Learning from Objects: the use of advanced numerical methods to exploit a complete set of information from experimental data, for the Mona Lisa's Digital Twin
Venue: IOP Conference Series: Materials Science and Engineering
Year: 2020

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. Since 2004, the wooden panel on which Leonardo da Vinci painted his "Mona Lisa" has been studied by an international research Team, and several experimental campaigns have been carried out to understand its mechanical, hygroscopic and shape characteristics and behaviour, to evaluate its present state of conservation, and provide related suggestions in order to optimize its conservation. The artwork is painted on one face of a flat sawn Poplar (Populus alba L. panel, doubly curved (convexity toward the front face) and pressed against the rebate of the frame (in French chassis cadre, an intermediate frame,  by two crossbars screwed onto the frame itself. The chassis cadre, with the panel inside, is placed and fixed by metal brackets in a sculptured and gilded external frame, which significantly contributes to the stiffness of the system. An ancient crack runs through the wood from the upper edge of the panel down to the top of the Lady's forehead.  The Team, formed by specialists in Wood Science and Technology (LMGC of Montpellier and DAGRI of University of Florence) and in Optical Measurements (PPrime Institute, University of Poitiers) closely interacted with the Curators, the Scientists from C2RMF and with the Restorers taking care of the artwork, and approached the work according to the following four main tightly intertwining topics: studying the artwork by direct observation and measurements (once a year, during the few hours when it is removed from its climate controlled exhibition case, for the routine inspection of its conservation conditions, or for the execution of exceptional measurements) analysing the propagation risk of the fracture  monitoring the behaviour of the panel during its permanence in the exhibition case, by special ad hoc equipment, conceived and implemented specifically for this task  developing and calibrating a numerical model (a so called "Digital Twin" capable of reproducing accurately the original artwork's reactions to simulated external stresses (hygroscopic and mechanical) that might (actually or potentially) affect it. The observations methods include: (i) scientific and technological analysis of the wooden panel, including wood anatomy, macrostructure and physical and mechanical properties; (ii) optical measurements of its shape  (iii) continuous monitoring of the forces acting on the panel and of its deformations; (iv) detection and description of contact areas between the panel and the chassis cadre using pressuresensitive film. In the course of fifteen years, the Team's knowledge about the panel has progressively increased along with measurement and modelling techniques; based on the collected data, numerical models of the wooden panel have been developed to accurately simulate its hygro mechanical behaviour and its constraints. The aspect that the Authors want to emphasize in the present paper is that numerical modelling tools are also being used in order to enrich experimental investigations, thus allowing to reach deeper information levels. 1. The Digital Twin and its meaning The general problem that arises in the modelling of panel paintings is the need to correctly understand its hygro mechanical characteristics and structure and based on that give information to the conservators to and then protect beforehand the artworks; which makes mandatory the use of noninvasive technologies for characterization. At the same time, the uniqueness of the artworks (inter alia due to the variability of wood, the interaction between the elements composing the system, the conservation history including restoration works executed in the past) makes it difficult to apply literature parameters in the definition of a predictive numerical model. In any case, understanding the stresses and strains acting on the actual art piece is of great interest for its conservation and for the study of potentially dangerous conditions. For these reasons the systematic series of non invasive experimental observations made on the Mona Lisa panel aimed towards, and made it possible, to develop a numerical model totally calibrated on the artwork itself. The model was calibrated by means of the following non destructive measurements [4] the shape of the panel was derived from optical surveys and reconstructed in a numerical threedimensional model; the boundary conditions, i.e. contact zones and pressures between the panel and the framing components surrounding it, have been detected using ad hoc developed techniques, and then have been transferred within the three dimensional model; through visual anatomical observations and results from X ray investigations, the anatomical directions of the wood at each point of the panel have been reconstructed, and this made it possible to construct a model consistent with the anatomy and the stiffness orientation of the actual wooden board; from the load cells readings, it was possible, through an optimization process, to calculate the actual stiffness characteristics of the wooden panel (including the preparation and pictorial layers) In depth studies are available in the literature that examine the fundamental aspects of the above methods [5,6,7,8] The present paper focuses on the study of contact areas in various configurations, necessary for the correct modelling of the panel, and on analytical techniques to compare the results of two numerical analyses representing two different mechanical conditions. 2. Materials and Methods 2.1. Experimental campaigns on contact areas Two experimental campaigns were conducted to investigate the areas of contact between the panel and the chassis cadre. In the first one (performed in 2012) the panel was directly in contact with the wood of the chassis cadre [9] In the second one (performed in 2016) the effects of the interposition of a closed cell polymer foam (Plastazote(c) between the wood of the panel and the chassis cadre were investigated [data still unpublished] In order to identify and evaluate the contact zones, in both cases a pressure sensitive film (LLLW Ultra Super Low Pressure, two sheet film, Fujifilm Prescale(r) was used to perform some totally noninvasive tests: strips of the film were placed on the rebate surface of the chassis cadre, and the panel was carefully inserted and pressed during the prescribed short time (few seconds) reproducing the actual assembly situation, and then disassembled. Red patches appear on the film at the contact areas, and the level of pressure is indicated by the density of the colour  The restraining forces are applied by the crossbeams on the back the panel, near its four corners, in order to partially contain its tendency to cup; four miniature load cells continuously measure these forces, and the data are fed into a continuous recording system  this arrangement makes it possible to have available both the contact profiles and the four forces balancing the contact forces, in other words to have under control the whole system of the boundary conditions and the forces acting on the panel.  Contact zone in the upper and lower zone of the panel Figure 3 shows the difference between the contact areas in the two configurations, with and without Plastazote: since the total forces measured by the load cells are of the same order of magnitude, whereas the contact areas are quite larger in the 2016 tests (with Plastazote) it is evident that the contact pressures must have a very different intensity in the two cases. Unfortunately this difference does not result from the figures shown, both because these are in black and white, and because two different types of films have been used, with different sensitivities. 2.1. Numerical modeling The interpretation of the above results made it necessary to create an ad hoc FEM model, since it was not possible to evaluate the stresses and strains resulting from the two constraint configurations from the mere observation of the patterns of stains An elastic orthotropic model was therefore developed, respecting the constraints represented by the contact areas identified by the tests and the forces measured at the points on the back where the load cells are located. This model is only an approximation as far as viscoelastic behaviour is concerned, but it is efficient in representing "photographing" the mechanical situations of the panel in both specific cases of the test by applying the experimentally detected conditions. The shape of the panel was determined by optic