Crack propagation simulation without crack tracking algorithm: Embedded discontinuity formulation with incompatible modes

We show that for the simulation of crack propagation in quasi-brittle, two-dimensional solids, very good results can be obtained with an embedded strong discontinuity quadrilateral finite element has incompatible modes. Even more importantly, we demonstrate these without using a tracking algorithm. Therefore, patterns several cracks, including branching, becomes possible. The avoidance algorithm is mainly enabled by application novel, local (Gauss-point based) criterion nucleation, which determines time embedding localisation line as well its position and orientation. treat evolution terms thermodynamical framework, softening variables describing internal dissipative mechanisms material degradation. As presented numerical examples, many elements mesh may develop crack, but only some them actually open and/or slide, dissipate fracture energy, eventually form pattern. novel approach been implemented statics dynamics, computed difficult examples (including Kalthoff's test) illustrate satisfying performance. It effectively overcomes unfavourable restrictions standard formulations, namely single only. Moreover, it computationally fast straightforward to implement. Our solutions match experimental tests previously reported pattern, dissipated load-displacement curve.