Fracture mechanics of bond in reinforced concrete

Ingraffea, A.R.; Gerstle, Walter H.; Gergely, P.; Saouma, Victor E.

doi:10.1016/0010-4485(84)90128-3

Cited by 18 publications

(25 citation statements)

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“…Either (33) or (34) could be used but the stress condition (34) is simpler and will be used here. The direction of crack growth is determined by using the stress intensity factors [21,23,33,34], so…”

Section: The Condition For Smooth Crack Closing and The Direction Of mentioning

confidence: 99%

New crack‐tip elements for XFEM and applications to cohesive cracks

Belytschko

2003

Numerical Meth Engineering

486

352

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SUMMARYAn extended ÿnite element method scheme for a static cohesive crack is developed with a new formulation for elements containing crack tips. This method can treat arbitrary cracks independent of the mesh and crack growth without remeshing. All cracked elements are enriched by the sign function so that no blending of the local partition of unity is required. This method is able to treat the entire crack with only one type of enrichment function, including the elements containing the crack tip. This scheme is applied to linear 3-node triangular elements and quadratic 6-node triangular elements. To ensure smooth crack closing of the cohesive crack, the stress projection normal to the crack tip is imposed to be equal to the material strength. The equilibrium equation and the traction condition are solved by the Newton-Raphson method to obtain the nodal displacements and the external load simultaneously. The results obtained by the new extended ÿnite element method are compared to reference solutions and show excellent agreement.

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Section: The Condition For Smooth Crack Closing and The Direction Of mentioning

confidence: 99%

New crack‐tip elements for XFEM and applications to cohesive cracks

Belytschko

2003

Numerical Meth Engineering

486

352

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“…Our algorithm tests (13) at all three Gauss points, and if any exceeds the fracture criterion, then we activate the element. The values we encode into the model are found by linearly interpolating between the previous (pre-activation) values of the interface tractions and the current values, with the interpolation coe cient chosen so that one Gauss point is encoded with a value that satisÿes the criterion as an equality.…”

Section: A Possible Remedymentioning

confidence: 99%

Time continuity in cohesive finite element modeling

Papoulia

Sam

Vavasis

2003

Numerical Meth Engineering

112

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SUMMARYWe introduce the notion of time continuity for the analysis of cohesive zone interface ÿnite element models. We focus on 'initially rigid' models in which an interface is inactive until the traction across it reaches a critical level. We argue that methods in this class are time discontinuous, unless special provision is made for the opposite. Time discontinuity leads to pitfalls in numerical implementations: oscillatory behavior, non-convergence in time and dependence on nonphysical regularization parameters. These problems arise at least partly from the attempt to extend uniaxial traction-displacement relationships to multiaxial loading. We also argue that any formulation of a time-continuous functional traction-displacement cohesive model entails encoding the value of the traction components at incipient softening into the model. We exhibit an example of such a model. Most of our numerical experiments concern explicit dynamics. Copyright COHESIVE ZONE MODELINGCohesive zone modeling is one of the most widely used techniques for modeling fracture. It is predicated on the fact that a process zone forms ahead of the crack front, in which material softening takes place. In the spirit of Dugdale [1] and Barenblatt [2] cohesive zone modeling idealizes the process zone with a weak interface of thickness zero. A material point on this interface is initially undamaged, but when the traction across the interface reaches some critical level it starts losing cohesion and gradually softens until a stress-free surface is created. In one dimension, softening is manifested as a gradual drop in traction with increasing relative displacement. Decohesion is usually modeled by a pointwise relationship between the traction across the interface and the relative displacement between the two faces of the interface.We formulate the problem in the following setting. Let the initial conÿguration of the body be denoted B 0 , and let M(X; t) : B 0 × [0; T ] → R 3 be its deformation map. The ÿrst argument to M is a coordinate X in the undeformed body, and the second argument is time. This map is * Correspondence to:

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“…Currently, there are many different approaches available in the literature, which can simulate material separation. Most approaches are based on nodal [1][2][3][4] or element enrichment techniques [5][6][7][8][9][10][11], or even on remeshing strategies [12][13][14]. These approaches were typically validated using benchmark tests with few cracks and by comparing overall displacements.…”

Section: Introductionmentioning

confidence: 99%