Advances in Mechanics of Time-Dependent Materials

Preface
Contents
1 Rheological Modeling—Historical Remarks and Actual Trends in Solid Mechanics
1.1 Rheology as a Science
1.2 Development of Rheology as an Independent Scientific Branch
1.3 The Method of Rheological Modelling of Palmov
1.4 Two-Dimensional Rheological Modelling
1.5 Advanced Rheological Models
1.6 Summary and Outlook
References
2 On Stieltjes Continued Fractions and Their Role in Determining Viscoelastic Spectra
2.1 Introduction
2.2 Mathematical Background
2.3 The Continuous Relaxation Spectrum and Its Moments
2.3.1 Unimodal Spectra with a Finite Number of Moments
2.3.2 Unimodal Spectra with an Infinite Number of Moments
2.3.3 Multi-modal Spectra
2.4 The Stieltjes Moment Problem
2.4.1 The S-Series and S-Fraction
2.5 Dirichlet Series and Discrete Spectra
2.5.1 Spectral M-Sets
2.5.2 Spectral P-Sets and Stieltjes Dictionaries
2.6 Two Case Studies
2.6.1 A Theoretical Spectrum
2.6.2 Polybutadiene
2.7 Discrete Retardation Spectra
2.8 Summary
References
3 Modulation of the Viscoelastic Response of Hydrogels with Supramolecular Bonds
3.1 Introduction
3.2 Constitutive Model
3.3 Fitting of Experimental Data
3.3.1 HA Gels with Hydrazine–Aldehyde Bonds
3.3.2 PEG Gels Cross-Linked by HIP and CB[7] Bonds
3.3.3 PAAm Gels Cross-Linked by HIP and CB[7] Bonds
3.4 Conclusions
References
4 Igor Emri, a Student, a Colleague and a Friend
References
5 Numerical Simulation for Tensile Failure of Fiber-Reinforced Polymer Composites Based on Viscoelastic-Entropy-Damage Criterion
5.1 Introduction
5.2 Application of Thermodynamic Entropy for Continuum Damage Mechanics
5.3 Numerical Simulation for Discontinuous CFRP
5.3.1 Layer-Wise Method
5.3.2 Finite Element Analysis
5.3.3 Periodic Boundary Condition
5.3.4 Algorithm of Viscoelastic-Entropy-Damage Criterion
5.3.5 Numerical Results
5.4 Conclusion
References
6 An Investigation of the Nonlinear Viscoelastic Behavior of PMMA Near the Glass Transition Using the Spectral Hole Burning Method
6.1 Introduction
6.2 Experiment Method
6.2.1 Mechanical Spectrum Hole Burning
6.2.2 Experiment
6.3 Results and Discussion
6.3.1 Linear Regime Determination
6.3.2 Exploration of Pump Amplitude and Frequency for PMMA
6.4 Experiments with Tuned Parameters
6.5 Conclusion
References
7 Accelerated Testing Methodology for Life Prediction of Unidirectional CFRP Under Tension Load
7.1 Introduction
7.2 Generalization of Time–Temperature Superposition Principle for Strength of CFRP
7.3 Formulations Based on ATM
7.4 Experiments
7.4.1 CFRP Strands Employed as Unidirectional CFRP
7.4.2 Test Methods
7.5 Results and Discussion
7.5.1 Viscoelasticity of Matrix Resins
7.5.2 Statistical Static Strengths of CFRP Strands
7.5.3 Statistical Creep Strengths of CFRP Strands
7.5.4 Statistical Fatigue Strengths of CFRP Strands
7.5.5 Predictions of Long-Term Statistical Creep and Fatigue Strengths of CFRP Strands
7.6 Conclusions
References
8 Application of Time–Temperature Superposition Principle for Polymer Lifetime Prediction
8.1 Introduction
8.2 Time-Influence Factor Superposition Principle
8.3 Time–Heat Treatment Conditions Superposition Principle
8.4 Time–Fiber Volume Fraction Superposition Principle
8.5 Time–Crystallinity Superposition Principle
8.6 Time–Crystallinity–Fiber Volume Fraction Superposition Principle
8.7 Conclusions
References
9 Viscoelastic and Viscoplastic Behavior of Polymer and Composite
9.1 Introduction
9.2 Viscoelastic–Viscoplastic Constitutive Model
9.2.1 Series-Connected Model of Viscoelastic and Viscoplastic Elements
9.2.2 Constitutive Equation of the Viscoelastic Elements
9.2.3 Constitutive Equation of the Viscoplastic Elements
9.3 Viscoelastic–Viscoplastic Behavior of PBT Resin
9.3.1 Viscoelastic Characteristics
9.3.2 Viscoplastic Characteristics
9.4 Viscoelastic–Viscoplastic Behavior of Short Glass Fiber-Reinforced PBT
9.4.1 Test Material
9.4.2 Prediction of Behavior of PBT Composite by Finite Element Analysis
9.5 Summary
References
10 Using Asymptotic Homogenization in Parametric Space to Determine Effective Thermo-Viscoelastic Properties of Fibrous Composites
10.1 Introduction
10.2 Viscoelastic Fiber-Reinforced Composites. Maxwell’s Model
10.3 Asymptotic Homogenization of the Equations with Complex Moduli in Parametric Space
10.4 The Solution of the Problem on Microscale
10.5 Numerical Results and Their Analysis
10.6 Conclusion
References
11 Biomechanical Modeling and Characterization of Cells
11.1 Introduction
11.2 Materials and Method
11.2.1 HMSC Cell Culturing Conditions
11.3 Experiments
11.4 Elastic, Viscoelastic, and Tensegrity Models
11.4.1 Elastic and Viscoelastic Models
11.4.2 Modeling the Viscoelastic Cell Behavior Using Tensegrity
11.5 Results and Discussions
11.6 Conclusions
11.7 Definitions of Variables and Constants Used in this Paper
References
12 Thermo-Rheological Analysis and Kinetic Modeling of Thermal and Thermo-Oxidative Degradation of Polyethylene
12.1 Introduction
12.2 Experimental
12.2.1 Materials
12.2.2 Sample Preparation
12.2.3 Differential Scanning Calorimetry
12.2.4 Thermogravimetric Analysis
12.2.5 Rheological Characterization
12.3 Kinetic Analysis
12.3.1 Model-Free Methods
12.3.2 Model-Fitting Method
12.4 Results and Discussion
12.4.1 Oxidative Induction Time in Differential Scanning Calorimetry and Thermogravimetric Analysis
12.4.2 Thermal and Thermo-Oxidative Degradation of Unstabilized and Stabilized LDPE in Nitrogen and Air
12.4.3 Kinetic Analysis of Non-isothermal TG Curves of Unstabilized and Stabilized LDPE
12.4.4 Thermorheological Analyses of Unstabilized and Stabilized LDPEs Using Time-Sweep Rheometry
12.5 Conclusions
References
13 Quantitative Characterization of Cracks and Contact Stresses Using Photoviscoelasticity
13.1 Introduction
13.2 Photoviscoelasticity
13.3 Evaluating Rolling Contact Stresses
13.3.1 Material Characteristics
13.3.2 Experimental Procedure
13.3.3 Finite Element Analysis
13.3.4 Results and Discussion
13.3.5 Summary
13.4 Evaluating Fracture Parameter
13.4.1 Material Characteristics
13.4.2 Specimen Geometry
13.4.3 Introducing Natural Crack
13.4.4 Experimental Procedure
13.4.5 Results for Stationary Cracks
13.4.6 Results for Moving Crack
13.4.7 Summary
13.5 Conclusions
References