Modelling of hygro-mechanical behaviour of wooden panel paintings: model calibration and artworks characterisation

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.