Abstract
The extended finite element method allows one to model displacement discontinuities which do not conform to interelement surfaces. This method is applied to modeling growth of arbitrary cohesive cracks. The growth of the cohesive zone is governed by requiring the stress intensity factors at the tip of the cohesive zone to vanish. This energetic approach avoids the evaluation of stresses at the mathematical tip of the crack. The effectiveness of the proposed approach is demonstrated by simulations of cohesive crack growth in concrete.
Highlights
Linear elastic fracture mechanics (LEFM) is only applicable when the size of the fracture process zone (FPZ) at the crack tip is small compared to the size of the crack and the size of the specimen [1]
The problem of finding the proper load factor for a given crack growth does not involve the evaluation of the stress field at the mathematical tip of the cohesive zone
Instead we rely on energetic considerations: the correct load factor is found by zeroing the Mode I stress intensity factor (SIF) at the tip
Summary
Linear elastic fracture mechanics (LEFM) is only applicable when the size of the fracture process zone (FPZ) at the crack tip is small compared to the size of the crack and the size of the specimen [1]. The propagation is governed by a traction displacement relation across the crack faces near the tip. The crack extends between elements and remeshing is necessary when the crack path is not known in advance This approach has been used to model cohesive crack growth in concrete in Refs. The X-FEM models the discontinuity in a displacement field along the crack path, wherever this path may be located with respect to the mesh This flexibility enables the method to simulate crack growth without remeshing. The modeling of cohesive cracks using the partition of unity property of finite elements was considered recently in Ref. The modeling of cohesive cracks using the partition of unity property of finite elements was considered recently in Ref. [28]
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