Numerical modelling of mechanical degradation of canvas paintings under desiccation
Authors: Lee D. S.-H. , Kim N.-S. , Scharff M. , Nielsen A. V. , Mecklenburg M. , Fuster-López L. , Bratasz L. , Andersen C. K. 
Published: August 2022

Abstract
Mechanical damage in oil paintings on canvas show up as cracks and loss of original paint. Several parameters can contribute to this type of degradation. These paintings have a complex layered structure, typically composed of minimum four or more hygroscopic materials, each of which has different (non-linear) material properties and geometrical complexities. The mechanical degradation of canvas paintings occurs because each of these materials have diverse responses under fluctuating environmental conditions, especially temperature and relative humidity (RH). By examining the geometrical complexities and the non-linear material properties, this paper presents an investigation of three degradation phenomena under desiccation: (1) bulging formation around the corners, (2) crack formation in glue and ground layers, and (3) plastic deformation in the ground and oil paint layers.
This on-going investigation provides further insights into the global and local stress distribution in typically constructed oil canvas paintings. This includes finite element method (FEM) and extended-FEM (XFEM) computer models at various scales, under desiccation from the initial RH of 90%, and 50–10%. The models consist of four to five different materials, namely lead white oil paint, red iron oxide oil paint, rabbit skin glue, linen canvas, and a spruce stretcher. The models were constructed using several combinations of materials to conduct parametric studies on the effects of glue shrinkage in paintings due to desiccation, and changing the mechanical properties of the ground layers. The relevant geometrical and mechanical properties with respect to the stress relaxation conditions are discussed in detail.
The simulation results of the full-scale models show that the shrinkage of glue lowers the level of induced tension stresses in the paint layers in the central area of the painting due to the inward bowing of the stretcher. The inward deformation of the stretcher can be 4.5 times as large in a painting with a glue layer as in one without. This indicates the difficulty in forming cracks near the center of paintings purely by desiccation; however, in close-up cross-section model, cracks of 20 μm in length could still be observed in the ground exposed to an extreme RH change of 90% to 10%.
The analysis of cross-section models with the full geometrical complexity for the corners showed that multiple cracks are likely to form in ground and paint layers in the corners when desiccated by 40%; RH 50–10%. Furthermore, in extreme cases with stiffer ground/paint such as zinc white, cracks can form from smaller drop in RH; RH 50% to 35%. Such cracks are form in the ground layers, and therefore, are not initially visible as they are positioned below the uncracked paint layer. This result can be the possible explanation for cracks in the ground, which are initially invisible with the naked eye, but can be revealed with X-radiographs.
The results support the hypothesis that fluctuations in relative humidity can cause hidden cracks in the lower layers, which can eventually propagate further into the upper-lying paint layers of paintings. The cracks typically form when the desiccation reaches a 40% drop, but in cases of brittle materials the drop causing cracks can be lower. The actual RH drop causing cracks depends on the specific material composition.