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This results in elements that contain both real material and empty regions. The missing material is contained in another copy (or copies) of this element. Our new virtual node algorithm automatically determines the number of replicas and the assignment of material to each. Moreover, it provides the degrees of freedom required to simulate the partially or fully fragmented material in a fashion consistent with the embedded geometry. This approach enables efficient simulation of complex geometry with a simple mesh, i.e. the geometry need not align itself with element boundaries. It also alleviates many shortcomings of traditional Lagrangian simulation techniques for meshes with changing topology. For example, slivers do not require small CFL time step restrictions since they are embedded in well shaped larger elements. To enable robust simulation of embedded geometry, we propose new algorithms for handling rigid body and self collisions. 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