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2021 | Buch

To Know Without Destroying? Kapitel lesen Erstes Kapitel lesen

Mathematical Modeling in Cultural Heritage

MACH2019

herausgegeben von: Prof. Elena Bonetti, Prof. Cecilia Cavaterra, Prof. Roberto Natalini, Prof. Margherita Solci

Verlag: Springer International Publishing

Buchreihe : Springer INdAM Series

Enthalten in: Springer Professional "Wirtschaft+Technik" , Springer Professional "Technik" , Springer Professional "Wirtschaft"

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Über dieses Buch

This work collects the contributions presented at the INdAM Workshop “Mathematical modeling and Analysis of degradation and restoration in Cultural Heritage – MACH2019” held in Rome in March 2019. The book is focused on mathematical modeling and simulation techniques with the aim of improving the current strategies of conservation and restoration in cultural heritage, sharing different experiences and approaches. The main topics are: corrosion and sulphation of materials, damage and fractures, stress in thermomechanical systems, contact and adhesion problems, phase transitions and reaction-diffusion models, restoration techniques, additive manufacturing. The final goal is to build a permanent bridge between the experts in cultural heritage and the mathematical community. The work is addressed to experts in cultural heritage and to mathematicians.

Inhaltsverzeichnis

Frontmatter
To Know Without Destroying?
Abstract
This paper proposes some considerations that arise from an experiment conducted in the Archaeological Park of Porto Torres, where a predictive and non-invasive diagnostic tool based on a numerical code (TEAM) was tested. It is an innovative research topic that, in recent years, has seen mathematics contribute to artistic protection as well as in the hard field of the protection of historical buildings and archaeological structures. Starting from a point of view that arise from a long archaeological experience, it was proposed an application in a context in which the use of predictive models of damage might answer to a real need. Adapting the recent structural analysis tools to the complex needs and to the lack of archaeological research data could open a path towards new and different solutions, no longer intrinsically destructive, for the investigation of the historical structures. It could be a new point of view that starts from the construction of a common language between so different disciplines, towards a real communication and mutual contamination.
Giovanni Azzena, Roberto Busonera
Representative Volume Elements for the Analysis of Concrete Like Materials by Computational Homogenization
Abstract
The problem of devising an appropriate Representative Volume Element (RVE) for the analysis of concrete-like-materials is throughly discussed in the range of the elastic behavior. To this end, assuming concrete as a two-phases material (mortar and aggregates), the geometry of the RVE is automatically generated on the basis of spherical or polyhedral aggregates by proposing a new algorithm for the case of the polyhedral shapes. The associated apparent macro-response is evaluated by computational homogenization and its feasible use is pointed out. The subsequent numerical experimentation aims to highlight the influence of the relevant parameters such as the RVE’s size, aggregates shapes, constitutive moduli of the constituents and applied boundary conditions on the evaluation of the RVE’s macro-response.
Antonio Bilotta, Andrea Causin, Margherita Solci, Emilio Turco
A New Nonlocal Temperature-Dependent Model for Adhesive Contact
Abstract
The aim of this note is twofold. First of all, we propose a very partial survey on the mathematical modeling and analysis of adhesive contact and delamination. Secondly, we advance a new model for adhesive contact with thermal effects that includes nonlocal adhesive forces and surface damage effects, as well as nonlocal heat flux contributions on the contact surface. In the derivation of the model, we follow the approach by M. Frémond applying it to nonlocal adhesive contact.
Elena Bonetti, Giovanna Bonfanti, Riccarda Rossi
Chemomechanical Degradation of Monumental Stones: Preliminary Results
Abstract
The degradation of monumental stones resulting from the mutual interaction between mechanical actions and environment/pollution conditions is investigated here. In particular, the stone degradation is estimated as a function of the environmental conditions and the prediction of damaging phenomena, which can compromise permanently the fruition of monuments. This is done through a macroscopic phenomenological model which accounts for the main aspects of the problem: the chemical reaction and the mechanical behavior of stones. The sulphation reaction and the diffusion of the pollutant agents are described by suitable differential equations coupled with a variational formulation of fracture mechanics. The proposed model permits to evaluate how much aggressive atmospheric agents contribute to the decay of the mechanical properties of the stones as well as to establish the impact of the synergic chemical aggression and stress state. The latter is also influenced by the chemical reaction and by the evolving mechanical properties of the material. The main features of this approach are illustrated by specific numerical simulations.
Elena Bonetti, Cecilia Cavaterra, Francesco Freddi, Maurizio Grasselli, Roberto Natalini
Modelling the Effects of Protective Treatments in Porous Materials
Abstract
The aim of this preliminary study is to understand and simulate the hydric behaviour of a porous material in the presence of protective treatments. In particular, here the limestone Lumaquela deAjarte is considered before and after the application of the silane-based product ANC.
