Keywords: simulation, finite element analysis, non-linear analysis, fracture and fatigue, cohesive zone modelling, adaptivity.

This paper deals with numerical modelling of crack propagation by the consideration of a cohesive process zone based on the publications of Dugdale [1] and Barenblatt [2]. In that range, a priori introduction of cohesive surfaces within the finite element method became a very popular method for a number of different investigations. Although this method is restricted by some fundamental drawbacks, it is successfully applied for the representation of discrete displacement jumps of interface failure and fracture processes of homogeneous materials on different scales of observation. For example, the strict separation between fracture process zone and bulk material description as well as the straightforward implementation makes this kind of procedure attractive.

To overcome the inherent problems of presumed crack paths and effective stiffness reduction, a strategy on the basis of a variable boundary representation during fracture is proposed to describe fracture in an implicit finite element framework. By now, the particular algorithmic procedure of adaptively implemented cohesive surfaces was related to the simulation of highly dynamic fracture events within an explicit finite element context (see Camacho and Ortiz [3]). Beneath the representation of the general strategy, aspects of an appropriate cohesive material and element formulation are pointed out. In contrast to the conventional cohesive zone implementation, the failure criterion is not an intrinsic part of the fracture model and has to be specified separately. A short introduction of appropriate stress and J-integral based quantities is given.

By means of suitable examples, the capabilities of the proposed approach are shown in dependence on the conventional, initially elastic approach and with respect to experimental investigations. Here, a symmetric three point bending test and a wedge splitting test specimen are investigated. As a preview on further extensions of the proposed initially rigid cohesive finite element implementation, an additional global mesh adaptation algorithm in relation to the predicted crack direction enables the representation of arbitrary crack paths. Therefore, a numerical example with imposed crack initiation and resultant curved crack paths is presented.

1

D. S. Dugdale, "Yielding of steel sheets containing slits", Journal of the Mechanics and Physics of Solids, 8, 100-104, 1960. doi:10.1016/0022-5096(60)90013-2

2

G. I. Barenblatt, "The mathematical theory of equilibrium cracks in brittle fracture", Advances in Applied Mechanics, 7, 55-129, 1962. doi:10.1016/S0065-2156(08)70121-2

3

G. T. Camacho, M. Ortiz, "Computational modelling of impact damage in brittle materials", International Journal of Solids and Structures, 33, 2899-2938, 1996. doi:10.1016/0020-7683(95)00255-3

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