An efficient exponential based integration for von Mises plasticity combined with Lemaitre damage model

Abstract

In elastoplastic problems, integrating the constitutive equations decides the final state of stress and the related plastic variables. Integration based on exponential-mapping strategy is a new and promising method to fulfill the task and has not been implemented for the problems of damage mechanics yet. For the first time, here, the exponential-mapping technique is developed for the elastoplastic finite element analyses of structures combined with Lemaitre damage model. Subsequently, the associated stress-updating algorithm is presented to clearly show the process of finding stress and its pertinent variables during a nonlinear finite element analysis with the derived method. Afterwards, an extensive range of numerical tests is carried out to evaluate the performance of the suggested formulae including verification, precision, convergence rate, and efficiency investigations. Consequently, the outcomes demonstrate a high level of performance by the new algorithm to solve the fundamental elastoplastic equations and update the stress in nonlinear finite element analyses.