The two-dimensional loading problem of an elastoplastic plane weakened by a hole (Q1824445)

A general approach to the solution of problems on finding the elasto- plastic boundaries of a plane under tension weakened by a hole, is considered. The propagation of the plastic domain in the plane is studied during the loading process, when part of the hole outline is in the elastic zone. A method is developed for carrying the matching conditions of the solutions from the elasto-plastic domain over to the hole contour, which would enable the determination of the elasto-plastic boundary to be reduced to the solution of a sequence of boundary value problems of elasticity theory. The possibility of applying the method developed to the problem of the uniaxial tension of an elasto-plastic plane weakened by a circular hole is analysed.