Final Conclusions and Future Research Directions

The book analyzes quasi-static fracture in plain concrete and reinforced concrete by means of constitutive models formulated within continuum mechanics. A continuous and discontinuous modelling approach was used. Using a continuous approach, analyses were performed using a finite element method and four different continuum concrete models: enhanced isotropic elasto-plastic, enhanced isotropic damage, enhanced anisotropic smeared crack and enhanced coupled elasto-plastic-damage model. The models were equipped with a characteristic length of micro-structure by means of a non-local and a second-gradient theory, so they could describe the formation of localized zones with a certain thickness and spacing and a related deterministic size effect. FE results converged to a finite size of localized zones via mesh refinement. In addition, numerical results of cracks in plain concrete using a discontinuous approach including cohesive (interface) elements and XFEM were presented which were also properly regularized. Numerical results were compared with corresponding laboratory tests from the scientific literature and own tests.