Constitutive relation error estimators for (visco)plastic finite element analysis with softening Original Research Article

A posteriori error estimators based on constitutive relation residuals have been developed for 20 years, in particular at Cachan. This approach has a strong physical meaning and is quite general. Here, we introduce an extended constitutive relation error estimators family able to measure the quality of finite element computations of structures which exhibit plastic/viscoplastic behavior with softening. These measures take into account, over the studied time interval, all the classical error sources involved in the computation: the space discretization (the mesh), the time discretization and the iterative technique used to solve the nonlinear discrete problem.