A recently developed mathematical model was applied in order to describe the capillary rise of water in stone specimens. The model was calibrated by using experimental data concerning the water absorption by capillarity in both treated and untreated stone specimens. With a suitable calibration of the main parameters of the model and of the boundary conditions, it was possible to reproduce the main features of the experimentally observed phenomenon.
Gabriella Bretti, Barbara De Filippo, Roberto Natalini, Sara Goidanich, Marco Roveri, Lucia Toniolo
Mathematical Models for Infrared Analysis Applied to Cultural Heritage
Abstract
Active pulsed infrared thermography is an effective technique consisting in moderately heating the specimen by means of the absorption of a visible light pulse and, then, in detecting the transient variation in the emitted infrared radiation by an infrared camera. Inhomogeneities and buried features eventually located into the specimen volume can be revealed by the recorded infrared images. Such a technique has been successfully applied to the analysis of cultural heritage artifacts like ancient bronzes and manuscripts. The former belong to the category of optically opaque materials, whereas the second to the one of optically semi-transparent materials. For both the two considered categories, a mathematical model for the analysis of the thermographic signal is here presented, together with an implementation in Matlab environment using the finite element technique. The developed models are then used to analyse the experimental results and, hence, to obtain both qualitative and quantitative information about the investigated items.
Giovanni Caruso, Noemi Orazi, Fulvio Mercuri, Stefano Paoloni, Ugo Zammit
Numerical Simulations of Marble Sulfation
Abstract
In this chapter we describe some computational techniques to approximate the evolution of gypsum crusts on marble monuments. Mathematical models of this phenomenon are typically based on partial differential equations and here we deliberately consider a quite simple one, so that we can focus on the numerical techniques that can be used to overcome the main difficulties of this kind of computations, namely the efficiency of the timestepping procedure and the complexity of the computational domains in real-world cases. First, the design of optimal preconditioners for Cartesian grid discretizations is reviewed. Then, we illustrate a technique to deal with non Cartesian domains by described via a level-set function. The chapter ends with a study of the influence of the surface curvature on the growth of the gypsum crust, that generalizes earlier analytical one-dimensional results.
Armando Coco, Marco Donatelli, Matteo Semplice, Stefano Serra Capizzano
The Damage Induced by Atmospheric Pollution on Stone Surfaces: The Chemical Characterization of Black Crusts
Abstract
Atmospheric pollution is one of the most important causes of monuments surfaces decay in highly polluted urban environments. The deterioration phenomenon known as black crusts formation is one of the most dangerous degradation processes due to airborne pollutants.
An in depth study has been carried out on the carbonaceous fraction (organic and elemental carbon, i.e. OC and EC) in black crusts samples coming from different Italian Monuments stones, mortars or bricks specimens sampled from monuments of historical interests and analysed by a multi-analytical approach. In particular, the characterization of organic carbon and elemental carbon was performed using a new analytical approach. The study of black crusts degradation has been completed with the quantifications of main ions, present on the altered stones surfaces. These species are also ascribable to atmospheric pollution and are responsible of degradation phenomenon such as sulphation.
Valeria Comite, Paola Fermo
Aging of Viscoelastic Materials: A Mathematical Model
Abstract
The aim of this note is to propose a mathematical model to describe aging effects occurring in viscoelastic materials. In the classical formulation, viscoelasticity is modeled through an integro-differential equation, where the convolution kernel takes into account the delay effects induced by viscosity. Usually, such a kernel is a given function, related to the rheological properties of the material. On the other hand, it is reasonable to conjecture that, as the material changes/deteriorates over time (and these changes are referred to as aging), the shape of the kernel should change as well. The key idea is then to consider an integro-differential equation where the convolution kernel is a function of time itself. This allows a more realistic description of the evolution, requiring the development of a new mathematical theory apt to treat dynamical systems acting on time-dependent spaces.
Monica Conti, Valeria Danese, Vittorino Pata
A Quasi-Static Model for Craquelure Patterns
Abstract
We consider the quasi-static evolution of a brittle layer on a stiff substrate; adhesion between layers is assumed to be elastic. Employing a phase-field approach we obtain the quasi-static evolution as the limit of time-discrete evolutions computed by an alternate minimization scheme. We study the limit evolution, providing a qualitative discussion of its behaviour and a rigorous characterization, in terms of parametrized balanced viscosity evolutions. Further, we study the transition layer of the phase-field, in a simplified setting, and show that it governs the spacing of cracks in the first stages of the evolution. Numerical results show a good consistency with the theoretical study and the local morphology of real life craquelure patterns.
Matteo Negri
Metadaten
Titel
Mathematical Modeling in Cultural Heritage
herausgegeben von
Prof. Elena Bonetti
Prof. Cecilia Cavaterra
Prof. Roberto Natalini
Prof. Margherita Solci
Copyright-Jahr
2021
Electronic ISBN
978-3-030-58077-3
Print ISBN
978-3-030-58076-6
DOI
https://doi.org/10.1007/978-3-030-58077-3

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