On mathematical models applied to material damage in cultural heritage conservation

In this paper some recent mathematical models applied to material damage are reviewed. The complexity of damage processes related to Cultural Heritage materials creates the necessity of developing predictive tools in order to monitor and detect surface alterations even before they are visible by naked eyes. The proposed models, elaborated by a research group of the Institute of Applied Mathematics - Research Council of Italy, are based on partial differential equations and well capture the main features of chemical processes (copper corrosion and salt crystallization), which occur on different materials such as stone and copper.