Modeling failure of brittle materials with eigenerosion

We describe through static and dynamic applications the implementation of the eigenerosion scheme within a material point discretization method. Eigenerosion is derived from the general eigenfracture scheme (Schmidt et al. 2009) by restricting the eigendeformations to be either zero, in which case the local behavior is elastic, or equal to the local displacement gradient, in which case the corresponding material neighborhood is eroded. When combined with spatial discretization, this scheme gives rise to element or material-point erosion, i.e., each element or material point can be either intact, in which case its behavior is elastic, or be eroded and has no load bearing capacity. The convergence properties of the eigenerosion scheme for Mode I fracture propagation in three dimensional problems have been discussed in (Pandolfi and Ortiz 2012). Here we show that, in brittle materials, the eigenerosion scheme can be applied efficiently to the simulation of mixed mode quasi static fracture experiments (Pandolfi et al. 2013) and of inverse Taylor impact experiments, where the the dynamic fragmentation assumes the aspect of a failure wave. Dynamic applications are achieved by combining eiegenerosion to the Optimal Transportation Meshless (OTM) method (Li et al. 2010). © 2014 Taylor & Francis Group.