Analysis of Contained Plastic Flow in Plane Solids

Quantitative analysis of general contained plastic flow in solids is an extremely difficult and analytically unsolved problem of plasticity theory. A numerical approach, involving the use of a lumped-parameter model, for such problems in plane solids is described. With the use of the lumped-parameter model, contained plastic flow in a solid is characterized by the plastic flow of a finite number of stress points in the model. By a recursive numerical process a set of displacements that induces a compatible set of stresses satisfying the stress equations of equilibrium is determined for each applied load level. Thus, a complete history of stress and strain corresponding to a given loading history can be obtained. The proposed method of analysis is demonstrated for problems involving increasing external loads.