Time Integration Schemes for 2D Dynamic Crack Propagation

1. Is there anyone familiar/working with the time integration schemes for 2D dynamic crack propagation in XFEM? I would like to discuss some of the issues I am facing. I will really appreciate any kind of help/suggestions!

2. I tried to implement the time integration scheme proposed by Combescure et. al (An energy-conserving scheme for dynamic crack growth using the extended finite element method). But I am not sure about some of the strategies they are following in that paper. Anyone can clarify some of the questions I have?

2(a) When a crack propagates within an element, we introduce new degrees of freedom associated with the new crack tip. But what to do with the old degrees of freedom associated with the old crack tip?

2(b)I see that, in that paper the authors keep the old tip enriched degrees of freedom at each time step and introduce new tip enriched degrees of freedom, then how to write the displacement approximation for an element that contains the crack tip ?(because you have degrees of freedom associated with the old and new crack tip position!).

I will really appreciate if somebody could clarify! Also, if anyone wants to discuss anything related to this, or can suggest any other time integration schemes for dynamic crack propagation in XFEM, I will really appreciate and welcome:my email:abmaab.1988@gmail.comalso my Phone number:806-317-8140.

Thank you all

Ali Bhuiyan