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Time integration scheme for XFEM? (dynamic crack propagation)

Hello everyone,

 

Can somebody suggest an implicit/explicit time integration scheme when the matrices involved(M,C,K) are time dependent? (They change at every time step because of the crack tip enrichment functions which are time dependent).

 

I used the implicit Newmark scheme (trapezoidal/constant average acceleartion method) but just discovered that all my matrices (M,C,K) are time dependent where the original scheme is probably for constant M,C and K matrices. I used the scheme as in reference [1]. 

 

Thank you all:) 

 

 

Reference:

1. Finite Element Procedures by Bathe, Chapter9, Section 9.2.4, The Newmark Method

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