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

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).

Moisture changes cause transient effects in various polymeric materials. In wood, they are mainly documented in semi-static or low-frequency domains and could explain various anomalies in wood behaviour, including the so-called mechano-sorptive effect. This article aimed at exploring and quantifying transient effects in wood vibrational properties, evidenced but in few publications. A series of 65 experiments on spruce and maple, in longitudinal (L) and radial (R) directions, spanning many humidity trajectories, were monitored through time (1-7 weeks) after step-change in relative humidity (RH). Changes in dimensions and specific dynamic modulus of elasticity (E′/γ) closely followed change in moisture content (MC). But the damping coefficient (tanδ) always increased (whether MC increased or decreased) within first hours/days, before slowly re-decreasing. This was quantitatively analysed by subtracting equilibrium moisture content (EMC) dependence from the global changes in tanδ, which simultaneously expressed destabilisation, followed by physical ageing (a slow process towards approaching equilibrium). For small EMC steps, the amplitude of destabilisation in L tanδ exceeded changes due to EMC dependence. Destabilisation was of similar importance relative to L or to R tanδ, while R tanδ showed much (2−4×) stronger EMC dependence. Amplitude of destabilisation increased with wider RH/EMC-steps (and faster sorption rates). Within an experiment, maximum destabilisation occurred nearly concomitantly with maximum sorption rate. Equilibrium was usually reached in MC, even within one week, but seldom in tanδ, even after several weeks. Results suggested that: (i) drying caused similar amplitudes of destabilisation, but that occurred sooner, and recovered faster, than humidifying; (ii) small RH-steps caused relatively smaller amplitudes of destabi-lisation, but that occurred later, and spanned over longer time before recovering equilibrium, than wide RH-steps. Some possible hypotheses are introduced to explain the observed phenomena. These phenomena also have important practical consequences in real-life wood uses and, particularly, in the design of experimental protocols.

For in situ timber structures applications, heat and mass transfer are strongly dependent on temperature. This work focuses on a parametrical modeling to evaluate and quantify temperature effect at each stage. The model is classically based on a coupling between Fourier's Law, which establishes the temporal and spatial distribution of temperature, and Fick's Law dealing specifically with the water field distribution. Several hypotheses are proposed and discussed in this work as regards thermal coupling. In particular, it is shown how to integrate temperature into a permeability correction. Also proposed herein is an interaction between temperature and the sorption isotherm. The model incorporates partial adsorption and desorption isotherms. Implementation in a finite element software allows highlighting the various couplings, in comparison with more standard calculus approaches.