Accurate finite element simulation of stationary and moving dynamic cracks under impact loading

A new numerical technique that was developed for wave propagation problems has been implemented in current work for the simulation of elastodynamic fracture problems. Modeling of stresses near the crack tip and the calculation of dynamic stress intensity factors (DSIFs) have been done with the new technique. This technique includes the use of linear finite elements with reduced dispersion (RD) as well as the two stage time-integration method that quantifies and filters spurious high frequency oscillations. Several benchmark stationary and moving dynamic crack problems under impact loading have been solved. For the stationary cracks, it was found that the accuracy of stress calculations near the crack tip and the calculations of DSIFs can be significantly improved by using the linear elements with reduced dispersion. It was also interesting to note that the linear elements with reduced numerical dispersion yield much better results than the popular extended finite element method (XFEM) that uses special crack tip enrichment functions for the treatment of singularity in the vicinity of the crack tip. The implementation of RD is also much simpler than the implementation of XFEM. It is also interesting to mention that there is no necessity of the filtering stage for elastodynamic stationary crack problems under impact loading when using the finite elements with reduced dispersion (the spurious oscillations in DSIFs are very small and they decrease with mesh refinement). One benchmark impact problem with a propagating crack has been solved using XFEM. The numerical solution of this problem by XFEM includes spurious oscillations in the DSIFs. The simulation of moving cracks in XFEM framework depends on a variety of different factors such as the form of the enrichment functions used, the location of points with the enrichment functions for moving cracks, the quadrature rule in XFEM, etc. In the future research, we will study the combination of XFEM and the linear elements with reduced dispersion in order to improve the accuracy of the numerical results for propagating cracks.