Mathematical Modeling in Cultural Heritage: MACH2019

Description

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.   Preface Contents To Know Without Destroying? 1 The MADAR Project: Historical Heritage and Math Towards a Common Path 2 Potential and Weaknesses of the Porto Torres (Sardinia) Case Study 3 Construction Techniques, Features and Historical Phases of the Complex of Central Baths 4 To Know Without Destroying References Representative Volume Elements for the Analysis of Concrete Like Materials by Computational Homogenization 1 Introduction 2 Generation of the Geometry of the RVE 2.1 Spherical Aggregate Particles 2.1.1 Taking Process 2.1.2 Placing Process 2.2 Polyhedral Aggregate Particles 3 Micro–to–Macro Computational Homogenization 3.1 Periodic Boundary Conditions 4 Numerical Results 5 Conclusions References A New Nonlocal Temperature-Dependent Model for Adhesive Contact 1 Introduction 1.1 Rate-Independent Models 1.2 Rate-Dependent Models 1.3 Adhesive Contact with Nonlocal Effects 2 The Model and the PDE System 2.1 The State and Dissipative Variables 2.2 The Free Energy 2.3 The Dissipation Potential 2.4 The Balance Equations and the Constitutive Laws 2.5 The PDE System 2.6 Outlook to the Analysis References Chemomechanical Degradation of Monumental Stones: Preliminary Results 1 Introduction 2 A Mathematical Model of Marble Sulphation 2.1 A Simplified Chemical Reaction 2.2 The Hydrodynamical Model 3 The Variational Approach to Fracture 4 A Chemo-Mechanic Model 4.1 Mechanical Properties 4.2 Diffusivity 4.3 Mathematical Model 5 A Numerical Example References Modelling the Effects of Protective Treatments in Porous Materials 1 Introduction 2 Materials and Methods 3 Modelling of Capillary Imbibition 3.1 Boundary Conditions 4 Numerical Results and Comparison with Experimental Data 4.1 Numerical Approximation 4.2 Calibration of Parameters a, c 5 Conclusions and Perspectives References Mathematical Models for Infrared Analysis Appliedto Cultural Heritage 1 Introduction 2 Models 2.1 Optically Opaque Materials 2.2 Optically Semi-transparent Materials 3 Finite Element Implementation 4 Numerical Simulations and Comparison with Experimental Results 4.1 Optically Opaque Materials 4.2 Optically Semi-transparent Materials References Numerical Simulations of Marble Sulfation 1 Introduction 2 Mathematical Model 3 Numerical Approximation for Cartesian Domains 3.1 Accuracy and Efficiency 4 Numerical Approximation for Arbitrary Domains 4.1 Accuracy Test 4.2 Efficiency of Solvers 4.3 Domains Defined by Images 5 The Tickness of the Gypsum Crust as a Function of the Curvature 6 Conclusions References The Damage Induced by Atmospheric Pollution on Stone Surfaces: The Chemical Characterization of Black Crusts 1 Introduction, Black Crusts Formation Process 2 Analytical Methods Proposed for BCs Characterizations 3 Some Case Studies 4 Conclusion References Aging of Viscoelastic Materials: A Mathematical Model 1 Introduction 1.1 What Is Viscoelasticity? 2 Rheological Models for Viscoelasticity 3 Modeling the Aging 3.1 Derivation of the Constitutive Equation 3.2 The Motion Equation 3.3 The Kelvin–Voigt Limit 4 Mathematical Analysis of the Problem References A Quasi-Static Model for Craquelure Patterns 1 Introduction 2 Quasi-Static Evolutions by Alternate Minimization 2.1 Phase-Field Energy 2.2 Time-Discrete Evolution 2.3 Time-Continuous Evolution 3 A One-Dimensional Case Study 3.1 Continuous Displacement and Boundary Layer 3.2 Evolution of Cracks by Minimality 3.3 Second and Further Generations of Cracks by Minimality 4 Alternate Minimization in the One Dimensional Setting 5 Numerical Results for Uni-Axial Problems 5.1 Dyadic Structure for Short Bars 5.2 Periodic Patterns for Longer Bars 5.3 Irreversibility 6 Local Craquelure Patterns for a Real Life Specimen References