Continuous - Discontinuous modelling of failure

The foundations of a safe structural design lie on the understanding of failure processes of engineering materials and in their correct representation. In a numerical context, failure representation in engineering materials can be pursued either in a continuous or in a discontinuous setting. Both approaches can model certain failure modes, but in some cases do not reflect the physical processes behind failure properly. To some extent, continuous failure representation can be improved by enriching the standard kinematics with displacement discontinuities, which can be thought of as a natural consequence of material failure processes. In this work, a continuous-discontinuous approach is applied to elastic, strain-hardening and regularised strain-softening media. It is shown that the success of a continuous-discontinuous analysis depends largely on the underlying continuous model. Analyses performed with elastic and strain-hardening media gave satisfactory results; conversely, when strainsoftening media were considered, the performance of the approach was related to the nature of the regularisation employed. It is shown that, in a continuous-discontinuous setting, softening models in which the underlying continuum description is enriched through a temporal regularisation formalism (rate-dependence) perform better than models obeying a spatial regularisation concept (non-locality). This issue is examined with respect to a differential version of a non-local model (implicit gradient-enhanced damage continuum model) and a rate-dependent elastoplastic-damage model. More specifically, it is shown that a class of regularised models based on a non-local dissipation driving variable is not adequate for failure description in arbitrary loading scenarios. Several applications illustrate the improved flexibility of a continuous-discontinuous approach to failure when compared to a continuous approach alone.