Mixed FEM for Shells of Revolution Based on Flow Theory and its Modifications

Abstract

For describing elastoplastic deformation, three versions of constitutive equations are used. The first version employs the governing equations of the flow theory. In the second version, elastic strain increments are defined the same way as in the flow theory, and the plastic strain increments are expressed in terms of stress increments using the condition of their proportionality to the components of the incremental stress deviator tensor. In the third version, the constitutive equations for a load step were obtained without using the hypothesis of separating strains into the elastic and plastic parts. To obtain them, the condition of proportionality of the components of the incremental strain deviator tensor to the components of the incremental stress deviator tensor was applied. The equations are implemented using a hybrid prismatic finite element with a triangular base. A sample calculation shows the advantage of the third version of the constitutive equations.