Table of Contents

Applied Mechanics of Polymers, George Youssef, ISBN: 9780128210789

Chapter 1: Introduction and background

Polymers are an exciting class of engineering materials with many applications and substantial potential for many more. Polymers have been researched for more than a century and continue to fascinate many researchers in academia and industry. In this chapter, the study of polymers is first motivated, followed by a brief historical note. Types of polymers are introduced and discussed based on common classifications and categorizations approaches. The main fields of studies in polymers, including polymer chemistry, polymer physics, and polymer mechanics, are presented. Some closing remarks are included at the end of the chapter, encompassing practical tidbits.

  • 1.1 Introduction
  • 1.2 Historical perspective
  • 1.3 Type of polymers
  • 1.4 Areas of study in polymer science
    • 1.4.1 Polymer chemistry
    • 1.4.2 Polymer physics
    • 1.4.3 Polymer mechanics
  • 1.5 Industrial applications of polymers
  • 1.6 Closing remarks
  • References

Chapter 2: General properties of polymers

This chapter emphasizes the general properties of polymers and their independence on loading time, loading rate, and temperature. A drastic change in the mechanical behavior of polymers is foreseen as the temperature increases or decreases, in some cases, by only a few degrees. Meaningful analysis of polymer-based structures hinges on testing done in environmental, loading, and operating conditions congruent to those present in deployment. Therefore, the entire chapter is dedicated to discussing the quasi-static, long-term, and dynamic properties in the context of temperature and molecular structure. The chapter includes a refresher on the definitions of basic mechanical parameters, such as stress and strain. The chapter is augmented with examples to illustrate how certain concepts can be applied and analyzed, making the knowledge presented herein as a prerequisite for many of the subsequent chapters.

  • 2.1 Introduction
  • 2.2 Quasi-static mechanical response
  • 2.3 Long-term properties
    • 2.3.1 Creep
    • 2.3.2 Relaxation
  • 2.4 Dynamic properties
  • 2.5 Other properties
  • Practice problems
  • References

Chapter 3: Processing and Manufacturing of Polymers

The ultimate feat of any product design lies in manufacturing. In this chapter, a survey of the most common polymer manufacturing processes is presented. The processes were selected based on their industrial importance, being mass-production processes. The basic theory of operation, advantages, and disadvantages of each process as well as common polymers and products were discussed. With the increase importance of additive manufacturing, it was imperative to provide a brief topical review of the different categories within the realm of this class of advanced manufacturing.

  • 3.1 Introduction
  • 3.2 Extrusion
  • 3.3 Sheets, films, and filaments
  • 3.4 Thermoforming
  • 3.5 Injection molding
  • 3.6 Additive manufacturing
  • Practice problems
  • References

Chapter 4: Linear Elastic Behavior of Polymers

The design analysis of parts and components requires a formal approach that relates the stress and strain states due to different operating and loading conditions. The continuum mechanics approach is suitable for carrying on the design analysis using closed-form or finite element methods. In this chapter, a simplified introduction to solid continuum mechanics is introduced, pertaining to the thermomechanical response of linear elastic polymers. The presented analysis framework is appropriate for analyzing polymers deployed in environments where the applied or induced strains are small (within the linear region) and at temperatures below their glass transition, i.e., in the glassy regime. The chapter ends with practical examples of integrating the presented framework in the analysis of polymer-based parts and components.

  • 4.1 Introduction
  • 4.2 Stress and equilibrium
    • 4.2.1 Plane stress
    • 4.2.2 Simple tension
    • 4.2.3 Simple shear
    • 4.2.4 Hydrostatic stress
  • 4.3 Strain and compatibility
    • 4.3.1 Plane strain
  • 4.4 Linear elastic material behavior
    • 4.4.1 Isotropic materials
    • 4.4.2 Orthotropic materials
    • 4.4.3 Transverse isotropic materials
  • 4.5 Structural component design
  • 4.6 Applied FEA simulation example
  • Practice problems
  • References

Chapter 5: Hyperelastic Behavior of Polymers

Hyperelasticity describes the nonlinear elastic response of rubbers and elastomers, found in many practical applications. Understanding hyperelastic models hinge on rigorous mathematical descriptions of different metrics of stress and strain (or deformation). Necessary theoretical preliminaries are first discussed to develop different strain and stress tensors later used in writing hyperelastic models. The need for the different representations stems from the approach these models were initially developed. An emphasis is given to the physical significance of these mathematical constructs in an attempt to achieve a better grasp of the concepts. The end of the chapter includes a practical example of using hyperelasticity in the design analysis of O-rings, an important sealing mechanism in many fields.

