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.
•A novel quadrilateral finite element Q6 with embedded strong discontinuity is presented.•A novel criterion for crack nucleation is described.•The proposed embedded discontinuity model is used for static and dynamic simulations of crack propagation.•Numerical examples are computed without using a crack tracking algorithm.
In this work, we present a finite element model capable of describing both the plastic deformation which accumulates during the hardening phase as the precursor to failure and the failure process ...leading to softening phenomena induced by shear slip lines. This is achieved by activating subsequently hardening and softening mechanisms with the localization condition which separates them. The chosen model problem of von Mises plasticity is addressed in detail, along with particular combination of mixed and enhanced finite element approximations which are selected to control the locking phenomena and guarantee mesh-invariant computation of plastic dissipation. Several numerical simulations are presented in order to illustrate the ability of the presented model to predict the final orientation of the shear slip lines for the case of non-proportional loading.
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