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Erzar B.,CEA DAM Gramat | Forquin P.,CNRS Grenoble Laboratory for Soils, Solids, Structures, and Risks
International Journal of Solids and Structures | Year: 2014

With the exponential increase of computational power, numerical simulations are more and more used to model the response of concrete structures subjected to dynamic loadings such as detonation near a concrete structural element or projectile-impact. Such loadings lead to intense damage modes resulting from high strain-rate tensile loadings in the concrete structure. However, the modelling of the post-peak tensile response of concrete still remains difficult due to the lack of experimental data at high strain-rates. This work aims at improving the modelling of the softening behaviour of concrete based on the following statement: despite the propagation of unstable cracks in the tested specimen cohesion strength exists in the vicinity of triggered cracks and is driving the whole softening behaviour of concrete. This statement is justified in the present work by means of experiments and Monte-Carlo calculations: firstly, concrete samples have been subjected to a dynamic tensile loading by means of spalling experiments. Several specimens have been recovered in a damaged but unbroken state and have been subsequently loaded in quasi-static tensile experiments to characterise the residual strength and damage level in the sample. In addition, Monte-Carlo simulations have been conducted to clarify the possible influence of cohesion strength in the vicinity of cracks. Finally, the DFH (Denoual-Forquin-Hild) anisotropic damage model has been adapted to take into account the cohesion strength in the damaged zone and to describe the softening behaviour of concrete. Numerical simulations of experiments conducted on dry and saturated samples at different levels of loading-rate illustrate the new capability of the model. © 2014 Elsevier Ltd. All rights reserved.

Lewandowska J.,French National Center for Scientific Research | Auriault J.-L.,CNRS Grenoble Laboratory for Soils, Solids, Structures, and Risks
International Journal for Numerical and Analytical Methods in Geomechanics | Year: 2013

The purpose of this paper is to develop the macroscopic model of hydro-mechanical coupling for the case of a porous medium containing isolated cracks or/and vugs. In the development, we apply the asymptotic expansion homogenization method. It is shown that the general structure of Biot's model is the same as in the case of homogeneous medium, but the poro-elastic parameters are modified. Two numerical examples are presented. They concern the computations of Biot's parameters in isotropic and anisotropic cases. It can also be seen how the presence of near-zero-volume cracks influences Biot's parameters of the porous matrix. It can significantly affect the coupled hydro-mechanical behaviour of damaged porous medium. © 2012 John Wiley & Sons, Ltd.

Francois B.,FRS FNRS Fonds National de la Recherche Scientifique | Francois B.,University of Liège | Dascalu C.,CNRS Grenoble Laboratory for Soils, Solids, Structures, and Risks
Journal of the Mechanics and Physics of Solids | Year: 2010

This paper presents the theoretical developments and the numerical applications of a time-dependent damage law. This law is deduced from considerations at the micro-scale where non-planar growth of micro-cracks, following a subcritical propagation criterion, is assumed. The orientation of the crack growth is governed by the maximum energy release rate at the crack tips and the introduction of an equivalent straight crack. The passage from micro-scale to macro-scale is done through an asymptotic homogenization approach. The model is built in two steps. First, the effective coefficients are calculated at the micro-scale in finite periodical cells, with respect to the micro-cracks length and their orientation. Then, a subcritical damage law is developed in order to establish the evolution of damage. This damage law is obtained as a differential equation depending on the microscopic stress intensity factors, which are a priori calculated for different crack lengths and orientations. The developed model enables to reproduce not only the classical short-term stressstrain response of materials (in tension and compression) but also the long-term behavior encountering relaxation and creep effects. Numerical simulations show the ability of the developed model to reproduce this time-dependent damage response of materials. © 2010 Elsevier Ltd. All rights reserved.

Boutin C.,National School of Public Civil Engineering | Geindreau C.,CNRS Grenoble Laboratory for Soils, Solids, Structures, and Risks
Physical Review E - Statistical, Nonlinear, and Soft Matter Physics | Year: 2010

This paper presents a study of transport parameters (diffusion, dynamic permeability, thermal permeability, trapping constant) of porous media by combining the homogenization of periodic media (HPM) and the self-consistent scheme (SCM) based on a bicomposite spherical pattern. The link between the HPM and SCM approaches is first established by using a systematic argument independent of the problem under consideration. It is shown that the periodicity condition can be replaced by zero flux and energy through the whole surface of the representative elementary volume. Consequently the SCM solution can be considered as a geometrical approximation of the local problem derived through HPM for materials such that the morphology of the period is "close" to the SCM pattern. These results are then applied to derive the estimates of the effective diffusion, the dynamic permeability, the thermal permeability and the trapping constant of porous media. These SCM estimates are compared with numerical HPM results obtained on periodic arrays of spheres and polyhedrons. It is shown that SCM estimates provide good analytical approximations of the effective parameters for periodic packings of spheres at porosities larger than 0.6, while the agreement is excellent for periodic packings of polyhedrons in the whole range of porosity. © 2010 The American Physical Society.

