Singular stress fields at V-notch tips in elastoplastic pressure-sensitive materials
The author presents an asymptotic analysis of stress fields at the apex notch tip for a pressure-sensitive material. The constitutive behaviour of the continuum is described by the Ramberg-Osgood stress-strain relation, together with a modified Drucker-Prager yield criterion. A two-term expansion of the plane strain, respectively plane stress solutions is examined. The leading-order problem consists of four nonlinear homogeneous ordinary differential equations, while the second-order problem is formulated by using inhomogeneous ordinary differential equations. The equations are solved by multiple-shooting technique combined with a semi-extrapolating integrator. For the plane strain problem, the solution with separated variables can be reduced to some pressure sensitivities, while it is not the case for the plane stress solution. Finally, the author gives a parametric analysis of the singularity structure depending on the notch angle.
scientific article; zbMATH DE number 1004510