Application of the Generalized Method of Moving Coordinates to Calculating Stress Fields near an Elliptical Hole.

The distribution of stresses near holes is of great importance in fracture mechanics and material modeling. The present paper provides a general stress solution near a traction-free surface for an arbitrary piecewise linear yield criterion, assuming plane-strain conditions. The generalized method of moving coordinates is proven efficient in this case. In particular, the solution reduces to evaluating one ordinary integral. The boundary value problem solved is a Cauchy problem for a hyperbolic system of equations. Therefore, the stress solution in the plastic region is independent of other boundary conditions, though the occurrence of plastic yielding at a specific point is path-dependent. The general solution applies to calculating the stress field near an elliptic hole. It is shown that the parameter that controls the pressure-dependency of the yield criterion affects the stress field significantly. The aspect ratio is less significant as compared to that parameter. However, for a given material, the aspect ratio should also be considered to predict the stress field accurately, especially in the near vicinity of the hole. The solution reduces to an available solution for the pressure-independent yield criterion, which is a particular yield criterion of the considered class of yield criteria.