• Sciences de l'ingénieur/Mécanique/Matériaux et structures en mécanique
  
• Sciences de l'ingénieur/Mécanique
  
• Sciences de l'ingénieur/ photonique
  
• Sciences de l'ingénieur/Matériaux
  
• Sciences de l'ingénieur/Mécanique/Mécanique des matériaux
  
• Physique/Mécanique/Mécanique des matériaux
  
• Sciences de l'Homme et Société
  
• Sciences de l'Homme et Société/Anthropologie biologique
  
• Sciences de l'ingénieur/Mécanique/Mécanique des solides
  
• Sciences de l'ingénieur/Mécanique/Mécanique des structures
  
• Sciences du Vivant
  
• Sciences de l'ingénieur
  
• Mathématiques/Analyse numérique [math.NA]
  
• Sciences de l'ingénieur/Mécanique/Mécanique des fluides
  
• Physique
  
• Sciences de l'ingénieur/Electromagnétisme
  
• Informatique/Traitement du signal et de l'image [eess.SP]
  
• Sciences de l'ingénieur/Mécanique/Biomécanique
  
• Sciences de l'ingénieur/Mécanique/Thermique
  
• Physique/Physique/Physique Générale
  
• Sciences de l'ingénieur/Traitement du signal et de l'image [eess.SP]
  
• Sciences de l'environnement/Biodiversité et Ecologie
  
• Physique/Mécanique/Biomécanique
  
• Sciences de l'Homme et Société/Art et histoire de l'art
  
• Sciences de l'Homme et Société/Héritage culturel et muséologie
  
• Physique/Mécanique/Mécanique des solides
  
• Physique/Mécanique/Mécanique des structures
  
• Physique/Mécanique/Matériaux et structures en mécanique
  
• Sciences du Vivant/Génétique/Génétique des plantes
  
• Chimie/Cristallographie
  
• Physique/Matière Condensée/Science des matériaux
  

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.

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).

Grenadilla wood (Dalbergia melanoxylon Guill. & Perr.) is a hardwood species found in Tanzania, Mozambique, and other countries in the tropical part of Africa, especially in the Eastern-Central region. Thanks to its high density and good hygro-scopic stability, it is used in the making of various musical instruments and fine furniture. Due to the scarcity of published data on this wood species, more studies on its properties are needed to improve its processing and use, and even to search for sustainable alternative materials as its trade is increasingly limited by new regulations. This work is focused on the hygromechanical properties, which hold an important role in the applications of this wood: diffusion coefficients and adsorption-desorp-tion curve (both measured at T = 20 • C), swelling-shrinkage coefficients and full orthotropic elastic constants using an ultrasonic method. Results show that grenadilla wood possesses small water diffusion coefficients (from 1.54 ± 0.49 × 10 −7 cm 2 ∕s in T direction to 4.58 ± 0.84 × 10 −7 cm 2 ∕s in L direction), which is probably related to its high density (1250.0 ± 26.2 kg∕m 2); unique equilibrium moisture content (sorp-tion) curve with a lower fiber saturation point (0.173 ± 0.003); smaller swelling-shrinkage coefficients (0.20 ± 0.03 and 0.32 ± 0.05 in T and R directions, respectively); and elastic constants lower in the longitudinal direction (15.56 ± 1.79 GPa) and higher in the transverse ones (5.10 ± 0.46 GPa and 4.05 ± 0.35 GPa in R and T directions, respectively) than what could be expected with a standard model based on the density only. Several explanations were described here, from the effects of a high extractive content to the possibility of a high microfibril and/or fiber angle.