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SUMMARYA methodology for the simulation of quasi-static cohesive crack propagation in quasi-brittle materials is presented. In the framework of the recently proposed extended ÿnite element method, the partition of unity property of nodal shape functions has been exploited to introduce a higher-order displacement discontinuity in a standard ÿnite element model. In this way, a cubic displacement discontinuity, able to reproduce the typical cusp-like shape of the process zone at the tip of a cohesive crack, is allowed to propagate without any need to modify the background ÿnite element mesh. The e ectiveness of the proposed method has been assessed by simulating mode-I and mixed-mode experimental tests.

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

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