Strong discontinuity analysis of a class of anisotropic continuum damage constitutive models - Part I: Theoretical considerations

Several modeling techniques aiming at considering cracks as kinematics discontinuities have been proposed for the past years. Within this scope, the embedded finite element method (E-FEM) was introduced a couple of years ago. Among the features of this approach, it has been shown that a kinematic enhancement of the displacement field allows constructing a discrete model (expressed in terms of traction vector-displacement jump) from any continuous model (expressed in terms of stress-strain). This result has been rigorously established if the continuous model is formulated within the framework of either isotropic continuum damage or plasticity theories. The objectives of this study are (i) to extend this result in case where the continuous model belongs to a class of anisotropic continuum damage constitutive models and (ii) to show the main features of a specific traction/separation law derived from the aforementioned class of constitutive models through several numerical case-studies. In this paper, the light is put on the theoretical considerations which allow deriving discrete models in a consistent way.