Constructional Viscoelastic Composite Materials: Theory and Application

Description

Viscoelasticity is a complicated theorem that is generally used in several aspects of material characterization and modeling of polymers, resins, fiber-reinforced composites, bituminous composites, etc. On the other hand, the heterogeneous nature of composites like asphalt concrete and fiber-reinforced polymers has motivated lots of researchers to investigate the mechanical and rheological properties of these materials. This book mainly consists of the theory and application of viscoelastic materials used for construction. It starts with a comprehensible presentation of the theory of linear and nonlinear viscoelasticity. Wherein, the application of viscoelastic equations and principles on constructional viscoelastic composite materials considering time, temperature, loading rate dependency, and heterogeneity of composite substances is highlighted. The principles and equations of the viscoelasticity theorem are presented in several books, but here it is tried to present them more understandable and straightforwardly. This helps in solving real problems of heterogeneous composite materials, especially those which are used in construction. Moreover, the fundamental experiments for characterizing the elastic and viscoelastic properties of fibrous and bituminous composites are introduced and summarized. Then after, some analytical and empirical formulations for deriving the material properties of composites from the properties of the basic constituents are presented. These are followed by numerical simulation techniques using the finite element method to simulate composite materials. Contents 1 Introduction 1.1 Viscoelasticity 1.2 Fibrous Composites in Construction 1.3 Bituminous Composites in Construction References 2 Viscoelasticity Theoretical Background 2.1 Relaxation Modulus 2.2 Creep Compliance 2.3 Mechanical Models for Representing Viscoelastic Behavior 2.3.1 Maxwell Model 2.3.2 Kelvin-Voigt Model 2.3.3 The Burgers Model 2.3.4 The Generalized Models 2.3.5 General Format of Constitutive Equations 2.4 Hereditary Approach for Representing Viscoelastic Behavior 2.5 Correspondence Principle 2.6 Interconversion of Constitutive Viscoelastic Functions 2.6.1 Hopkins and Hamming Method 2.6.2 System of Linear Algebraic Equations 2.7 Time–Temperature Superposition 2.7.1 Effect of Time, Temperature, and Loading Rate 2.7.2 Master Curve References 3 Nonlinear Viscoelasticity 3.1 Introduction 3.2 Schapery Single-Integral Nonlinear Model 3.2.1 A Brief Review on Linear Viscoelasticity 3.2.2 The Schapery Equation 3.2.3 Schapery Equation for a Two-Step Stress 3.2.4 Schapery Equation for a Creep and Creep-Recovery Test 3.2.5 Determination of Material Parameters from a Creep and Creep-Recovery Test 3.3 Numerical Formulation 3.3.1 One-Dimensional Formulation References 4 Experimental Characterization 4.1 Fibers and Inclusions 4.1.1 Single Fiber Test 4.1.2 Ultrasonic Test 4.2 Matrix Component 4.2.1 Experiments Under Static Loading 4.2.2 Dynamic Mechanical Analysis 4.3 Composites 4.3.1 Experiments Under Static Loading References 5 Analytical and Empirical Formulation 5.1 Rule of Mixture in Composite Materials with Continuous Inclusions 5.1.1 Analytical Equations 5.1.2 Semi-Analytical Equations 5.2 Rule of Mixture in Composite Materials with Discontinuous Inclusions 5.2.1 Fibrous Composites 5.2.2 Granular Composites References 6 Numerical Simulation 6.1 A Review on Finite Element Method 6.1.1 Fem for Two-Dimensional Solids 6.1.2 FEM for Plates and Shells 6.1.3 FEM for 3D Solids 6.2 Incremental Viscoelastic Formulation 6.3 Geometrically Homogenous Composite Modeling 6.3.1 Geometry Construction 6.3.2 Material Characterization 6.3.3 Boundary Conditions 6.4 Geometrically Heterogeneous Composite Modeling 6.4.1 Geometry Construction 6.4.2 Boundary Conditions and Interactions 6.5 An Extension of FEM for Discontinuity Modeling 6.5.1 Fundamentals and Formulations 6.5.2 Applications References