A new method of failure analysis

The present paper develops a new failure analysis method under plane strain conditions considering a generalized linear yield criterion. The yield criterion and the stress equilibrium equations constitute a hyperbolic system of equations. It is shown that two auxiliary variables satisfy the equation of telegraphy. Simple analytical relationships connect these variables and the radii of curvature of the characteristic curves. The calculated radii of curvature allow for the corresponding characteristic net to be constructed. Then, the stress field is determined using another set of analytical relationships. Thus, a numerical procedure is only necessary for solving the equation of telegraphy. This equation can be integrated by the method of Riemann. In particular, Green’s function is the Bessel function of zero order. A simple example illustrates the general method.