A symmetric nonlocal damage theory

Borino, Guido; Failla, Boris; Parrinello, Francesco

doi:10.1016/s0020-7683(03)00144-6

Cited by 148 publications

(112 citation statements)

References 22 publications

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“…(A.1). In this regard, note that the same conclusions have been previously drawn by several authors (Borino et al, 2003;Marotti De Sciarra, 2008), who have used a properly modified attenuation function to attain symmetry of the considered matrices.…”

supporting

confidence: 75%

Solution strategies for 1D elastic continuum with long-range interactions: Smooth and fractional decay

Failla

Santini

Zingales

2010

Mechanics Research Communications

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Keywords:Non-local elasticity Long-range interactions Weak formulation of elastic problems Fractional calculus Fractional finite differences a b s t r a c t An elastic continuum model with long-range forces is addressed in this study within the context of approximate analytical methods. Such a model stems from a mechanically-based approach to non-local theory where long-range central forces are introduced between non-adjacent volume elements. Specifically, long-range forces depend on the relative displacement, on the volume product between interacting elements and they are proportional to a proper, material-dependent, distance-decaying function. Smooth-decay functions lead to integro-differential governing equations whereas hypersingular, fractional-decay functions lead to a fractional differential governing equation of Marchaud type. In this paper the Galerkin and the Rayleigh-Ritz method are used to build approximate solutions to the integro-differential and the fractional differential governing equations. Numerical applications show the accuracy of the proposed approximate solutions as compared to the finite difference approximation and to the fractional finite difference approximation.

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supporting

confidence: 75%

Solution strategies for 1D elastic continuum with long-range interactions: Smooth and fractional decay

Failla

Santini

Zingales

2010

Mechanics Research Communications

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“…(9) not symmetric with respect to its arguments x and n. This lack of symmetry leads to the nonsymmetry of the tangent operator [4,19,12]. A symmetric nonlocal formulation ensuring enhancement rule has been recently proposed [6]:…”

Section: Nonlocal Formulationmentioning

confidence: 99%

“…In the subsequent calculations performed with modified weight functions, the shape of the damage profile during spall formation does not evolve and the final profiles of damage and nonlocal strain will be plotted only. With the weight function modified according to [6] denoted as SLC, some improvement is observed as maximum damage is not located at the extremity of the bar (Fig. 5).…”

Section: One-dimensional Example: Spalling Testmentioning

confidence: 99%

“…Because the nonlocal interactions are changing nearby the boundary of the solid, the constitutive formulation [20] does not derive from a thermodynamic free energy potential. The modified symmetric nonlocal damage theory due to Borino and coworkers [6] derives from a potential and fulfill thermodynamic principles. To this end, the weight function is modified near the boundary.…”

Section: Introductionmentioning

confidence: 99%

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Boundary effect on weight function in nonlocal damage model

Krayani

Pijaudier‐Cabot

Dufour

2009

Engineering Fracture Mechanics

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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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“…Polizzotto et al [34] laid down a thermodynamic consistent formulation of non-local plasticity. In turn, Borino et al [35] and Nguyen [36] proposed a thermodynamic consistent formulation of non-local damage. Usually, in elasto-plastic formulations, it is sufficient to achieve mesh-independent FE results to treat non-locally one state variable controlling material softening (e.g.…”

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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A symmetric nonlocal damage theory

Cited by 148 publications

References 22 publications

Solution strategies for 1D elastic continuum with long-range interactions: Smooth and fractional decay

Solution strategies for 1D elastic continuum with long-range interactions: Smooth and fractional decay

Boundary effect on weight function in nonlocal damage model

Computational modelling of concrete behaviour under static and dynamic conditions

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