Abstract

The paper demonstrates the analysis of the stress and strain states of an inhomogeneous structure with an axial symmetrical spheroidal inclusion in an infinite solid under a remote uniform tension load derived from the conditions of the theory of elasticity. With respect to the inhomogeneous structure, the deformations produce constraints that require a complete 3-dimensional analysis in the z, r-coordinate system. The solution generates the stress state of the inclusion and at the interface of the matrix. Spheroidal inclusions in an uniform outer tension stress field deform self-similarly to a rather elongated spheroid. With respect to the compatibility condition and depending on the different elastic moduli and Poisson’s ratios in the inclusion and matrix, the solution procedure leads to a system of two linear equations with the magnitudes of the two tractions as unknowns. In this way, the solution is shortened to a twofold statically indeterminate system. The analysis performed leads to an exact solution of the general spheroidal problem in a formulation of stress concentration factors considering the different stiffness parameters of inclusion and matrix.

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