Arminjon M.,CNRS Grenoble Laboratory for Soils, Solids, Structures, and Risks
International Journal of Geometric Methods in Modern Physics | Year: 2013

Although the standard generally covariant Dirac equation is unique in a topologically simple spacetime, it has been shown that it leads to non-uniqueness problems for the Hamiltonian and energy operators, including the non-uniqueness of the energy spectrum. These problems should be solved by restricting the choice of the Dirac gamma field in a consistent way. Recently, we proposed to impose the value of the rotation rate of the tetrad field. This is not necessarily easy to implement and works only in a given reference frame. Here, we propose that the gamma field should change only by constant gauge transformations. To get that situation, we are naturally led to assume that the metric can be put in a space-isotropic diagonal form. When this is the case, it distinguishes a preferred reference frame. We show that by defining the gamma field from the "diagonal tetrad" in a chart in which the metric has that form, the uniqueness problems are solved at once for all reference frames. We discuss the physical relevance of the metric considered and our restriction to first-quantized theory. © 2013 World Scientific Publishing Company.

Arminjon M.,CNRS Grenoble Laboratory for Soils, Solids, Structures, and Risks
International Journal of Theoretical Physics | Year: 2015

Some precisions are given about the definition of the Hamiltonian operator H and its transformation properties, for a linear wave equation in a general spacetime. In the presence of time-dependent unitary gauge transformations, H as an operator depends on the gauge choice. The other observables of QM and their rates also become gauge-dependent unless a proper account for the gauge choice is done in their definition. We show the explicit effect of these non-uniqueness issues in the case of the Dirac equation in a general spacetime with the Schwinger gauge. We show also in detail why, the meaning of the energy in QM being inherited from classical Hamiltonian mechanics, the energy operator and its mean values ought to be well defined in a general spacetime. © 2014, Springer Science+Business Media New York.

Zanette J.,CNRS Grenoble Laboratory for Soils, Solids, Structures, and Risks | Imbault D.,CNRS Grenoble Laboratory for Soils, Solids, Structures, and Risks | Tourabi A.,CNRS Grenoble Laboratory for Soils, Solids, Structures, and Risks
Renewable Energy | Year: 2010

This contribution deals with the design of cross flow water turbines. The mechanical stress sustained by the blades depends on the basic geometrical specifications of the cross flow water turbine, its rotational speed, the exact geometry of the blades and the velocity of the upstream water current. During the operation, the blades are submitted to severe cyclic loadings generated by pressure field's variation as function of angular position. This paper proposes a simplified design methodology for structural analysis of cross flow water turbine blades, with quite low computational time. A new trapezoidal-bladed turbine obtained from this method promises to be more efficient than the classical designs. Its most distinctive characteristic is a variable profiled cross-section area, which should significantly reduce the intensity of cyclic loadings in the material and improve the turbine's durability. The advantages of this new geometry will be compared with three other geometries based on NACA0018 hydrofoil. © 2009 Elsevier Ltd. All rights reserved.

Nicot F.,IRSTEA | Darve F.,CNRS Grenoble Laboratory for Soils, Solids, Structures, and Risks
Mechanics of Materials | Year: 2011

Solving boundary value problems requires implementation of sufficiently robust constitutive models. Most models try to incorporate a great deal of phenomenological ingredients, but this refining often leads to overcomplicated formulations, requiring a large number of parameters to be identified. A powerful alternative can be found with micromechanical models, where the medium is described as a distribution of elementary sets of grains. The complexity is not related to the constitutive description, but to the multiplicity of contacts oriented along all the directions of the physical space. This paper proposes an advanced micromechanical model that introduces an intermediate scale (mesoscopic scale): elementary hexagonal patterns of adjoining particles. This is advantageous with respect to current micromechanical models that generally describe the material through a single distribution of contacts. This new approach makes it possible to take many constitutive properties into account in a very natural way, such as the occurrence of diffuse failure modes. These preliminary results are presented in order to give clear insights into the capability of such multiscale approaches. © 2011 Elsevier Ltd. All rights reserved.

Baroth J.,CNRS Grenoble Laboratory for Soils, Solids, Structures, and Risks | Malecot Y.,CNRS Grenoble Laboratory for Soils, Solids, Structures, and Risks
Computers and Geotechnics | Year: 2010

This study presents the probabilistic analysis of the inverse analysis of an excavation problem. Two techniques are used during two successive stages. First, a genetic algorithm inverse analysis is conducted to identify soil parameters from in situ measurements (i.e. first stage of the construction project). For a given tolerable error between the measurement and the response of the numerical model the genetic algorithm is able to generate a statistical set of soil parameters, which may then serve as input data to a stochastic finite element method. The second analysis allows predicting a confidence interval for the final behaviour of the geotechnical structure (i.e. second stage of the project). The tools employed in this study have already been presented in previous papers, but the originality herein consists of coupling them. To illustrate this method, a synthetic excavation problem with a very simple geometry is used. © 2010 Elsevier Ltd. All rights reserved.

Arminjon M.,CNRS Grenoble Laboratory for Soils, Solids, Structures, and Risks
Journal of Physics: Conference Series | Year: 2015

The definition of the Hamiltonian operator H for a general wave equation in a general spacetime is discussed. We recall that H depends on the coordinate system merely through the corresponding reference frame. When the wave equation involves a gauge choice and the gauge change is time-dependent, H asan operator depends on the gauge choice. This dependence extends to the energy operator E, which is the Hermitian part of H. We distinguish between this ambiguity issue of E and the one that occurs due to a mere change of the "representation" (e.g. transforming the Dirac wave function from the "Dirac representation" to a "Foldy-Wouthuy senre presentation"). We also assert that the energy operator ought to be well defined in a given reference frame at a given time, e.g. by comparing the situation for this operator with the main features of the energy for a classical Hamiltonian particle. © Published under licence by IOP Publishing Ltd.

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