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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Nomenclature 2a

Diameter of the penny-shaped crack

AUC

Area Under the Curve

BV

Border Volume

CNN

Convolutional Neural Network

FE FN

Finite Element False Negative

FNR

False Negative Rate

FP

False Positive

FPR GNN ℎ � HS L, s ML � RH ROC SED

False Positive Rate Graph Neural Nets

Height of the penny-shaped crack

Heritage Science

Main dimensions of the model

Machine Learning

Fictious control volume radius

Relative Humidity

Receiver Operating Characteristic Strain Energy Density Separation Line Temperature True Negative True Positive True Positive Rate Thickness of the gesso layer Thickness of the wooden support

SL � TN TP � � � � T

TPR

Local SED Critical SED

XGBoost

Extreme Gradient Boosting

2. Materials Variations in the relative humidity induce deformations in panel paintings that, due to the different moisture related expansion coefficients, result in an induced stress field with detrimental effects, i.e. , the formation of craquelure patterns and its development in the gesso layer, due to its brittle behavior and to its lower thickness with respect to the wood layer’s one. During its history, a panel painting can experience two different kind of moisture induced deformations. The first type is related to the drying shrinkage of the gesso that induces strain in both x and z directions ( y direction is not considered due to the limited extent of the layer thickness with respect to the other dimensions), according to Figure 1, while the second one is related to the moisture response of wood that is highly dependent on the moisture related expansion coefficient of wood in different directions, being wood an orthotropic material; usually the highest moisture related expansion coefficients are along the radial ( y -direction) and tangential ( x -direction) directions while the longitudinal direction ( z -direction) is considered to be dimensionally stable (Bratasz et al. (2020)). Such considerations on the moisture response of the two layers are useful to understand the stress field that can be induced in panel paintings and to define the boundary conditions to simulate the damage phenomenon with FE software. The current study has been conducted on the simplified 3D model of a panel painting with craquelures made by a layer of wood and a thin layer of gesso; layers of paints and varnishes have been neglected due to their significantly lower thickness with respect to the gesso and the wood layer and to an assumed low effect in determining the induced stress field in the component. From the entire model, just a craquelure island has been extracted and considered; in