Boundary effect on weight function in nonlocal damage model

Krayani, Abbas; Pijaudier‐Cabot, Gilles; Dufour, Frédéric

doi:10.1016/j.engfracmech.2009.07.007

Cited by 77 publications

(62 citation statements)

References 20 publications

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“…The difference from the nonlocal stress at the points of the interior domain is that it is defined only for boundary layer thickness as a whole and not for an arbitrary generic point across the thickness. Further note that the local treatment of the stress in the boundary layer has previously been advocated for the deterministic nonlocal models, to introduce diminishing nonlocality as the boundary is approached (Krayani et al 2009). It has been shown that the proposed nonlocal boundary layer model agrees well with the original weakest-link model for structures with regular geometries, e.g., rectangular beams under pure bending (Bažant et al 2010).…”

Section: Review Of Weakest-link Model and Its Nonlocal Extensionmentioning

confidence: 99%

Computation of Probability Distribution of Strength of Quasibrittle Structures Failing at Macrocrack Initiation

Eliáš

Bažant

2012

J. Eng. Mech.

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Engineering structures must be designed for an extremely low failure probability, P f < 10 À6 . To determine the corresponding structural strength, a mechanics-based probability distribution model is required. Recent studies have shown that quasibrittle structures that fail at the macrocrack initiation from a single representative volume element (RVE) can be statistically modeled as a finite chain of RVEs. It has further been demonstrated that, based on atomistic fracture mechanics and a statistical multiscale transition model, the strength distribution of each RVE can be approximately described by a Gaussian distribution, onto which a Weibull tail is grafted at a point of the probability about 10 À4 to 10 À3 . The model implies that the strength distribution of quasibrittle structures depends on the structure size, varying gradually from the Gaussian distribution modified by a far-left Weibull tail applicable for small-size structures, to the Weibull distribution applicable for large-size structures. Compared with the classical Weibull strength distribution, which is limited to perfectly brittle structures, the grafted Weibull-Gaussian distribution of the RVE strength makes the computation of the strength distribution of quasibrittle structures inevitably more complicated. This paper presents two methods to facilitate this computation: (1) for structures with a simple stress field, an approximate closed-form expression for the strength distribution based on the Taylor series expansion of the grafted WeibullGaussian distribution; and (2) for structures with a complex stress field, a random RVE placing method based on the centroidal Voronoi tessellation. Numerical examples including three-point and four-point bend beams, and a two-dimensional analysis of the ill-fated Malpasset dam, show that Method 1 agrees well with Method 2 as well as with the previously proposed nonlocal boundary method.

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Section: Review Of Weakest-link Model and Its Nonlocal Extensionmentioning

confidence: 99%

Computation of Probability Distribution of Strength of Quasibrittle Structures Failing at Macrocrack Initiation

Eliáš

Bažant

2012

J. Eng. Mech.

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“…In addition, it is straightforward to employ more sophisticated damage mechanisms such as anisotropic damage models. The treatment of nonlocal quantities in the vicinity of the boundary also requires some modifications according to the works of Krayani et al (2009), Pijaudier-Cabot andDufour (2010). A study is also necessary on the interactive radius, a parameter that is usually determined by experiments.…”

Section: Discussionmentioning

confidence: 99%

“…Jirasek (1998) explored different non-local formulations based on the type of non-local variables. Boundary effects in non-local models must be avoided (Pijaudier-Cabot and Grégoire 2014) which is accomplished by normalizing the weight function or using only the local material response on the boundaries (see also, Krayani et al 2009;Pijaudier-Cabot and Dufour 2010). For the finite element framework, Pijaudier-Cabot and Huerta (1991) derived the general form of the tangent stiffness matrix for non-local isotropic damage models (see also, Askes and Sluys 2000).…”

