An extended FE strategy for transition from continuum damage to mode I cohesive crack propagation

Abstract

An integrated strategy is proposed for the simulation of damage development and crack propagation in concrete structures. In the initial stage of damage growth, concrete is considered to be macroscopically integer and is modeled by a non-symmetric isotropic non-local damage model. The transition to the discrete cohesive crack model depends on the local mesh size and is driven by an analytical estimate of the current bandwidth. When a crack is introduced in the model an extended finite element approach is used to follow the propagation path, independent of the background mesh. The proposed methodology is tested on a notched tension specimen and then applied to the analysis of a wedge splitting test. Copyright © 2006 John Wiley & Sons, Ltd

The extended/generalized finite element method: An overview of the method and its applications

“…Several types of enrichment have been used: with relative normal displacements allowed on the boundary or only relative slip allowed. When only slip is allowed, the Heaviside step function is applied only to the tangential component, and the enrichment is (27) where e If normal separation between grains is to be modeled along the grain boundary by a cohesive law [119], then the displacement field for a grain boundary is identical to that for cracks (3), but without the crack tip enrichment. In addition, a penalty force or some other constraint technique must be applied to prevent interpenetration along the grain boundaries, see for example [33].…”

“…An energy conservation criterion has been proposed for mode I cracks by Comi et al [27], where the transition from damage to fracture is defined through an energy balance in such a way that the residual energy in the damage band is transferred to the cohesive crack interface. They present an estimate of the minimum number of elements required to resolve the localization band for a given accuracy by perturbation analysis.…”

Elastic damage to crack transition in a coupled non-local implicit discontinuous Galerkin/extrinsic cohesive law framework

“…As developed by other researchers [32,28,38,39], the crack nucleation can be governed by a critical transition damage D T . The crack propagation direction is either pre-defined, such as in the intrinsic cohesive model, or evaluated through the damage gradient, such as in xFEM framework or when using remeshing techniques.…”

“…(36)(37)(38)(39)(40)(41). Peerlings [5] has derived a semi-analytical solution in the particular case of a damage law equivalent to perfect plasticity, i.e.…”

“…Finally, upon damage to crack transition, the TSL of the CZM is defined to respect the equivalence between the fracture energy of the non-local damage and cohesive crack following the work in [35,36,37]. Note that this theoretical framework has already been used for brittle materials to define the transition from a non-local implicit CDM to a CZM embedded in the XFEM method [38] and the transition from a gradient enhanced damage model to an intrinsic cohesive crack in a predefined direction (mode I) [39].…”