An eigenerosion approach to brittle fracture

Abstract

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

Acoustic scattering in a waveguide with a height discontinuity bridged by a membrane: a tailored Galerkin approach

“…The direction of propagation is determined to be normal to the direction of the first principal stress σ 1 . We remark that although XFEM is a well-tested technique and well suited to our single tear problem, recent approaches such as eigen-erosion [20], and phase field [21] have also been developed, and could be more powerful in modelling branching and other complex fractures. Fig.…”

Computational Methods for Fracture in Brittle and Quasi-Brittle Solids: State-of-the-Art Review and Future Perspectives

“…For brittle fracture, Pandolfi and Ortiz [71] derived an interesting eigenerosion approach. Their idea is based on the eigenfracture approach by Schmidt et al [72], where the eigendeformation is restricted in a binary sense.…”

Dynamic crack propagation with a variational phase-field model: limiting speed, crack branching and velocity-toughening mechanisms

“…One can mention the non-local integral approach [53,31,67], gradient-enhanced models [51], eigenerosion [49], peridynamics [7], thick-level sets [47] and phase-field approaches, which will be described later in more details. Generally, such non-local approaches do not require additional criteria to obtain branched patterns [34,27,29,30].…”