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).
Wooden Panel Paintings (WPP) are among the most significant historical and artistic artifacts from the Middle Ages and Renaissance and pose a challenge to conservators and scientists in both their comprehension and conservation. From a structural point of view, they can be considered as multi-layered objects, consisting of a wooden support and several pictorial layers. The wooden support, hygroscopic in nature, constantly seeks equilibrium with the humidity of the environment, and consequently deforms. Based on a series of hygroscopic tests carried out on six original WPPs, the present work aims to model their deformation tendencies induced by moisture changes and to characterise them by means of an inverse identification process. The sensitivity analysis of this study provided valuable insights into the complexity of the phenomenon of WPP deformation: even small variations in input variables (board anatomy, stiffness and emissivity of pictorial layers) led to significant changes in the deformation trend over time, highlighting the high variability of the physical problem under investigation. Sobol's analysis variance confirmed this complexity, demonstrating the different levels of influence of input variables and the existence of interactions between them. Overall, the results of this analysis highlighted the need to carefully evaluate the interactions and uncertainties in input variables to fully understand the complexity of the system. The iterative optimization process led to numerical results tending to agree with experimental data, with most results showing a very high correlation. This suggests that the chosen variables and modelling assumptions sufficiently described the physical system and that numerical models can be accurately calibrated. The proposed concept of 'learning from objects', by conducting experimental investigations specifically dedicated to understanding the deformation tendencies of the artwork, is essential. In this approach, numerical analysis is used in conjunction with experiments to gain a deeper understanding of the artwork, characterise it and extract valuable information.
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 of the panel’s Digital-Twin possible. 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.
Wooden panel paintings are among the most important historical and artistic artworks from the Middle Ages and the Renaissance period. Currently, they represent a challenge for conservators and scientists who face complex issues related to their conservation. Panel paintings can be considered multilayer objects, that for brevity can be considered to consist of a wooden support and various paint layers. The wooden support is known to be hygroscopic and is continuously seeking hygroscopic equilibrium with the humidity of the environment, thus it tends to deform. Based on various hygroscopic tests carried out on 6 real panel paintings chosen by expert restorers to represent different periods and construction techniques, this paper describes the deformation tendencies of the selected panel paintings. Among possible variables, three most important variables were identified: (a) tree ring orientation of the wooden support, (b) stiffness and (c) emissivity of the paint layers. The internal equilibrium of the forces, governed by the moisture gradients across the thickness of the wood, changes drastically according to the varying characterisation of these factors. To observe their individual contributions, the 6 panel paintings underwent various humidity cycles, were completely free to deform and were always in complete safety. To characterise the stiffness and emissivity of the paint layers, the 6 panel paintings underwent a few humidity cycles with the front face totally waterproofed; thus, the moisture exchange was forced from the back only, and one of the three variables was eliminated. A complex system emerges where the tree ring orientation of the wooden support, the stiffness and emissivity of the paint layers are strongly coupled and determine the deformation modes of the panel paintings. A numerical analysis was conducted to classify the various general deformation modes of panel paintings and the specific classification of the 6 real panel paintings analysed experimentally. The complexity of the interaction of the variables studied suggests that experimental procedures must be conducted in preparation for numerical analyses of real panel paintings.
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