  • 5.1 Introduction
  • 5.2 Theoretical preliminaries
    • 5.2.1 Displacement field
    • 5.2.2 Deformation gradient
    • 5.2.3 Polar decomposition
    • 5.2.4 Strain tensors
    • 5.2.5 Stress tensors
  • 5.3 Stress–strain relationships
  • 5.4 Hyperelastic models
    • 5.4.1 Neo-Hookean model
    • 5.4.2 Mooney-Rivlin model
    • 5.4.3 Yeoh model
    • 5.4.4 Gent model
    • 5.4.5 Ogden model
    • 5.4.6 Ogden hyper-foam model
  • 5.5 Applications of hyperelastic models in component design
  • Practice problems
  • References

Chapter 6: Creep Behavior of Polymers

Long-term loading of polymer-based parts, components, and structures is imminent. Polymers experience creep strain response when submitted to constant stress, even at controlled environmental conditions (such as constant temperature and relative humidity), resulting in catastrophic failure, e.g., creep rupture. Therefore, creep analyses are imperative to guard polymer-based products from unexpected failure. This chapter starts with re-introducing the creep behavior of polymers while emphasizing the time-dependent behavior of polymers. Several analytical models are included and discussed to assist in the creep analysis. Like its predecessors, the chapter is supplemented with several solved examples and a set of practice problems.

  • 6.1 Introduction
  • 6.2 Simple creep models
    • 6.2.1 Maxwell model
    • 6.2.2 Kelvin model
    • 6.2.3 Four-parameters model
    • 6.2.4 Zener model
  • 6.3 Additional creep models
    • 6.3.1 Findley power law
    • 6.3.2 Norton–bailey law
    • 6.3.3 Prandtl–Garofalo law
  • 6.4 Applications of creep in component design
  • 6.5 Applied FEA simulation example
  • Practice problems
  • References

Chapter 7: Viscoelastic Behavior of Polymers

The hallmark characteristic of polymers as time-dependent materials is discussed in this chapter in the context of linear viscoelasticity. The Boltzmann superposition principle and the generalized Maxwell and Kelvin models are first contextualized as a preface for small and large strains viscoelasticity. Small strain viscoelasticity leverages linear elastic response (Chapter 4) and linear viscoelasticity. Alternatively, the large strain formulation hinges on hyperelasticity (Chapter 5) and linear viscoelasticity. Emphasis is given in this chapter to isotropic material, but the framework can readily be extended for general anisotropic materials. Several examples are presented throughout the chapter, and finite element implementation is discussed at the outset.

  • 7.1 Introduction
  • 7.2 Theoretical preliminaries
    • 7.2.1 Boltzmann superposition principle
    • 7.2.2 Generalized Maxwell model
    • 7.2.3 Generalized Kelvin model
  • 7.3 Linear viscoelasticity
    • 7.3.1 Small-strain linear viscoelasticity
    • 7.3.2 Large-strain linear viscoelasticity
  • 7.4 Applications of linear viscoelasticity in component design
  • 7.5 Applied FEA simulation example
  • Practice problems
  • References

Chapter 8: Electroactive Polymers

Electroactive polymers are an important class of materials with substantial potential in applications ranging from biomedical to robotics due to the intrinsic coupling between different energies (e.g., mechanical and electrical). For example, flexible and wearable electronics are poised to benefit significantly from the unique properties of electroactive polymers, where mechanical work during daily activities can be harnessed and stored to power different wearable devices. Polymers also are more compliant than other material classes, making them suitable for flexible electronics. In short, electroactive polymers can be used as sensors or actuators in these applications. This chapter introduces this exciting class of materials by first discussing theoretical physical preliminaries, including electrostatics and linear piezoelectric constitutive model. The rest of the chapter is dedicated to electroactive polymers with electromechanical coupling through a comprehensive discussion of electrostrictive polymers and dielectric elastomer actuators. A list of prominent applications is also included, and an applied finite element example is discussed.

