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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.

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.

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.

Francois B.,FRS FNRS Fonds National de la Recherche Scientifique | Francois B.,University of Liege | 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.

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