circular inhomogeneity whereas the non-elliptical shape of the inhomogeneity is caused solely by the presence of the non-circular inhomogeneity. Numerical examples are presented to demonstrate the general solutions obtained in each of the three non-circular shapes of the inhomogeneity.
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