A Diffusion-Mechanical Interface Damage Model for Numerical Simulation of Fracture in Historical Paintings

  • Pirmoradi, Pouriya (Eindhoven University of Technology)
  • Bosco, Emanuela (Eindhoven University of Technology)

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A large percentage of historical paintings in museum collections worldwide suffer from mechanical degradation that are typically due to fluctuating environmental conditions, specifically variations in relative humidity and temperature [1]. In the present study, a coupled diffusion-mechanical interface damage model is developed for modelling fracture initiation and propagation in historical paintings under desiccation. The fracture process in the paint medium is simulated with interface elements equipped with the traction-separation formulation initially presented by Alfaro et al. [2]. The mass flux-concentration relation at the interfaces is specified as a function of mechanical damage at the interface. The coupled interface damage model is extended to a rate-dependent description by defining appropriate kinetic laws to avoid numerical convergence problems induced by crack bifurcations. The framework is demonstrated through a diffusion-mechanical boundary value problems of a fracturing paint layer where the bulk domain is meshed with coupled finite elements. To allow for the arbitrary nucleation and propagation of fractures in the domain, coupled interface elements describing the cracking process are generated between all continuum elements, in accordance with the approach firstly proposed by Xu and Needleman [3]. The influence of various mechanical and diffusion material properties, including tensile strength, fracture toughness, moisture expansion coefficient, and diffusivity coefficient, on damage and fracture response of paint layers under desiccation is investigated. Additionally, the effect of pre-existing micro-cracks throughout the paint layer is specifically investigated on diffused and localized fracturing response of the oil paint medium under desiccation. REFERENCES [1] D.H. Lee, N.S. Kim, M. Scharff, A.V. Nielsen, M. Mecklenburg, L. Fuster-Lopez, L. Brastaz, and C.K. Anderson. Numerical modelling of mechanical degradation of canvas paintings under desiccation. Heritage Science, (2022). [2] M.V.C. Alfaro, A.S.J. Suiker, R. de Borst, and J.J. Remmer. Analysis of fracture and delamination in laminates using 3D numerical modelling. Engineering Fracture Mechanics, 2009. [3] X.P. Xu and A. Needleman. Numerical simulations of fast crack growth in brittle solids. Journal of the Mechanics and Physics of Solids, 1994.