Abstract: Under the condition that any perfectly plastic stress component at a crack tip is nothing but the function of θ only, making use of equilibrium equations, stress-strain-rate relations, compatibility equations and yield condition, in this paper, we derive the general analytical expressions of the perfectly plastic stress field at a Mixed-Mode crack tip under plane and anti-plane strain. Applying this general analytical expressions to the Mixed-Mode cracks, we can obtain the analytical expressions of perfectly plastic stress fields at the tips of Mixed-Mode Ⅰ-Ⅲ,Ⅱ-Ⅲ and Ⅰ-Ⅱ-Ⅲ cracks.

Key words: almost disturbance decoupling, internal stability, nonlinear gain