The role of domain decomposition techniques for the study of heterogeneous quasi-brittle materials

We focus on the analysis of fracture in quasi-brittle materials by exploiting the potential of domain decomposition techniques. More specifically, we restrict our attention to the FETI (Finite Element Tearing and Interconnecting) method which is used as a solver in our non-linear solution scheme. We develop criteria to anticipate the linear/non-linear character of different regions in the structure according to a damage constitutive model. A first application of our scheme focuses on the efficiency increase of a monoscale analysis by simplifying the computations in those areas that remain linear. The second application treats the problem in a multiscale fashion where the resolution of the non-linear domains is increased in order to describe failure phenomena with a higher degree of accuracy. Both applications represent a significant improvement from a computational standpoint when the main non-linear regions are small compared to the size of the whole specimen. This is often the case for brittle and quasi-brittle materials where strain localization is expected to occur upon failure