Analytical solution for an infinite elastic power-law hardening plate containing an elastic circular inhomogeneity and subjected to equi-biaxial tension

This paper presents an clasto-plastic analytical solution for the plane stress inclusion problem of an elastic power-law hardening plate containing an elastic circular inhomogeneity and subjected to equi-biaxial far-field tension. Hencky's deformation theory (for compressible materials) and von Mises' yield criterion are applied, and infinitesimal deformations are assumed. The solution is derived by using a stress formulation and with the help of a modified Nadai's auxiliary-variable method and the extended Michell theorem. All expressions for the stress, strain and displacement components are derived in explicit forms in terms of an auxiliary variable and four constant parameters, which are determined from the given boundary conditions. Three specific solutions of practical interest are presented as limiting cases, one of which is the closed-form solution for the plate containing a traction-free circular hole. Numerical results are also provided to demonstrate quantitatively applications of the solution in the opening and reinforcement design of spherical pressure vessels.