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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and the location of a crack inside the gesso layer. The presence of the crack is needed to consider FM approaches to investigate the damaging process of the panel paintings; in particular a crack length 2a=0.2mm has been considered on the basis of the works of Bratasz et al. (2020). Regardless of the SED low sensitivity to the mesh refinement, a sensitivity analysis was required in order to consider as few FEs as possible in the model, while obtaining still accurate results; the need to investigate several combinations of the involved parameters required for a model having the lowest computational time, i.e., the lowest number of FEs. Besides, from the sensitivity analysis, a tendency to overestimate the SED value has been noticed, as visible in Figure 2, that leads to the conclusion that even if small errors- not avoidable in FE simulations regardless of the used method - may be present, they are in favor of safety for the studied component. The crack location inside the gesso layer has been investigated in order to have a clear understanding of the conditions that can lead to the most critical conditions for the component. Indeed, it is worth noting that, even if the existence of various defects inside the gesso layer has been proved, their exact location and morphology cannot be always known in advance; besides, the consideration of the most critical conditions, that can affect a panel painting, results in conservative evaluations of the relative humidity variations to which the component may be exposed without further damages. After having checked the good performances of the 3D FE model, several combinations of the geometrical parameters describing the component have been investigated in order to verify the range of applicability of the model itself; the evaluated range is wide enough to comprehend the geometrical parameters combinations that it is possible to find in real panel paintings, validating the model for the investigation of these objects.

Figure 2 - 3D model with a microcrack inside the gesso layer in a panel painting and sensitivity analysis of the model with changing the number of elements to identify the lowest number of FEs ensuring accurate results. 3. Methods 3.1. Geometrical considerations During all the carried out numerical simulations, the SED has been evaluated and compared to its critical value to assess whether the considered configuration is subjected to crack initiation. This way, inside the 3D panel painting sub-model, it has been possible to discriminate between the safe (no further climate-induced damage) and unsafe (further climate-induced damage) zones. In Table 1 there is the summary of the numbered labels chosen for the twelve configurations of the model obtained by varying the two geometrical parameters of interest ( � and � � � ), while in Figure 3 they are schematized with the same numbered labels used in Table 1. Each configuration is identified by a configuration number and all of them are characterized by the presence of a cloud of points in which the SED failure criterion has been applied: red dots are the points in which the critical SED has been exceeded, blue squares are those in which the critical SED has not been exceeded.