PSI - Issue 41

America Califano et al. / Procedia Structural Integrity 41 (2022) 145–157 Author name / Structural Integrity Procedia 00 (2019) 000–000

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1. Introduction Panel paintings are work of arts characterized by heterogeneous and hygroscopic features. The heterogeneous nature is due to the presence of layers of different materials such as wood, gesso (a mixture of animal glue and chalk), paint and varnishes; the hygroscopic nature is mainly due to the presence of the wooden support (panel) that is highly susceptible to water, especially when variations in temperature (T) and relative humidity (RH) are in play (Mecklenburg et al. (1998)). Moreover, the mismatch in the moisture response of a stiff gesso layer and of the underlying wood panel produces risk of fracture in the pictorial layer. For this reason, when paintings are, for example, moved during loan, from one exhibition to another and their microenvironment naturally changes, the microclimatic variations may have a detrimental effect on these work of arts’ mechanical strength and features (Lukomski (2012)). In this framework, there is the need of a strong knowledge of the mechanical behavior of panel paintings when subjected to microclimatic variations, in the framework of conservation and preservation of the movable cultural heritage. Several studies have been based on monitoring, experimental and numerical campaigns to gather as much knowledge as possible about ways of minimizing cracks, and craquelures occurrence. Aste et al. (2019) established a one-year monitoring campaign in the Milan Cathedral (Italy) in order to acquire microclimatic data characterizing the hygrothermal behavior of objects, sculptures and panel paintings. A two-year monitoring campaign, instead, has been carried out by De Backer et al. (2018) to evaluate the display conditions of the panel painting altarpiece of St. Bavo Cathedral (Belgium). In addition, experiments on the hygro-mechanical behavior of historic paintings on wooden panels have been established by controlling and measuring, for several months, the RH in the showcase framing the paintings (Dupre et al. (2020)) or by testing wooden specimens under RH variations determined through humidifiers (Arends et al. (2018)) or climate chambers (Bertolin et al. (2021)). Additional studies on modelling the cracking phenomena in paintings due to RH fluctuations have been based on numerical simulations to investigate the through thickness cracks (Zhang et al. (2021)), the interaction among different fracture mechanisms (channeling, delamination etc.) (Bosco et al. (2021)) and the low-cycle fatigue caused by temperature and relative humidity cycles (Jamalabadi (2021)). However, monitoring, experimental, and numerical campaigns are usually time-consuming as they need to comply with the timescales of microclimatic variations/fluctuations and with the characteristic response time of the multi-materials system during diffusive phenomena. This is why, to obtain reliable results and quick indications on how to proceed with the actuation of preventive conservation practices, a new frontier in the field of Heritage Science (HS) and Conservation could be based on mixing consolidated failure criteria coming from the fracture mechanics and mechanical engineering field with the extreme generalization capabilities of machine learning (ML). Albeit several works of ML applied to HS have been proposed recently (Mishra et al. (2020)), this field is still in evolution. Concerning the conservation of panel paintings, ML approaches have been lately proposed about localizing the surface cracks through convolutional neural networks (CNN) (Sizyakin et al. (2020)), describing the craquelure patterns through graph neural nets (GNN) (Sidorov and Hardeberg (2019)) and detecting cracks and defects by means of clustering algorithms (Liu et al. (2021)). The current work is about a novel way of implementing ML algorithms in this framework; it is herein proposed to predict the development of safe or unsafe conditions in panel paintings with cracks by using the strain energy density (SED) failure criterion as decision rule. The SED criterion is widely recognized and used in the field of fracture mechanics as it has shown its versatility in several applications with different kind of materials, loading conditions and crack configurations. Here, this criterion has been used to assess, through Finite Element (FE) simulations, whether the simplified model of a panel painting with a penny-shaped crack in it. Results obtained from the FE analyses have been used to train and test the novel extreme gradient boosting (XGBoost) (Chen and Guestrin (2016)) machines. In particular, a simple XGBoost classification model has been implemented, with the final goal to evaluate its potential in predicting whether given geometrical conditions of the gesso layer and the wooden panel may cause the evolution towards unsafe conditions in the considered case study, due to the presence of a pre-existing crack, in order to limit the computational cost and time of FE simulations. The work is structured as follows: the geometrical and finite element case study is described in Section 2; preliminary geometrical considerations about the case study are highlighted in Section 3.1 and used for the implementation of the chosen ML algorithm (Section 3.2). The obtained results are, then, presented and discussed in Section 4 and the main conclusions are reported in Section 5.