Keywords: cohesive zone law, partition of unity, mode-I fracture.

Many models have been presented in literature to overcome mesh sensitivity problems introduced when classical continuum damage/plasticity models are used in fracture analysis. In contrast with continuum models, where the kinematic fields remain continuous, discontinuous models introduce discontinuous functions into the strain field (weak discontinuity) or into the displacement field (strong discontinuity). In this paper, two methodologies for obtaining displacement discontinuities are studied: a discontinuous finite element model and the cohesive surface methodology. The first incorporates a discontinuity in the kinematic description of the displacement field. The enriched expression for the displacement field is implemented into finite elements using the partition of unity property of finite element shape functions. Using this property, the Heaviside step function is used as enhanced basis and the crack is represented by additional degrees of freedom [1]. The second methodology places interface elements on element boundaries, allowing the elements to separate when a crack grows. Cohesive zones are scattered throughout the complete mesh as pioneered by Xu and Needleman [2]. In this way, a whole set of possible crack trajectories is available and no remeshing is needed during computation. For both models, a cohesive zone law is necessary to describe the behaviour within the discontinuity. In this work, a plasticity-based cohesive zone law is applied.

In the first part of the paper, both methods are presented. The numerical implementation of methodologies is explained. The governing equations are derived. For the discontinuous finite element method, attention is paid to the interaction rules of discontinuities. Then the plasticity-based cohesive zone model is introduced. The model is based on a hyperbolic yield surface as proposed by Carol et al. [3]. In the second part of the paper, both methods are compared. For the comparison, a bench-mark problem is treated. The numerical simulation of double edge-notched tensile is performed. Firstly, the mesh sensitivity of both methods is investigated. It will be shown that the cohesive surface suffers some mesh sensitivity while for the discontinuous finite elements cracks propagate independent of the discretization. However, the interaction rules can lead to some problems. Furthermore, the discontinuous finite element method is more efficient since additional degrees of freedom are only added when necessary.

1

Wells, G.N. and Sluys, L.J. "A new method for modeling cohesive cracks using finite elements", International Journal for Numerical Methods in Engineering, 50(12), 2667-2682, 2001. doi:10.1002/nme.143

2

Xu, X.P. and Needleman, A. "Numerical simulations of fast crack growth in brittle solids", Journal of the Mechanics and Physics of Solids, 42, 1397-1434, 1994. doi:10.1016/0022-5096(94)90003-5

3

Carol, I., Prat, P.C. and Lopez, C.M. "Normal/shear cracking model: application to discrete crack analysis", Journal of Engineering Mechanics, 123, 765-773, 1997. doi:10.1061/(ASCE)0733-9399(1997)123:8(765)

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