A numerical study of the return mapping application for the subloading surface model

Purpose Many practical problems in engineering require fast, accurate numerical results. In particular, in cyclic plasticity or fatigue simulations, the high number of loading cycles increases the computation effort and time. The purpose of this study is to show that the return mapping technique in the framework of unconventional plasticity theories is a good compromise between efficiency and accuracy in finite element analyses. Design/methodology/approach The accuracy of the closest point projection method and the cutting plane method implementations for the subloading surface model are discussed under different loading conditions by analyzing the error as a function of the input step size and the efficiency of the algorithms. Findings Monotonic tests show that the two different implicit integration schemes have the same accuracy and are in good agreement with the solution obtained using an explicit forward Euler scheme, even for large input steps. However, the closest point projection method seems to describe better the evolution of the similarity centre in the cyclic loading analyses. Practical implications The purpose of this work is to show two alternative implicit integration schemes of the extended subloading surface method for metallic materials. The backward Euler integrations can guarantee a good description of the material behaviour and, at the same time, reduce the computational cost. This aspect is particularly important in the field of low or high cycle fatigue, because of the large number of cycles involved. Originality/value A detailed description of both the cutting plane and closest point projection methods is offered in this work. In particular, the two integrations schemes are compared in terms of accuracy and computation time for monotonic and cyclic loading tests.

AVALIAÇÃO DO DESEMPENHO DO MÉTODO CPPM EM ANÁLISES ELASTOPLÁSTICAS

RESUMO: O método de projeção do ponto mais próximo (CPPM, closest point projection method) é amplamente utilizado quando se apresentam respostas não lineares no comportamento dos materiais. Este artigo destina-se ao detalhamento e formulação analítica do método e avaliar com exemplos simples seu desempenho utilizando distintas leis de endurecimento não lineares para definir a evolução das deformações plásticas. O método é implementado sob uma cinemática de deformações infinitesimais. É considerado que o material possui propriedades elásticas constantes. O critério de escoamento de von Mises é utilizado com uma regra associativa de fluxo para descrever o comportamento tensão-deformação do material. A principal contribuição deste trabalho é verificar a robustez do método e apresentar explicação completa da formulação analítica. ABSTRACT: The closest point projection method is widely used when nonlinear responses occur in the behavior of the materials. The aim of this work is detailing its analytical formulation with simple examples and evaluates the performance of the method using different nonlinear hardening laws to define the evolution of plastic deformation. The method is implemented under a kinematic of infinitesimal strains, it is considered a material with constant elastic properties, the von Mises yield criterion and an associative flow rule is used to describe the stress - strain behavior of the material. The main contribution of this work is to verify the robustness of the method and the complete explanation of the analytical formulation. RESUMEN. El método de proyección al punto más próximo (CPPM, closest point projection method) es ampliamente utilizado cuando se presentan respuestas no lineales en el comportamiento de los materiales. Se pretende con este trabajo detallar su formulación analítica y evaluar con ejemplos simples el desempeño del método utilizando diferentes leyes de endurecimiento no lineales para definir la evolución de las deformaciones plásticas. El método es implementado bajo una cinemática de deformaciones infinitesimales. Se considera un material con propiedades elásticas constantes, se emplea el criterio de fluencia de von Mises y una regla asociativa de flujo para describir el comportamiento tensión - deformación del material. La principal contribución de este trabajo es la verificación de la robustez del método y la explicación completa de la formulación analítica.