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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addition, a penny-shaped crack has been assumed to be inside the gesso layer, centred along the symmetrical planes. The entire model and the sub-model are reported in Figure 1a and Figure 1b respectively. In Fig. 1a the considered model of the panel painting made by the wooden support (light brown block), the gesso layer (grey block), the craquelures in the gesso layer (black lines in the grey layer) and the penny-shaped crack (light red circle), with diameter 2a , is depicted. In Fig. 1b there is an enlargement of the craquelure island, where � is the thickness of the wooden support, � is the thickness of the gesso layer, ℎ � is the height of the crack and and the main dimensions of the sub system.

Figure 1 - (a) Simplified model of a panel painting made by a wooden support and a layer of gesso with craquelures and a penny-shaped crack; (b) enlargement of the craquelure island as extracted by the main model with its main geometrical features

Boundary conditions to simulate the moisture response of wood have been considered applying a 1% strain along the x -direction. The possible combinations between the geometrical parameters describing the two different layers are various and may results in different behaviors. The development of a parametric FE model in which not only the geometrical dimensions but also the mechanical properties of the two layers can be changed is of paramount importance for a deep understanding of these components. However, in the modelling, considering as many parameters as possible influencing the craquelure formation and development, combined with FM parameters, that are usually computationally expensive, can be a demanding task. In order to decrease as much as possible the required computational time, the Strain Energy Density (SED) criterion (Lazzarin and Zambardi (2001), Lazzarin and Zambardi (2002)) has been chosen due to its low sensitivity to the mesh refinement (Lazzarin et al. (2010), Foti et al. (2021)), facilitating and quickening the investigation; the method has already been used in literature for similar numerical investigations proving its advantages (Foti et al. (2019), Foti et al. (2021)). The SED represent a well-established method hugely validated to investigate failures both in static and dynamic conditions (Berto and Lazzarin (2014)). According to this method, the brittle fracture occurs when the local SED, � , evaluated in a given control volume, reaches a critical value � � � � independent of the notch opening angle and of the loading type as demonstrated by Lazzarin et al. (2001). The concepts stated above represent the basic idea of the SED method. For more considerations about the analytic frame, the validation and the several advantages of this method we remand to Berto and Lazzarin (2014). For the application of this damage criterion to panel paintings, the considered critical SED value was � ���� � 0.1753 � ⁄ obtained assuming a fictitious control volume radius � � 0.01 and the experimental value of the fracture toughness obtained by Bratasz et al. (2020). A toroidal control volume has been considered to evaluate � along the edge of the penny-shaped crack, as considering just the most critical point along the crack edge does not result in significant change in the achieved conclusions. A parametric 3D FE model, shown in Figure 2, has been developed through the software Ansys APDL® that, in combination with the software MatLab®, allows the definition of a highly automated procedure for the investigation of the several parameters involved in the damaging process of a panel painting. The definition of the 3D FE model followed several steps. The first step was the parametric definition of the model to change its geometrical dimensions