An eigenerosion approach to brittle fracture
The present work is concerned with the verification and validation of a variant of the eigenfracture scheme of Schmidt et al. (2009) based on element erosion, which we refer to as eigenerosion. Eigenerosion is derived from the general eigenfracture scheme by restricting the eigendeformations in a binary sense: they can be either zero, in which case the local behavior is elastic, or they can be equal to the local displacement gradient, in which case the corresponding material neighborhood is failed or eroded. When combined with a finite-element approximation, this scheme gives rise to element erosion, i.e., the elements can be either intact, in which case their behavior is elastic, or be completly failed, or eroded, and have no load bearing capacity. We verify the eigenerosion scheme through comparisons with analytical solutions and through convergence studies for mode I fracture propagation, both in two and three dimensions and for structured and random meshes. Finally, by way of validation, we apply the eigenerosion scheme to the simulation of mixed modes I–III experiments in poly-methyl methacrylate plates.
© 2012 John Wiley & Sons, Ltd. Received 24 December 2011; Revised 10 April 2012; Accepted 13 April 2012. The collaboration of Santiago Lombeyda for the rendering of the crack pictures is gratefully acknowledged. AP wants to thank Michael Aivazis for his clear and helpful introduction to parallel computing. This material is based upon work supported by the Department of Energy National Nuclear Security Administration under Award Number DE-FC52-08NA28613 through Caltech's ASC/PSAAP Center for the Predictive Modeling and Simulation of High-Energy Density Dynamic Response of Materials. Dedicated to the memory of Professor Osvaldo De Donato.