Elastic Strain Effects on Wave Scattering: Implications for Coda Wave Interferometry (CWI)

Coda Wave Interferometry (CWI) is a highly sensitive monitoring technique built on the sensitivity of elastic coda waves to small changes in a diffusive medium. However, a clear connection between the physical processes involved in the evolution of the medium and the time changes observed by CWI has not been clearly described yet. Here, we quantify the impact of elastic deformation on CWI measurements at laboratory scales. We compare experimental results from wave scattering measurements during a uniaxial compression test to those of a numerical approach based on the combination of two codes (SPECFEM2D and Code_Aster), which allows us to model wave propagation in complex diffusive media during its elastic deformation. In both approaches, the reversible time delays measured between waveforms increase with the elastic deformation of the sample. From the numerical modeling, we gain insight to the relative contributions of different physical effects on the CWI measurement: local density changes from volumetric strain, the deformation of scatterers, and acoustoelastic effects. Our results suggest that acoustoelastics effects related to nonlinear elasticity are dominant

Predictability of the Evolution of the Soil Structure using Water Flow Modeling for a Constructed Technosol

International audienceThis paper focuses on the rela on between the structure of a constructed Technosol and its hydraulic characteris cs during its early pedogenesis. The method is based on a 3-yr comparison of, on one hand, experimental measurements from an in situ gravita on lysimeter and, on the other hand, a modeling approach with HYDRUS-1D. The change of water fl ow pa erns with me was described. It was consistent with previous results for constructed Technosol aggrega on. Apart from seasonal varia ons, the specifi city of the hydraulic func oning of the constructed Technosol was shown to be due to the nature of its technogenic parent materials. The in situ evolu on of the hydrodynamics has been established and partly linked to external factors (climate, vegeta on). The direct modeling and the op miza on of the parameters over fi rst a 3-yr period and then three 9-mo periods accurately represented global water fl ow trends at the pedon scale. However it failed to simulate precisely the main events, such as massive leachate ou low. An evolu on with me of some of the hydraulic proper es was shown, expressing the structuring of the soil. The existence of two dis nct me-scales (slow and steady/fast and cyclic) of the evolu on of hydraulic parameters was then formulated as a new hypothesis. Abbrevia ons: Hz, horizon; TDR, me domain refl ectometry

Formulation thermodynamique de lois de comportement hors-équilibre

Strategies for the elaboration of Lagrangian formulations of the constitutive laws of continuous media subjected to local dissipation are developed. The computation of the resulting variational and local continuous symmetries constitutes the backbone of this work. The theoretical framework chosen is based on a thermodynamics of relaxations, which allows the consideration of microstructural variables evolution, accounting for the kinetic law describing the evolution of the microstructure. It is demonstrated that the self-adjointness condition, which is the necessary and sufficient condition for the existence of a lagrangian associated to a system of partial differential equations, is fulfilled by the chosen constitutive laws, provided the fundamental Euler relation is being generalized for situations outside equilibrium. This postulate is one of the cornerstone of a thermodynamics of relaxation called DNLR (alias Distribution of Nonlinear Relaxations). The kinetics equations governing the evolution of the microstructural variables has been further incorporated into the Lagrangian by means of mul- tipliers. The second aspect exploted in this work concerns the analysis of the Lie symmetries of the constitutive behaviour, following two different routes, The first one consists in computing the variational symmetries, associated to given constitutive equations. A particular symmetry is highlighted in the case of a simplified DNLR model, that is related to the time-temperature equivalence principle. Enlarging the point of view, a methodology for setting up the constitutive behaviour of the material itself is proposed. It relies on the construction of experimental master curves that are given a Lie group structure, further leading to a formal structure of the constitutive equations. This method has been applied for a stick submitted to an impact loading under large strain.L'objet principal de ce travail est une exploration des extensions possibles du formalisme de Lagrange à la mécanique des milieux continus dissipatifs. Ce premier objectif conduit à la recherche concomitante des symétries variationnelles et locales associées au principe de la moindre action ainsi construit. Le cadre thermodynamique choisi pour l'écriture des lois de comportement est celui de la thermomécanique de la relaxation, qui prend en compte des variables internes de microstructure et les cinétiques qui en fixent les lois d'évolution. On montre que l'auto-adjonction (condition nécessaire et suffisante d'existence d'un lagrangien) du jeu d'équations thermodynamiques qui décrit le comportement peut être assurée par une généralisation de la relation d'Euler aux situations de non-équilibre. Cette généralisation est conforme aux fondements d'une approche thermodynamique de la relaxation baptisée DNLR. Les équations cinétiques régissant l'évolution des variables internes ont ensuite été intégrées dans le lagrangien sous forme de contraintes. Le deuxième volet exploré dans ce mémoire concerne l'étude des symétries des équations de comportement. Deux voies complémentaires sont explorées: une méthode de calcul des symétries variationnelles d'une loi de comportement supposée connue a été élaborée. Cette étude met en évidence une symétrie particulière dans le cas d'une approche DNLR simplifiée, qui se traduit par un principe d'équivalence en temps / température. Dans une seconde étape, nous mettons en place une stratégie de modélisation du comportement qui s'appuie sur la construction de courbes maîtresses expérimentales. L'existence de ces dernières est décrite mathématiquement par un groupe de Lie, qui permet a priori de dégager une structure de loi de comportement. Cette démarche a été mise en oeuvre pour un matériau de type colle, sollicité de façon dynamique

