Asymptotic fields at the tip of a cohesive crack

Karihaloo, Bhushan Lal; Xiao, Q. Z.

doi:10.1007/s10704-008-9218-2

Cited by 39 publications

(36 citation statements)

References 23 publications

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“…As a possible extension of the proposed method, analytical crack tip fields with a cohesive law such as those derived by Karihaloo and Xiao [32] may be introduced using the proposed formalism to simulate the cohesive crack growth. Last, the developments discussed herein from a numerical standpoint are currently implemented in an experimental technique to measure displacement fields of crack bodies (by digital image correlation).…”

Section: Resultsmentioning

confidence: 99%

Hybrid analytical and extended finite element method (HAX‐FEM): A new enrichment procedure for cracked solids

Réthoré

Roux

Hild

2009

Numerical Meth Engineering

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To cite this version:Julien Réthoré, Stéphane Roux, François Hild. Hybrid analytical and extended finite element method (HAX-FEM): A new enrichment procedure for cracked solids. International Journal for Numerical Methods in Engineering, Wiley, 2010, 81, pp.269-285. 10 SUMMARYA new numerical method is proposed to estimate directly stress intensity factors at the tip of a crack in an elastic body. In the same spirit as for the extended finite element method, the approximation of the displacement field is enriched in the vicinity of the crack tip. Yet the method proposed herein differs by the way the enrichment is introduced. Instead of using partition of unity concepts, a two-description formulation is implemented. The first one uses standard finite elements while the second one, in the vicinity of the crack tip, resorts to a few purely analytical expressions. These two descriptions are then coupled by partitioning the energy with an overlapping zone. The performance of this new enrichment technique is illustrated and compared with existing techniques by means of two examples.

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Section: Resultsmentioning

confidence: 99%

Hybrid analytical and extended finite element method (HAX‐FEM): A new enrichment procedure for cracked solids

Réthoré

Roux

Hild

2009

Numerical Meth Engineering

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“…The mathematical formulation is fully described in [Karihaloo and Xiao 2008], so that only a very brief overview will suffice here. For plane problems, the stresses and displacements in the Cartesian coordinate system centred at the cohesive crack tip can be expressed in terms of two analytic functions φ(z) and χ (z) of the complex variable z = r e iθ :…”

Section: Mathematical Formulationmentioning

confidence: 99%

“…In [Xiao and Karihaloo 2006a;Karihaloo and Xiao 2008;2010] we have obtained universal asymptotic expansions at a cohesive crack tip, analogous to the Williams expansions at a traction-free crack tip for any normal cohesion-separation law (softening law) that can be expressed in a special polynomial with integer or fractional powers. This special form ensures that the radial and angular variations of the asymptotic fields are separable as in the Williams expansions.…”

Section: Introductionmentioning

confidence: 99%

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Accurate simulation of mixed-mode cohesive crack propagation in quasi-brittle structures using exact asymptotic fields in XFEM: an overview

Karihaloo

Xiao

2011

J. Mech. Mater. Struct.

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The extended finite element (XFEM) enriches the standard local FE approximations with known information about the problem, with the use of the partition of unity. This allows the use of meshes that do not conform to a discontinuity and avoids adaptive re-meshing as the discontinuity grows as required with the conventional FEM. When the crack tip asymptotic field is available and used as the enrichment function, XFEM is more accurate than FEM allowing the use of a much coarser mesh around the crack tip. Such asymptotic fields have been known for a long time for traction-free cracks (the Williams expansions) but have only recently been derived for cohesive cracks (Karihaloo-Xiao expansions). In this paper an overview of latter expansions is given for a range of cohesive laws and their usefulness in the simulation of cohesive crack propagation is demonstrated on two examples of concrete and fibre-reinforced concrete flexural members.

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“…For quasi-brittle materials, asymptotic expansions of the crack-tip fields accounting for Coulomb-type friction law have been reported by Karihaloo and Xiao (2008) and by Barpi and Valente (2010). Several models capture the evolution from adhesion to frictional regime exploiting different strategies, with a progressive or a sudden transition (Raous et al, 1999).…”

Section: Introductionmentioning

confidence: 99%

A thermodynamically consistent derivation of a frictional-damage cohesive-zone model with different mode I and mode II fracture energies

Serpieri¹,

Sacco²,

Alfano³

2015

European Journal of Mechanics - A/Solids

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The present paper deals with the derivation of an interface model characterized by macroscopic fracture energies which are different in modes I and II, the macroscopic fracture energy being the total energy dissipated per unit of fracture area.It is first shown that thermo-dynamical consistency for a model governed by a single damage variable, combined with the choice of employing an equivalent relative displacement and of a linear softening in the stress-relative displacement law, leads to the coincidence of fracture energies in modes I and II. To retrieve the experimental evidence of a greater fracture energy in mode II, a micro-structured geometry is considered at the typical point of the interface where a Representative Interface Element (RIE) characterized by a periodic arrangement of distinct inclined planes is introduced. The interaction within each of these surfaces is governed by a coupled damage-friction law.A sensitivity analysis of the correlation between micromechanical parameters and the numerically computed single-point microstructural response in mode II is reported. An assessment of the capability of the model in predicting different mixed mode fracture energies is carried out both at the single microstructural interface point level and with a structural example. For the latter a double cantilever beam with uneven bending moments has been analyzed and numerical results are compared with experimental data reported in the literature for 1 different values of mode mixity.

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Asymptotic fields at the tip of a cohesive crack

Cited by 39 publications

References 23 publications

Hybrid analytical and extended finite element method (HAX‐FEM): A new enrichment procedure for cracked solids

Hybrid analytical and extended finite element method (HAX‐FEM): A new enrichment procedure for cracked solids

Accurate simulation of mixed-mode cohesive crack propagation in quasi-brittle structures using exact asymptotic fields in XFEM: an overview

A thermodynamically consistent derivation of a frictional-damage cohesive-zone model with different mode I and mode II fracture energies

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