Effect of material compressibility on the solution of the elastoplastic plane strain problem

A model problem of plane strain of an elastoplastic material is considered. It is shown that the type of stress state in the loading plane affects the dependence of the solution on Poisson’s ratio. It is found that for the state in which the principal stresses in the loading plane are approximately equal, the effect of compressibility is significant, so that it must be taken into account. It is shown that if the principal stresses in the loading plane have different signs, the solutions for compressible and incompressible materials are almost the same.