Parametric nature of the non-linear hardening plastic constitutive equations and their integration

Most materials showing an elastic-plastic constitutive behaviour are governed, in the post-yielding phase, by a non-linear hardening law. As a consequence, even though a simple uniaxial case with a monotonic load is considered, a non-linear problem has to be solved. With the exception of a few cases, only approximate solution procedures are available, which in general are based on iterative methods. This paper, first, enhances the parametric nature of the rate equations governing the evolution of plastic strains. Then, it presents an integration procedure of both kinematic and isotropic, non-linear hardening constitutive equations. The proposed procedure leads to the solution for plastic strains in the form of a numerical series for the uniaxial case with any non-linear form governing the hardening behaviour. (C) Elsevier, Paris.