A generalized approach to formulate the consistent tangent stiffness in plasticity with application to the GLD porous material model

It has been shown that the use of the consistent tangent moduli is crucial for preserving the quadratic convergence rate of the global Newton iterations in the solution of the incremental problem. In this paper, we present a general method to formulate the consistent tangent stiffness for plasticity. The robustness and efficiency of the proposed approach are examined by applying it to the isotropic material with J2 flow plasticity and comparing the performance and the analysis results with the original implementation in the commercial finite element program ABAQUS. The proposed approach is then applied to an anisotropic porous plasticity model, the Gologanu-Leblond-Devaux model. Performance comparison between the consistent tangent stiffness and the conventional continuum tangent stiffness demonstrates significant improvement in convergence characteristics of the overall Newton iterations caused by using the consistent tangent matrix.