• Sciences de l'ingénieur/Mécanique/Mécanique des matériaux
  
• Sciences de l'ingénieur/Mécanique/Matériaux et structures en mécanique
  

Living wood in the tree performs a muscular action by generating forces at sapwood periphery and residual strains in dead sapwood fibres. Dissymmetric force generation around tree trunk is the motor system allowing movement, posture control and tree reshaping after accidents. Rather young trees are able to restore the verticality of their trunk after accidental rotation of the soil-root system due to wind or landslide, leading to typically curved stems shape. The very high dissymmetry of forces for the motor action is associated with the occurrence of reaction wood on one side of the inclined stem during many successive years. A method to reconstitute this biomechanical history from observations after tree felling, on either green or dry wood, is discussed. A selection of 17 such trees coming from 15 different species (13 different families), tropical or temperate, hardwoods or softwoods, were selected and peripheral residual strains were measured in situ before felling, on 8 position for each stem. Matched wooden rods were sawn and measured for their mechanical and physical properties at green and dry states, allowing the estimation of tree growth stress, i.e., the force created by the living wood. It was possible to build easy-to-use conversion coefficients between growth stress indicator (GSI), measured in situ by the single hole method, and growth strain and growth stress with the knowledge of basic density and green longitudinal elastic modulus. Maturation strain, specific modulus (as a proxy of micro-fibril angle) and longitudinal shrinkage are properties independent from basic density, whose variation among species was very large. On the whole range of compression wood, normal wood and tension wood strong relationships between these 3 properties were observed, but altogether no single model based on cell-wall microfibril angle only could be used. Growth forces are the product of 4 parameters: ring width, basic density, basic specific modulus and maturation strain, all of them being the result of wood formation. Thanks to the wide range of wood types and species, simple and highly significant formulas were obtained for the relationship between basic and dry density, green and dry longitudinal modulus of elasticity, basic and dry specific modulus. To estimate ring width in green state from values in dry state, radial shrinkage needs to be measured afterwards on dry specimens. Maturation strains is less accurately linked to late measurements on dry wood, but longitudinal shrinkage offers a rather good solution for an estimation provided that the wood type (softwood, hardwood with-G layer, hardwood without G-Layer) is known.

Toute l’année, mais particulièrement pendant l’été, un phénomène encore incompris est souvent observé :la chute imprévisible et soudaine de grosses branches. Cette ‘casse estivale’ est à l’origine de nombreux dégâts matériels et humains. Avec l’objectif de mieux comprendre ce phénomène, le travail de thèse consiste en partie à appréhender et modéliser le comportement mécanique des branches afin de comprendre la particularité des charpentières plagiotropes. Dans ce résumé, une attention particulière est portée sur l’aspect numérique du projet. Il s’agit du développement à l’échelle de la section d’un modèle de contraintes de croissance longitudinales. Ce développement permettra à terme de prédire des caractéristiques de branches pouvant mener à des niveaux de contraintes limites vis à vis d’une potentielle casse.Rappelons que les contraintes de croissance se mettent en place dans les arbres du fait de la mise en place progressive du bois et des sollicitations mécaniques qu’il subit à chaque étape de sa formation. Celles-ci sont de deux natures, donnant lieu à deux composantes du champ de contraintes qu’on peut supposer additives dans le cadre de l’élasticité linéaire (Thibaut et gril 2003) : d’une part le poids des nouvelles parties de l’arbre, supporté par toute la structureexistante à un instant donné (contraintes de support) ; d’autre part la déformation du nouveau bois déposé en périphérie du fait de la maturation cellulaire (contrainte de maturation). La distribution des contraintes de croissance dans la tige d’un arbre, en équilibre avec l’effet de la gravité à tout instant, n’a rien à voir avec ce dont on a l’habitude en génie civil. En revanche, l’action de sollicitations à court terme, comme le vent, se traduirait par des contraintes supplémentaires conforme aux distributions habituelles lors de la flexion d’un milieu curviligne.De nombreux modèles existent à ce jour. On mentionnera le modèle analytique de Kübler (1959a), qui est le premier modèle biomécanique de contraintes de maturation. La section est alors considérée comme homogène, la maturation des cellules instantanée et les déformations purement élastiques. Côté géométrie, la section est un disque parfait centré sur la moelle. De nombreux auteurs se sont attelés à reprendre et améliorer ce premier modèle. Fournier (1989)a proposé dans les années 1990 un modèle semi-analytique de contraintes de croissance, en prenant en compte des gradients circulaires de maturation (pour expliquer un éventuel port ou redressement), ainsi que des gradients de rigidité. Dans les années suivantes, de nombreux modèles analytiques 1D ont été développés (Alméras et al 2005, Alméras et Fournier 2009, Alméras et al 2018, Huang et al 2010). Ces derniers intègrent notamment la prise en compte dela contrainte de support. 9èmes journées scientifiques du GDR 3544 « Sciences du bois » - Grenoble, 18-20 novembre 2020 Poster C05 159 L’objectif du travail en cours est de mettre en place un modèle semi-analytique qui prend en compte une plasticité mécanique des tissus. Dans un premier temps, nous avons confronté notre méthode de modélisation avec un code élastique, qui prend en compte bon nombre des caractéristiques développées dans la littérature : excentricité, gradient circulaire de maturation et intégration des contraintes de support (poids de la structure). Nous avons ensuite adjoint au code existant une version élastoplastique, qui présente des défauts de convergence quand l’excentricité augmente. Nous avons alors retravaillé notre méthode de maillage. Le travail en cours porte sur l’évaluation de ce nouveau maillage sur une loi élastique.

