Addendum to 'The equivariant spectral function of an invariant elliptic operator'

Let $M$ be a compact boundaryless Riemannian manifold, carrying an effective and isometric action of a torus $T$, and $P_0$ an invariant elliptic classical pseudodifferential operator on $M$. In this note, we strengthen asymptotics for the equivariant (or reduced) spectral function of $P_0$ derived previously, which are already sharp in the eigenvalue aspect, to become almost sharp in the isotypic aspect. In particular, this leads to hybrid equivariant $L^p$-bounds for eigenfunctions that are almost sharp in the eigenvalue and isotypic aspect.Comment: 14 pages. arXiv admin note: text overlap with arXiv:1512.0219

Effect of time and thermo-mechanical couplings on polymers

National audienceAnalysis of the thermo-mechanical behaviour of polymers has been and still is the subject of many rheological studies both experimentally and theoretically. For small deformations, the modelling framework retained by rheologists is often of linear visco-elasticity, which led to the definition of complex modules and used to identify the glass transition temperature as the so called rule of time-temperature superposition. In this context, the effects of time are almost unanimously associated with viscous effects. It has also been observed that the dissipative effects associated with viscous effects are often very small compared to the coupling of sources indicating a high sensitivity of polymeric materials to temperature variations. This work is mainly focused on establishing the exact role of coupling effects, which also induce the effect of time. Using traditional experimental methods of visco-analysis (DMTA) and via an energy analysis of the behaviour, the goal of the thesis is to try to restate the time-temperature equivalence rule under the Thermodynamics of Irreversible Processes, taking into account the dissipative effects and coupling induced process deformation

The effect of the G-Layer on the viscoelastic properties of tropical hardwoods

International audienceContext and aim : This study aimed to examine the effect of the tension wood G‐layer on the viscoelastic properties of wood. Methods : Tension wood and opposite wood samples were obtained from six French Guianese tropical rainforest species (Sextonia rubra, Ocotea guyanensis, Inga alba, Tachigali melinoni, Iyranthera sagotiana and Virola michelii); the tension wood of the former three of these species had a Glayer, whilst the tension wood from the latter three had no Glayer. Tensile dynamic mechanical analysis (DMA) was performed on green never dried wood samples in the longitudinal direction with samples submerged in a water bath at a temperature (30°C) and frequency (1 Hz) representative of the conditions experienced by wood within a living tree. Then, DMA was repeated with samples conditioned to an air-dried state. Finally, samples were oven-dried to measure longitudinal shrinkage. Results : Tension wood did not always have a higher longitudinal storage (elastic) modulus than opposite wood from the same tree regardless of the presence or absence of a G‐layer. For the species containing a G‐layer, tension wood had a higher damping coefficient and experienced a greater longitudinal shrinkage upon drying than opposite wood from the same species. No difference was found in damping coefficients between tension wood and opposite wood for the species that had no G‐layer. Conclusion : It is proposed that the different molecular composition of the G-layer matrix has an influence on the viscoelasticity of wood, even if a biomechanical gain is not yet clear. This study shows that rheological properties and longitudinal shrinkage can be used to detect the presence of a G‐layer in tension wood

Cell wall thickening in developing tension wood of artificially bent poplar trees

International audienceTrees can control their shape and resist gravity thanks to their ability to produce wood under tensile stress. This stress is known to be produced during the maturation of wood fibres but the mechanism of its generation remains unclear. This study focuses on the formation of the secondary wall in tension wood produced in artificially tilted poplar saplings. Thickness of secondary wall layer (SL) and gelatinous layer (GL) were measured from cambium to mature wood in several trees sampled at different times after tilting. Measurements on wood fibres produced before tilting show the progressive increase of secondary wall thickness during the growing season. After the tilting date, SL thickness decreased markedly from normal wood to tension wood while the total thickness increased compared to normal wood, with the development of a thick GL. However, even after GL formation, SL thickness continues to increase during the growing season. GL thickening was observed to be faster than SL thickening. The development of the unlignified GL is proposed to be a low cost, efficient strategy for a fast generation of tensile stress in broadleaved trees

Experimental micromechanical characterisation of wood cell walls

International audienceThe properties of wood and wood based materials are strongly dependent on the properties of its fibres; i.e. the cell wall properties. The ability to characterize these in order to increase our understanding of structure-property relationships is thus highly important. This article gives a brief overview of the state of the art in experimental techniques to characterize the mechanical properties of wood at both the level of the single cell and that of the cell-wall. Challenges, opportunities, drawbacks and limitations of single fibre tensile tests and nanoindentation are discussed with respect to the wood material properties

Effect of extractions on dynamic mechanical properties of white mulberry (Morus alba)

International audienceVibrational properties of wood are affected by several parameters, of which extractives can be one of the most important ones. Wood for European musical instruments has been often studied, but traditional Middle Eastern ones had been left unnoticed. In this study white mulberry (Morus alba L.), the main material for long-necked lutes in Iran, was extracted by five solvents of various polarities (water included). Free-free bar forced vibrations were used to measure longitudinal (L) loss tangent (tanδ), storage (elastic) modulus (E′) and specific modulus (E′/γ) in the acoustic range. Their anisotropy between the 3 axes of orthotropy was determined by DMA (dynamic mechanical analysis). Native wood had a quite low EL′/γ but its tanδ was smaller than expected, and the anisotropy of tanδ and E′/γ was very low. Removal of extractives caused tanδ to increase and moduli to decrease. Acetone, the most effective solvent on damping despite a moderate extraction yield, increased tanδL by at least 20% but did not modify E′/γ as much. When used successively, its effects masked those of solvents used afterwards. Anisotropy of E′/γ was nearly unchanged after extraction in methanol or hot water, while tanδ was much more increased in R than in T direction. Results suggest that in white mulberry, damping is governed more by nature and localization of extractives rather than by their crud abundance

Searching for material symmetries in the burr wood of thuja by a direct contact ultrasonic method on spherical samples

International audienceThis work is part of a program that aims at studying the burr wood of thuja (Tetraclinis articulata). The goal of this work is to identify material symmetries of burr wood to improve its machining. To have a sufficient number of data and to limit the variability between samples, an ultrasonic experimental device, in direct contact on spherical samples, has been developed and improved. Until now, the geometry used in direct contact ultrasonic methods was either cubic or polyhedral allowing to obtain, on the same sample, 3 (cube) to 13 (polyhedron) measurements or usable data. By choosing a reasonable angular gap, the spherical geometry allows the ultrasonic velocity to be measured in 133 different directions on the same specimen. We present here the adaptation and development of the ultrasonic experimental device and results obtained on (i) aluminum chosen as a reference material, (ii) beech wood and (iii) burr wood of thuja