Stress inversion and basement-cover stress transmission across weak layers in the Paris basin, France

International audienceWe investigate the source of non-purely gravitational horizontal stresses in the Paris basin, a nowadays tectonically quiet intracratonic basin, in its eastern border of which outstandingly dense stress measurements are available. Based on a synthesis of published data, the stress state in the basin is first shown to be very close to the one that may be extrapolated for the underlying basement, in terms of principal stress orientations and horizontal to vertical stress ratios. This is in favour of a mechanical coupling between the basement and its sedimentary cover, which may seem contradictory to the presence of several weak rock layers in the basin fill, e.g. an argillite layer that was shown to bear low deviatoric stresses, and salt layers that are implicated in a major decollement elsewhere. To unravel this apparent contradiction, a 3D-numerical modelling is performed, following a rigorous inverse problem approach, to determine the long-term elastic properties of both the basement and the basin rocks. The objective is to find the set of elastic constants that provides the best fit between the calculated stress state in the basin and the in situ data, by assuming that the stress state in the basement is known. This methodology provides a realistic set of mechanical parameters, in agreement with previous studies, which leads to the conclusion that the horizontal stresses in the basin constitute its mechanical response to the stresses that developed in the underlying basement during and since the last tectonic event (Alpine phase). The fact that horizontal stresses could be transmitted across the weak horizons, contrary to what may be expected at first glance, is explained both by the geometry of the basin and the fact that, over the long term, the stiffnesses of the various sedimentary rocks are only slightly different from each other

Formulation thermodynamique de lois de comportement hors-équilibre (groupes de symétrie continue issus d'une approche lagrangienne réversible)