The approach to wooden artefacts of historical importance, and panel paintings in particular, is a task that requires a multidisciplinary approach based on experimental observation of the artwork and advanced techniques to make these data actually useful for the knowledge and preservation of the object. This study illustrates how a series of scientific observations and instrumental analyses can be used to construct a numerical simulation that allows a deeper understanding of the physical structure and behaviour of the object itself, namely to construct a hygro-mechanical predictive model (a “Digital-Twin”) of Leonardo da Vinci's Mona Lisa panel. Based on specific request from the Louvre Museum, a group of experts with different and complementary skills cooperated and are still cooperating to construct a complete set of experimental observation and non-invasive tests; so, the integration of the collected data made the construction possible of the panel’s Digital-Twin. This paper also specifically examines how the Digital-Twin can be used to compare two framing conditions of the panel; although the two experimental configurations are not inherently comparable, the comparison is made possible by the introduction of a technique of projection of the fields obtained as results of the two analyses, named the Projected Model Comparison (PMC), which has been developed specifically for this research.

Spruce wood specimens were treated under mild temperatures 130°C and 150°C and different relative humidity from 0% to 25%. EMC reduced significantly for all the treatments. Weight loss (WL) increased insignificantly while the colour parameter, L*, decreased dramatically. Tanδ reduced significantly while the E/d has increased. After reconditioning, the partially reversibility has been achieved for EMC, tanδ and E/d. But, still an irreversible changes remains, which suggested being due to the chemical changes in wood polymers. While reversible changes has been resulted from the annealing of amorphous polymers. Since, the mild hygrothermal treatment applied to the specimens coincided with no significant WL, there was no obvious damage in wood structure while the irreversible changes present an improvement in vibrational properties by decrease in damping (tanδ), which could be due to the intermediate relative humidity of the treatment.

This article describes the experimental devices and the processes used to study the hygromechanical behaviour of a historic painted wooden panel (La Sainte Trinité couronnant la vierge, 1516, anonymous, Fabre Museum of Montpellier). A climate showcase was designed for in-museum use, with two glasses allowing visitors as well as scientists to observe both sides simultaneously. The evaluation of the hygroscopic behaviour was done by measuring relative humidity (RH), temperature and variations of panel weight. Variations of panel shape, strain and curvature were observed by two methods: locally with three pairs of displacement transducers fixed on the rear face, and over the entire panel surface by a non-contact optical technique, stereo mark tracking, used simultaneously on both faces. The correlation between local and whole-field measurements was very good. Continuous monitoring (several data per hour over three years) was required to observe the behaviour of the panel during imposed climate variations. The first test, detailed in this paper, was performed before frame removal and panel restoration. It consisted in a stabilization of the panel at 52% RH during 2 months and an increase to 63% RH during 3 months. The small amount of total mass variations, from 31.980 kg to 31.910 kg at 52% RH and 32.088 kg at 63% RH, could not be explained without taking into account the phenomenon of sorption hysteresis. The whole field relief measurement exhibited a concave shape with a maximum amplitude of 16 mm. It showed that shape deformation, ie out-of-plane displacement, was convex bending with a maximum deflection of 1.5 mm and a maximum strain of 0.1 %. Comparable local data had been obtained by the optical and DKs methods. DKs results were ten times more accurate than optical ones. The horizontal strain exhibited a global shrinkage during initial stabilization and a global swelling during RH increase. Heterogeneity of the strain field can be related to the cracks observed on the back face, and to the glued crossbeams. Assuming a linear relationship between swelling and moisture content, we expected, for a 0.6% increase of moisture content, a radial strain of 0.10% and a tangential strain of 0.22%. These results are higher than the ones measured, which can be explained by the cross bars glued on the boards and the cracks. This comparison will be continued for the next stages (crossbars removal, panel restoration).