Interpolation requirements for implicit gradient-enhanced continuum damage models

摘要

Some properties of a gradient-enhanced continuum damage model were discussed by means of a numerical and theoretical study. In particular, it is demonstrated that the discretization of this model does not belong to the class of mixed finite element formulations (although the model has the format of a general coupled problem). Hence, the Babuska-Brezzi condition does not apply to this type of models. Consequently, the use of linear interpolation functions for displacements as well for non-local equivalent strains yields excellent performance in terms of rate of convergence and of convergence of the numerical procedure.