  • 8.1 Introduction
  • 8.2 Theoretical preliminaries
  • 8.3 Electrostrictive polymers
  • 8.4 Dielectric elastomers
  • 8.5 Applications of electroactive polymers
  • 8.6 Applied FEA simulation example
  • Practice problems
  • References

Chapter 9: Hydrogels

Hydrogels are an essential class of polymers, especially for biomedical applications. Hydrogels are compliant polymers (soft materials) that can experience swelling several folds over its original volume. Impressively, this change can be reversible and can be activated using solvents, physical, or chemical stimuli. Hydrogels, being a broad range of materials, are classified in many ways, including natural and synthetic (based on their sources), chemical and physical, the formation methods, and conventional and smart (based on responsiveness). In this chapter, a brief introduction of hydrogels is presented first, including the mechanical, swelling, mesh size, and degradability properties. Two approaches are presented for the analysis of hydrogels based on continuum mechanics. At the end of the chapter, an example of finite element modeling is developed to analyze hydrogels.

  • 9.1 Introduction
  • 9.2 Mechanics of hydrogels
  • 9.2.1 Hydrogel deformation theory
  • 9.2.2 Poroelasticity
  • 9.3 Applications of hydrogels
  • 9.4 Applied FEA simulation example
  • Practice problems
  • References

Chapter 10: Failure and Fracture of Polymers

Failure in polymers can take several forms, leading to catastrophic rupture deeming the product useless. Hence, engineers must perform a comprehensive analysis to define the appropriate loading, operating, and environmental conditions. Failure can be categorized into shear yielding, crazing, fracture, and fatigue in polymers, with different continuum and molecular mechanisms ascribed to each category. The ultimate result of the design analysis based on these categories is the recommendation/rejection of geometrical and material attributes defining the product, i.e., complete product definition. Therefore, this chapter is dedicated to discussing each of the failure categories mentioned above. After a few brief introductory remarks, each failure mode is discussed using the continuum mechanics approach in a separate section. The chapter is supplemented with several examples throughout each section.

  • 10.1 Introduction
  • 10.2 Shear yielding
  • 10.3 Crazing
  • 10.4 Fracture mechanics
  • 10.5 Fatigue
  • Practice problems
  • References

Chapter 11: Characterization of Polymers

Fundamental understanding of the mechanical performance of polymers requires additional multiscale characterizations using various techniques in addition to the standard mechanical testing approaches. The thermal response of polymers using differential scanning calorimetry can supplement the properties attained using the dynamic mechanical analyzer by providing accurate accounts of thermal transitions, including the glass transition, crystallization, and melting temperatures. The thermogravimetric analyzer is a valuable tool to investigate the thermal stability and decomposition of polymers, and compositional analysis of composites and blend polymers. Additionally, microscopic and spectroscopic characterization techniques are essential to pinpoint the process-structure-property-performance interrelationships responsible for deformation and failure mechanisms. This chapter surveys several thermal, microscopy, and spectroscopy techniques required for insightful investigations of polymers while highlighting crucial applications of these approaches and providing examples. While the list of techniques is not complete, the introduced approaches are the most common and suitable for studying polymers.

  • 11.1 Introduction
  • 11.2 Thermal characterizations
    • 11.2.1 Differential scanning calorimetry
    • 11.2.2 Thermogravimetric analyzer
  • 11.3 Microscopy characterizations
    • 11.3.1 Optical microscopy
    • 11.3.2 Scanning electron microscopy
    • 11.3.3 Transmission electron microscopy
    • 11.3.4 Atomic force microscopy
  • 11.4 Spectroscopy characterizations 000
    • 11.4.1 UV–visible spectroscopy
    • 11.4.2 Fourier transform infrared spectroscopy
    • 11.4.3 Raman spectroscopy
    • 11.4.4 Terahertz time-domain spectroscopy
  • Practice problems
  • References