Examination of flux projection-type error estimators in nonlinear finite element analysis

This paper presents a comparative study of a series of flux projection-type error estimators for elastic-plastic and viscoplastic materials undergoing large strains and large rotations. The error estimators are: L₂ norms of stress error, total strain error, equivalent strain error, incremental total strain error per load step and energy rate norm error, respectively. Although numerical examples are presented in two dimensions only, the error estimators are valid in both two and three dimensions. The information provided by these error estimators may be used for adaptive mesh refinement and for subsequent data transfer (rezoning) in a large deformation analysis. The error estimators based on the energy rate and the incremental total strain were found to be accurate in the prediction of the discretization error for the test cases considered. The behaviors of the remaining error estimators were observed to be mildly influenced by the material model used and the type of problem being solved, along with the level of discretization error present in the finite element model. The L₂ norm of incremental strain error estimator consistently gave the most conservative estimate of error.