A new integration algorithm for finite strain J2 plasticity based on midpoint rule

Integrating the rate form equations governing the behavior of material is an important step in solving every plasticity problem. Providing a compromise between accuracy and computational effort demands the combination of low order elements with efficient integration algorithms. First and second order accurate integration algorithms are well established in the realm of infinitesimal theory. However for large deformation plasticity models, second order integration algorithms are not given much attention in the literature. Inspired by midpoint rule algorithms conventionally used in small deformations, a new integration algorithm is proposed for finite strain J2 plasticity that outperforms the classical backward Euler method. Algorithmic setup as well as the derivation of tangent operator which is crucial for quadratic rate of convergence of the Newton-Raphson algorithm is discussed in detail. Employing four node quadrilateral elements in solving benchmark examples it is shown that the proposed algorithm is very stable from numerical standpoint and has outstanding convergence properties.