A two-dimensional augmented finite element for dynamic crack initiation and propagation

In this study, an implicit formulation of a 2D finite element based on a recently developed augmented finite element method is proposed for stable and efficient simulation of dynamic fracture in elastic solids. The 2D A-FE ensures smooth transition from a continuous state to a discontinuous state with an arbitrary intra-element cohesive crack, without the need of additional degree of freedoms (DoFs). Internal nodal DoFs are introduced for sub-domain integration and cohesive stress integration and they are then condensed at elemental level by a consistency-check based algorithm. The numerical performance of the proposed A-FE has been assessed through simulations of several benchmark dynamic fracture problems and in all cases the numerical results are in good agreement with the respective experimental results and other simulation results in literature. It has further been demonstrated that, (i) the dynamic A-FE is rather insensitive to mesh sizes and mesh structures; (ii) with similar solution accuracy it allows for the use of time steps 1-2 orders of magnitude larger than those used in other similar studies; and (iii) the implicit nature of the proposed A-FE allows for the use of a Courant number as large as 3.0-3.5 while maintaining solution stability.