L'objet principal de ce travail est une exploration des extensions possibles du formalisme de Lagrange à la mécanique des milieux continus dissipatifs. Ce premier objectif conduit à la recherche concomitante des symétries variationnelles et locales associées au principe de la moindre action ainsi construit. Le cadre thermodynamique choisi pour l'écriture des lois de comportement est celui de la thermomécanique de la relaxation, qui prend en compte des variables internes de microstructure et les cinétiques qui en fixent les lois d'évolution. On montre que l'auto-adjonction (condition nécessaire et suffisante d'existence d'un lagrangien) du jeu d'équations thermodynamiques qui décrit le comportement peut être assurée par une généralisation de la relation d'Euler aux situations de non-équilibre. Cette généralisation est conforme aux fondements d'une approche thermodynamique de la relaxation baptisée DNLR. Les équations cinétiques régissant l'évolution des variables internes ont ensuite été intégrées dans le lagrangien sous forme de contraintes. Le deuxième volet exploré dans ce mémoire concerne l'étude des symétries des équations de comportement. Deux voies complémentaires sont explorées: une méthode de calcul des symétries variationnelles d'une loi de comportement supposée connue a été élaborée. Cette étude met en évidence une symétrie particulière dans le cas d'une approche DNLR simplifiée, qui se traduit par un principe d'équivalence en temps / température. Dans une seconde étape, nous mettons en place une stratégie de modélisation du comportement qui s'appuie sur la construction de courbes maîtresses expérimentales. L'existence de ces dernières est décrite mathématiquement par un groupe de Lie, qui permet a priori de dégager une structure de loi de comportement. Cette démarche a été mise en oeuvre pour un matériau de type colle, sollicité de façon dynamique.Strategies for the elaboration of Lagrangian formulations of the constitutive laws of continuous media subjected to local dissipation are developed. The computation of the resulting variational and local continuous symmetries constitutes the backbone of this work. The theoretical framework chosen is based on a thermodynamics of relaxations, which allows the consideration of microstructural variables evolution, accounting for the kinetic law describing the evolution of the microstructure. It is demonstrated that the self-adjointness condition, which is the necessary and sufficient condition for the existence of a lagrangian associated to a system of partial differential equations, is fulfilled by the chosen constitutive laws, provided the fundamental Euler relation is being generalized for situations outside equilibrium. This postulate is one of the cornerstone of a thermodynamics of relaxation called DNLR (alias Distribution of Nonlinear Relaxations). The kinetiœ equations governing the evolution of the microstructural variables has been further incorporated into the Lagrangian by means of mul- tipliers. The second aspect exploted in this work concerns the analysis of the Lie symmetries of the constitutive behaviour, following two different routes, The first one consists in computing the variational symmetries, associated to given constitutive equations. A particular symmetry is highlighted in the case of a simplified DNLR model, that is related to the time-temperature equivalence principle. Enlarging the point of view, a methodology for setting up the constitutive behaviour of the material itself is proposed. It relies on the construction of experimental master curves that are given a Lie group structure, further leading to a formal structure of the constitutive equations. This method has been applied for a stick submitted to an impact loading under large strain.NANCY-INPL-Bib. électronique (545479901) / SudocSudocFranceF

Another brick in the cell wall: biosynthesis dependent growth model.

Expansive growth of plant cell is conditioned by the cell wall ability to extend irreversibly. This process is possible if (i) a tensile stress is developed in the cell wall due to the coupling effect between turgor pressure and the modulation of its mechanical properties through enzymatic and physicochemical reactions and if (ii) new cell wall elements can be synthesized and assembled to the existing wall. In other words, expansive growth is the result of coupling effects between mechanical, thermal and chemical energy. To have a better understanding of this process, models must describe the interplay between physical or mechanical variable with biological events. In this paper we propose a general unified and theoretical framework to model growth in function of energy forms and their coupling. This framework is based on irreversible thermodynamics. It is then applied to model growth of the internodal cell of Chara corallina modulated by changes in pressure and temperature. The results describe accurately cell growth in term of length increment but also in term of cell pectate biosynthesis and incorporation to the expanding wall. Moreover, the classical growth model based on Lockhart's equation such as the one proposed by Ortega, appears as a particular and restrictive case of the more general growth equation developed in this paper

Thermodynamical journey in plant biology

Nonequilibrium irreversible thermodynamics constitute a meaningful point of view suitable to explore life with a rich paradigm. This analytical framework can be used to span the gap from molecular processes to plant function and shows great promise to create a holistic description of life. Since living organisms dissipate energy, exchange entropy and matter with their environment, they can be assimilated to dissipative structures. This concept inherited from nonequilibrium thermodynamics has four properties which defines a scale independent framework suitable to provide a simpler and more comprehensive view of the highly complex plant biology. According to this approach, a biological function is modeled as a cascade of dissipative structures. Each dissipative structure, corresponds to a biological process, which is initiated by the amplification of a fluctuation. Evolution of the process leads to the breakage of the system symmetry and to the export of entropy. Exporting entropy to the surrounding environment corresponds to collecting information about it. Biological actors which break the symmetry of the system and which store information are by consequence, key actors on which experiments and data analysis focus most. This paper aims at illustrating properties of dissipative structure through familiar examples and thus initiating the dialogue between nonequilibrium thermodynamics and plant biology