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

Abstract

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.

Coupling numerical and experimental methods to characterise the mechanical behaviour of the Mona Lisa: a method to enhance the conservation of panel paintings

“…For the sensitivity analysis, the variance-based Sobol method was used as it can handle nonadditive, non-monotonic and non-linear systems, following the same schema of [22]. In a Sobol sensitivity analysis, the first-order index and total index are commonly used to measure the sensitivity of a model output to input parameters.…”

“…Some have investigated the hygro-mechanical behaviour of the main materials making up such artwork, tested on new materials [1][2][3][4][5], others the hygro-mechanical behaviour of mock-ups tested in the laboratory [6][7][8][9][10] and some others numerical modelling based on mock-up behaviour or literature data to interpret their behaviour [11,[12][13][14]. The present research rather focuses on an authentic artwork, as already proposed by [15][16][17][18][19][20], following the consideration that each panel painting shows a specific hygro-mechanical behaviour which should be known for its preventive and remedial conservation, as highlighted both by testing and numerical modelling in [21,22]. Since 2004, the wooden panel on which Leonardo da Vinci painted his Mona Lisa has been studied by an international research team under the request of the curators of the Louvre Museum.…”

“…Previously published work [23][24][25][26][27] confirmed the relevance of integrating computational tools with experimental data directly obtained from the original artwork being studied. This approach, which has been gaining ground in recent years [20][21][22]28], has necessarily required collaboration among scientists, conservators and restorers, and can be considered as an important step towards fully integrating this kind of research for the in-depth knowledge and conservation of the physical structure of the wooden artwork. Starting from such approach, the considerable difficulties found in fully interpreting the results of the experimental observations and measurements have highlighted the complexity of the phenomena observed, and the variability from case to case of the observed behaviours.…”

Fracture toughness of dried oil paints

“…So far, those properties have been determined predominantly for new materials, and an assumption has been made that they represent the properties of historical materials. Only a few sets of data have been obtained for historical materials (10,11,12) but due to the limited number of tested specimens, their statistical relevance is still to be con rmed. A recent compilation of material parameters for oil-based pictorial layers illustrated that they evolve over decades and might continue to evolve even over centuries (1).…”