Anisotropic damage in quasi-brittle solids: modelling, computational issues and applications

Dragon, André; Halm, Damien; Désoyer, Thierry

doi:10.1016/s0045-7825(99)00225-x

Cited by 81 publications

(77 citation statements)

References 18 publications

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“…Scalar models with two damage variables have also been proposed, in an attempt to distinguish between tension and compression damage mechanisms (Mazars, 1986;Faria et al, 1998;Comi and Perego, 2001;Marfia et al, 2004). Following the general formulation of Hansen and Schreyer (1994) and Murakami and Kamiya (1997), anisotropic damage models have been proposed introducing 4th or more frequently 2nd order tensors (Papa and Taliercio, 1996;Dragon et al, 2000;Sellier and Bary, 2002;Litewka and Debinski, 2003;Lü et al, 2004;Kuna-Ciskał and Skrzypek, 2004;Gambarotta, 2004). However, in many of these models the flow rules for the internal variables are established on an empirical basis and are not consistently derived from a proper dissipation functional; this may lead to inconsistencies in the implementation of the model.…”

mentioning

confidence: 99%

A framework of elastic–plastic damaging model for concrete under multiaxial stress states

Contrafatto

Cuomo

2006

International Journal of Plasticity

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mentioning

confidence: 99%

A framework of elastic–plastic damaging model for concrete under multiaxial stress states

Contrafatto

Cuomo

2006

International Journal of Plasticity

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“…Equation (20) with independent values for a 1 and a 2 (and not necessarily infinitesimal) has been widely used in the literature for representing the elasticity tensor of damaged materials. It has been obtained by Kachanov (1992) as the effective moduli of microcracked media and then widely used as a phenomenological model for damaged geomaterials (Chiarelli et al, 2003;Alliche, 2004) or as an intermediary between micromechanical and phenomenological models for further theoretical investigations (Halm and Dragon, 1988;Dragon et al, 2000). It is interesting to note that Equation (20) can be defined directly by an ellipsoidal property: for this model the surface F 2 (C) is ellipsoidal.…”

Section: Ellipsoidal Anisotropies In Linear Elasticitymentioning

confidence: 99%

“…The models introduced by Saint Venant do not correspond to crystalline types of anisotropy, but cover a large variety of models introduced in recent years for the elasticity tensor of damaged materials (Halm and Dragon, 1988;Kachanov, 1992;Dragon et al, 2000;Chiarelli et al, 2003;Alliche, 2004) or as effective moduli of heterogeneous media (Milgrom and Shtrikman, 1992;Milton, 2002). They allow the representation of a three-dimensional anisotropy with reduced number of parameters.…”

Section: Introductionmentioning

confidence: 99%

Ellipsoidal Anisotropies in Linear Elasticity: Extension of Saint Venant's Work to Phenomenological Modeling of Materials

Pouya¹

2007

International Journal of Damage Mechanics

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Several families of elastic anisotropies have been introduced by Saint Venant (Saint Venent, B. (de) (1863). Sur la distribution des e´lasticitie´s autour de chaque point d'un solide ou d'un milieu de contexture quelconque, particulie`rement lorsqu'il est amorphe sams eˆtre isotrope, Journal de Math. Pures et Applique´es, Tome VIII (2 e´me se´rie) pp. 257-430) for which the polar diagram of elastic parameters in different directions of the material (indicator surface) is ellipsoidal. These families cover a large variety of models introduced in recent years for damaged materials or as effective moduli of heterogeneous materials. Ellipsoidal anisotropy has also been used as a guideline in phenomenological modeling of materials. Then a question that naturally arises is to know in which conditions the assumption that some indicator surfaces are ellipsoidal allows one to entirely determine the elastic constants. This question has not been rigorously studied in the literature. In this study, first, several basic classes of ellipsoidal anisotropy are presented. Then the problem of the determination of elastic parameters from indicator surfaces is discussed in several basic cases that can occur in phenomenological modeling. Finally, the compatibility between the assumption of ellipsoidal form for different indicator surfaces is discussed. In particular, it is shown that if the indicator surfaces of ffiffiffiffiffiffiffiffiffi EðnÞ 4 p and of ffiffiffiffiffiffiffiffi cðnÞ À4 p (where E(n) and c(n) are, respectively, the Young's modulus and the elastic coefficient in the direction n) are ellipsoidal, then the two ellipsoids have necessarily the same principal axes, and the material in this case is orthotropic.

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“…6). This observation indicates that the most probable damaging mechanism is the result of the development of internal micro-defects (cavities, cracks) with tension [14][15][16][17][18]. A damaging factor d is classically defined as:…”

Section: Isotropic Damagementioning

confidence: 99%

Mechanical characterisation of a viscous-elastic plastic material, sensitive to hydrostatic pressure and temperature

Le¹,

Caliez²,

Gratton³

et al. 2006

WIT Transactions on the Built Environment, Vol 85

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This paper deals with the characterization of the static mechanical behaviour of an energetic material. Due to the constituents (crystals and a polymeric binder), the behaviour is influenced by the pressure, the temperature and the strain rate. The temperature, considered varying slowly, is a parameter and the computational problems are uncoupled. Therefore, a complete experimental protocol and a model have been developed. Inspired from the Visco-Scram model, the behaviour is described using a general Maxwell model in which all the branches are affected by an isotropic damage. The first branch takes into account elastic-plastic behaviour. The yield stress is given by a parabolic criterion, characterized using compressive, tensile and tri-axial tests. The hardening is isotropic and the plastic flow rule is nonassociated. The other branches are viscoelastic. A genetic algorithm is used to optimise the viscoelastic parameters, previously obtained using DMA measurements. Comparisons between the model and experiments are proposed for different temperatures, strain rates and pressures. At last, a user material subroutine has been developed in Abaqus Standard and finite element computations of the Brazilian test are compared to the experimental response.

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Anisotropic damage in quasi-brittle solids: modelling, computational issues and applications

Cited by 81 publications

References 18 publications

A framework of elastic–plastic damaging model for concrete under multiaxial stress states

A framework of elastic–plastic damaging model for concrete under multiaxial stress states

Ellipsoidal Anisotropies in Linear Elasticity: Extension of Saint Venant's Work to Phenomenological Modeling of Materials

Mechanical characterisation of a viscous-elastic plastic material, sensitive to hydrostatic pressure and temperature

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