Section: State-of-the-art Review Of Interface Elasticitymentioning

confidence: 99%

Coherent Energetic Interfaces Accounting for In-Plane Degradation

Esmaeili¹,

Javili²,

Steinmann³

2017

Defect and Material Mechanics

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Interfaces can play a dominant role in the overall response of a body. The importance of interfaces is particularly appreciated at small length scales due to large area to volume ratios. From the mechanical point of view, this scale dependent characteristic can be captured by endowing a coherent interface with its own elastic resistance as proposed by the interface elasticity theory. This theory proves to be an extremely powerful tool to explain size effects and to predict the behavior of nano-materials. To date, interface elasticity theory only accounts for the elastic response of coherent interfaces and obviously lacks an explanation for inelastic interface behavior such as damage or plasticity. The objective of this contribution is to extend interface elasticity theory to account for damage of coherent interfaces. To this end, a thermodynamically consistent interface elasticity theory with damage is proposed. A local damage model for the interface is presented and is extended towards a non-local damage model. The non-linear governing equations and the weak forms A. Esmaeili · P. Steinmann (B) Chair of Applied Mechanics, University of Erlangen-Nuremberg, Egerlandstrasse 5, 91058 Erlangen, Germany e-mail: paul.steinmann@ltm.uni-erlangen.de A. Esmaeili e-mail: ali.esmaeili@ltm.uni-erlangen.de A. Javili Department of Mechanical Engineering, Bilkent University, 06800 Ankara, Turkey e-mail: ajavili@bilkent.edu.tr thereof are derived. The numerical implementation is carried out using the finite element method and consistent tangents are listed. The computational algorithms are given in detail. Finally, a series of numerical examples is studied to provide further insight into the problem and to carefully elucidate key features of the proposed theory.

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“…Several analytical, experimental and numerical studies demonstrated that the evolution of micro-cracks cannot occur arbitrarily fast due to inertia effects [26][27][28]. Thus, if damage is used to describe microcracking , its evolution has to be retarded in case of high strain rates, i.e.…”

Section: Rate-dependent Damage Modelmentioning

confidence: 99%

Simulation of dynamic behavior of quasi-brittle materials with new rate dependent damage model

Pereira

Weerheijm²,

Sluijs³

2016

Proceedings of the 9th International Conference on Fracture Mechanics of Concrete and Concrete Structures

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Abstract. In concrete often complex fracture and fragmentation patterns develop when subjected to high straining loads. The proper simulation of the dynamic cracking process in concrete is crucial for good predictions of the residual bearing capacity of structures in the risk of being exposed to extraordinary events like explosions, high velocity impacts or earthquakes.As it is well known, concrete is a highly rate dependent material. Experimental and numerical studies indicate that the evolution of damage is governed by complex phenomena taking place simultaneously at different material scales, i.e. micro, meso and macro-scales. Therefore, the constitutive law, and its rate dependency, must be adjusted to the level of representation. For a proper phenomenological (macroscopic) representation of the reality, the constitutive law has to explicitly describe all phenomena taking place at the lower material scales. Macro-scale inertia effects are implicitly simulated by the equation of motion.In the current paper, dynamic crack propagation and branching is studied with a new rate-dependent stress-based nonlocal damage model. The definition of rate in the constitutive law is changed to account for the inherent meso-scale structural inertia effects. This is accomplished by a new concept of effective rate which governs the dynamic delayed response of the material to variations of the deformation (strain) rate, usually described as micro-inertia effects. The proposed model realistically simulates dynamic crack propagation and crack branching phenomena in concrete.

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Boundary effect on weight function in nonlocal damage model

Cited by 77 publications

References 20 publications

Computation of Probability Distribution of Strength of Quasibrittle Structures Failing at Macrocrack Initiation

Computation of Probability Distribution of Strength of Quasibrittle Structures Failing at Macrocrack Initiation

Coherent Energetic Interfaces Accounting for In-Plane Degradation

Simulation of dynamic behavior of quasi-brittle materials with new rate dependent damage model

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