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