Plastic Collocation Method Considering Strain-hardening Effects

Abstract

Previously, the authors developed the plastic collocation method for elastic-plastic analyses of homogeneous continuum in any geometrical shape. In this method, using ordinary finite elements, plastification is examined at the checking points for plasticity properly selected in the element. Regarding the yield conditions at the checking points as plastic potentials, and applying the plastic flow theory, the elastic-plastic stiffness matrices can be derived without integration over the element. Moreover, suitable selection of the checking points considering characteristics of the stress distributions in the element leads to improvement of the accuracy of the collapse loads.In this paper, expanding the basic theory of the plastic collocation method, a general theory for the analyses considering strain-hardening effects is proposed. In the plastic collocation method, plastic deformations are concentrated only to the nodes. Then, to take into account of strain-hardening effects, it becomes necessary to evaluate the spread of plastic region in the element and condense strain-hardening effects therein to be represented as the strain-hardening rate with respect to the plastic nodal displacements. Applying this expanded theory, several examples are analysed, and the effectiveness of this method is demonstrated.