Accuracy and stability of integration algorithms for elastoplastic constitutive relations

An analysis of accuracy and stability of algorithms for the integration of elastoplastic constitutive relations is carried out in this paper. Reference is made to a very general internal variable formulation of plasticity and to two families of algorithms that generalize the well-known trapezoidal and midpoint rules to fit the present context. Other integration schemes such as the radial return, mean normal and closest point procedures are particular cases of this general formulation. The meaning of first and second-order accuracy in the presence of the plastic consistency condition is examined in detail, and the criteria derived are used to identify two second-order accurate members of the proposed algorithms. A general methodology is also derived whereby the numerical stability properties of integration schemes can be systematically assessed. With the aid of this methodology, the generalized midpoint rule is seen to have far better stability properties than the generalized trapezoidal rule. Finally, numerical examples are presented that illustrate the performance of the algorithms