Accurate finite element simulation of stresses for stationary dynamic cracks under impact loading

The numerical technique for wave propagation problems recently developed in our papers has been applied to the accurate modeling of stresses in the vicinity of crack tips and the dynamic stress intensity factor (DSIF) for stationary cracks. The numerical technique includes the linear finite elements with reduced dispersion as well as the two-stage time-integration approach that quantifies and filters spurious high-frequency oscillations. Several benchmark problems for stationary cracks at impact loadings have been solved. The accuracy of the stress calculation in the vicinity of the crack tips and the DSIF can be significantly increased by the application of the finite elements with reduced dispersion. Surprisingly, even without a special treatment of singularities at crack tips, the linear finite elements with reduced dispersion (with no crack tip enrichment functions) yield much more accurate results than the XFEM with the special crack tip enrichment functions on comparable meshes. It is also interesting to mention that for the calculation of the DSIF by the finite elements with reduced dispersion there is no necessity in the filtering stage at impact loading (the spurious oscillations in the DSIF are small and decrease with mesh refinement).