Axisymmetrical Rigid Punch Problem of a Semi-Infinite Body with Nonhomogeneous Material Property

Abstract

In this study, a theoretical treatment of an elastic behavior for a nonhomogeneous medium is developed. As one nonhomogeneous medium, a semi-infinite body subjected to the action of a rigid punch on its surface is considered. It is assumed for the nonhomogeneous material property of the semi-infinite body that the shear modulus of elasticity G varies with the variable of the axial coordinate z by an arbitrary power product form. Making use of a fundamental equation system for such a nonhomogeneous medium, an axisymmetric problem for such a singular stress field is developed theoretically. Numerical calculations are carried out for several cases taking into account the variations of the nonhomogeneous parameter, and the numerical results for displacements, stresses and the stress intensity factor at the edge of the rigid punch are shown graphically. Thereafter, the influences of the nonhomogeneous material property on the elastic behaviors such as displacements, stresses and the stress intensity factor are examined.