Multi-scale model for time-dependent degradation of historic paper artefacts

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The degradation of paper is due to complex physical and chemical processes that occur as the paper ages, and is enhanced by environmental factors, such as the temperature and relative humidity, and by intrinsic parameters, such as the acidity of the paper. The literature reports that a large percentage of historic documents, manuscripts, and paper objects in museums, libraries and collections is susceptible to degradation phenomena, which may ultimately affect their integrity and longevity. This contribution presents a novel computational model to predict the degradation and lifetime of historic paper. The approach is based on: i) a multi-physics modelling framework, which considers the relevant chemical and mechanical degradation processes and the influence by the ambient environmental conditions, and ii) a multi-scale description, which includes the effect of the intrinsic hierarchical structure of paper, from the fibre- and fibrous network levels to the effective macro-scale, paper sheet level. The paper fibres constructing the fibrous network are characterized by an age-dependent, chemo-mechanical constitutive behaviour. In particular, an evolution equation describes the reduction of the degree of polymerization of cellulose as a function of time and the specific environmental conditions, which in turn is used for determining the fibre tensile strength. The fibre stresses induced by hygro-expansion and hygro-contraction under a change in relative humidity are computed using a coupled hygro-mechanical model, and lead to brittle damage once the fibre tensile strength is reached. Accordingly, the chemical degradation of individual fibres affects the local damage development and stress distribution in the fibrous network, and thereby governs the material response at the paper sheet scale. Asymptotic homogenization is used to calculate the effective hygro-mechanical properties of the fibrous network. A set of numerical simulations is performed to predict the time-dependent degradation of historic paper under a range of temperature, relative humidity and acidity conditions. From these results, isochrone degradation maps are constructed that illustrate the expected lifetime of historic paper as a function of the ambient climate conditions and the acidity of the paper. Further, a practical, analytical degradation function is derived that can be used for a fast estimation of the time-dependent stiffness degradation of paper. The outcome of this work may help conservators to determine the optimal indoor climate conditions in museums, archives and libraries for limiting or delaying time-dependent degradation of historic paper artefacts.

Original languageEnglish
Article number111609
Number of pages15
JournalInternational Journal of Solids and Structures
Publication statusPublished - Jul 2022


  • Asymptotic homogenization
  • Cellulose fibres
  • Chemo-mechanical degradation
  • Historic paper
  • Indoor climate conditions


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