On the limitations and extensions of eigenerosion methods for variational fracture modeling

An improved algorithmic formulation of the eigenerosion method for fracture modeling is presented in this work. From a mathematical and macroscopic perspective, fracture processes give rise to displacement discontinuities whose initiation and evolution are generally unknown a priori, thereby constituting so-called free discontinuity problems . Their numerical treatment within standard continuum mechanical frameworks is therefore particularly challenging. A widely established approach for the regularized treatment of such problems is the phase-field method. In a similar spirit, the comparatively less explored eigenerosion method is likewise based on a volumetric approximation of crack surfaces. In contrast to phase-field formulations, however, no additional field variable is required, rendering the approach computationally highly efficient. Moreover, owing to the conceptual representation of cracks by deleted elements, the method exhibits considerable advantages in terms of numerical implementation. While the convergence properties of the eigenerosion method are well established at the theoretical level, practical implementations frequently rely on numerical approximations whose influence on the computed response has not yet been systematically investigated. The present contribution therefore revisits central algorithmic ingredients of the eigenerosion framework and analyzes their impact on structural response and crack evolution. Through a series of benchmark examples and systematic numerical investigations, an improved algorithmic formulation of the eigenerosion method is elaborated. It is shown that this formulation consistently eliminates several deficiencies commonly observed in existing implementations. In particular, the revised treatment significantly enhances the predictive accuracy of the approach with respect to both structural response (e.g., the ultimate load) and crack geometry and evolution.