Explicit dynamics X-FEM simulation of heterogeneous materials

An explicit dynamics extended finite element method (X-FEM) is applied to the problems with material interfaces. To this end, the available X-FEM element mass matrix lumping techniques have been identified and assessed. It is shown that all the methods have their own limitations and are not general enough to handle the enrichment functions specifically developed for the elements with material interfaces. Hence, a general element mass matrix lumping technique has been introduced which exactly preserves the kinetic energies of the basic rigid body and enrichment modes. The idea is borrowed from the previously published method for a specific range of enrichment functions and extended to arbitrary enrichments. A closed-form solution for the critical time step of 1D bi-material element is introduced. Furthermore, a pre-processor program is developed to numerically calculate the critical time steps of 2D and 3D X-FEM bi-material elements. Finally, the new formula for the lumped mass matrix of the enriched elements is incorporated in an explicit X-FEM scheme and the reliability of the method has been demonstrated in a set of bi-material examples which compare well with the FE results.