Effect of the physical nonlinearity of a material on the stress state of a medium with an elastic spherical inclusion under uniform loading

We have used the perturbation method as the basis for obtaining an approximate solution of the three-dimensional problem for a physically nonlinear elastic medium with an elastic inclusion under uniform tension— compression. From this solution, we can obtain as a special case a solution for an elastic medium with a stress-free cavity and for an elastic medium with a rigid inclusion. We have plotted the normal and tangential stresses as a function of the radius and the ratio of shear moduli for the inclusion and the medium. We have investigated their behavior under different loading conditions. Translated from Prikladnaya Mekhanika, Vol. 34, No. 11, pp. 46–51, November, 1998.