Computational modelling of metal soap formation in historical oil paintings: the influence of fatty acid concentration and nucleus geometry on the induced chemo-mechanical damage

Metal soap formation is one of the most wide-spread degradation mechanisms observed in historical oil paintings, affecting works of art from museum collections worldwide. Metal soaps develop from a chemical reaction between metal ions present in the pigments and saturated fatty acids, which are released by the oil binder. The presence of large metal soap crystals inside paint layers or at the paint surface can be detrimental for the visual appearance of artworks. Moreover, metal soaps can possibly trigger mechanical damage, ultimately resulting in flaking of the paint. This paper departs from a recently proposed computational model to predict chemo-mechanical degradation in historical oil paintings, as presented in Eumelen et al. (J Mech Phys Solids 132:103683, 2019). The model describes metal soap formation and growth, which are phenomena that are driven by the diffusion of saturated fatty acids and proceed by a nucleation process from a crystalline nucleus of small size. This results into a chemically-induced strain in the paint, which may promote crack nucleation and propagation. The proposed model is here used to investigate the effects of saturated fatty acid concentration and initial nucleus geometry on the amount of chemo-mechanical damage generated. Numerical simulations show that both factors have a marginal influence on the growth rate of the metal soap crystal, but play a significant role on the extent of fracture induced in the paint.