Elasto-plastic analysis of a plane stress problem using linearized yield surface and mixed hardening rule

Abstract

The objective of this paper is to present the mathematical formulations in the incremental theory of plasticity, which is based on the mixed hardening rule and a linear yield surface. A three-parameter, uniaxial symmetric, linear yield surface suitable for tension-weak as well as equal tension and compression yield stress material is presented. This yield condition, along with the mixed hardening and associated flow rules is used to formulate the constitutive laws for sides and corners of the yield surface. The formulation is based on incremental plasticity with the assumption of small displacements and is suitable for plane stress problems under monotonie and cyclic loading. The mixed hardening rule, which is mathematically modeled, could be changed to either kinematic or isotropic hardening by a simple change in the model. This hardening rule could handle different degrees of Bauschinger effect, as opposed to kinematic hardening, which assumes only an ideal Bauschinger effect, or isotropic hardening, which does not account for the effect at all. The theory is applied to a ductile material using the finite element method and cyclic loading.