Non‐local damage model with evolving internal length

Some insights on boundary effects in nonlocal damage modelling are addressed. Interaction stresses that are at the origin of nonlocality are expected to vanish at the boundary of a solid, in the normal direction to this boundary. Existing models do not account for such an effect. We introduce tentative modifications of the classical nonlocal damage model aimed at accounting for this boundary layer effect in a continuum modelling setting. Computations show that some nonnegligible differences may be observed between the classical and modified formulations. In a one dimensional spalling test, only the modified formulation provides a spall of finite nonzero thickness, whereas spalls smaller than the internal length cannot be obtained according to the original formulation. For the same set of model parameters, including the internal length, the fracture energy derived from the size effect test method is also very different according to both approaches. Parameters in the size effect laws for notched and unnotched specimens, obtained from computation of geometrically similar bending beams, are more consistent with the modified nonlocal model compared to the original nonlocal formulation.

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“…A first possibility is inspired from consideration about micromechanics of interacting defects [22,23]. The weight function in Eq.…”

Section: Modified One-dimensional Modelmentioning

confidence: 99%

“…Refs. [2,21,22]). There are at least two outcomes from these approaches: first, the weight function that is introduced in the nonlocal averaging, along with the internal length, is recovered; second this weight function depends on the state of damage and it is direction dependent with respect to the state of stress.…”

Section: Introductionmentioning

confidence: 99%

Boundary effect on weight function in nonlocal damage model

Krayani

Pijaudier‐Cabot

Dufour

2009

Engineering Fracture Mechanics

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“…However, the determination of a representative characteristic length of micro-structure l c is very complex in concrete since the strain localization can include a mixed mode (tensile zones and shear zones) and a characteristic length (which is a scalar value) is related to the fracture process zone with a certain volume which changes during a deformation (the width of the fracture process zone increases according to e.g. Pijaudier-Cabot et al [41], but decreases after e.g. Simone [42]).…”

Section: Modelling Of Strain Localizationmentioning

confidence: 99%

Computational modelling of concrete behaviour under static and dynamic conditions

Marzec¹,

Tejchman²

2013

Bulletin of the Polish Academy of Sciences: Technical Sciences

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Abstract. The paper presents results of FE simulations of the concrete behaviour under quasi-static and dynamic loading. For quasi-static cyclic analyses, an enhanced coupled elasto-plastic-damage constitutive model has been used. To take the effect of the loading velocity into account, viscous and inertial terms have been also included. To ensure the mesh-independence and to properly reproduce strain localization in the entire range of strain rates, a constitutive formulation has been enhanced by a characteristic length of micro-structure by means of a non-local theory. Numerical results have been compared with some corresponding laboratory tests.

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“…The more recent thick level-set model 6 offers the advantage of a thermodynamically sound approach with a non constant internal length (helping thus to automatically control the evolution of the localization zone) and a smooth transition from damage to fracture. A non constant internal length is also introduced in 7 , 8 and 9 . Finally, the link between a discrete and a nonlocal continuum has been recently studied in 10 .…”

Section: Introductionmentioning

confidence: 99%

Using a penalty term to deal with spurious oscillations in second gradient finite elements

Soufflet

Jouan

Kotronis

et al. 2018

International Journal of Damage Mechanics

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It is well known that it is necessary to introduce a length scale parameter in a continuum damage mechanics model to correctly simulate strain localization. The second gradient model, a special case of kinematically enriched continua, considers an internal length parameter by taking into account the second order derivatives of the displacements in the virtual power principle. In this paper, we show that the original second gradient finite element of Chambon and co-workers can present spurious oscillations, especially for mode I crack propagation problems. After providing the plane stress second gradient constitutive law, we propose to add a penalty term in the original formulation in order to improve numerical convergence and to avoid spurious oscillations in the local variables distributions. Two numerical examples using classical damage mechanics laws, a three points reinforced concrete beam and a trapezoidal notched specimen are used to test the performance of the formulation. Parametrical studies are also shown on the influence of the penalty parameter. The problem of unrealistic damage spreading for damage values close to one, occurring often in mode I crack propagation problems, is finally discussed.

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Non‐local damage model with evolving internal length

Cited by 90 publications

References 18 publications

Boundary effect on weight function in nonlocal damage model

Boundary effect on weight function in nonlocal damage model

Computational modelling of concrete behaviour under static and dynamic conditions

Using a penalty term to deal with spurious oscillations in second gradient finite elements

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