An eigenerosion approach to brittle fracture
International Journal for Numerical Methods in Engineering
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
... ed or eroded. When combined with a finiteelement 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. ‡ AN EIGENEROSION APPROACH TO BRITTLE FRACTURE 695 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 completely failed, or eroded, and have no load bearing capacity. The implementation of the method, included the all-important -neighborhood construction, is exceedingly simple and applies to general situations, possibly involving complex three-dimensional fracture patterns such as branching and fragmentation. The accuracy and convergence of the eigenerosion approach are comparable-at a much reduced implementation cost and complexity-to that of other numerical fracture schemes. We note that element erosion has been extensively used to simulate fracture in a number of areas of application, including terminal ballistics       . However, some of these methods fail to converge or converge to the wrong limit  . By contrast, the eigenfracture scheme is known to properly converge to Griffith fracture in the limit of vanishingly small mesh sizes . In particular, the localneighborhood averaging of the energy that underlies the calculation of the effective energy release has the effect of eliminating spurious mesh dependencies. The paper is organized as follows. We begin by summarizing parts of the underlying Griffith's theory of fracture that are relevant to this work in Section 2. We describe the numerical implementation in Section 3. Then, we proceed to verify the approach through comparisons with analytical solutions available for linear elasticity in Section 4.1. We present further verification of the approach through convergence studies for mode I crack growth, both in two and three dimensions, in Section 4.2. We conclude with a final three-dimensional example aimed at validating the approach in applications concerned with mixed mode I-III experiments in polymethyl methacrylate (PMMA) plates in Section 4.3.