Creep and Relaxation of Nonlinear Viscoelastic Materials: With an Introduction to Linear ViscoelasticityThis pioneering book presents the basic theory, experimental methods, experimental results and solution of boundary value problems in a readable, useful way to designers as well as research workers and students. The mathematical background required has been kept to a minimum and supplemented by explanations where it has been necessary to introduce specialized mathematics. Also, appendices have been included to provide sufficient background in Laplace transforms and in step functions. Chapters 1 and 2 contain an introduction and historic review of creep. As an aid to the reader a background on stress, strain, and stress analysis is provided in Chapters 3 and 4, an introduction to linear viscoelasticity is found in Chapter 5 and linear viscoelastic stress analysis in Chapter 6. In the next six chapters the multiple integral representation of nonlinear creep and relaxation, and simplifications to single integral forms and incompressibility, are examined at length. After a consideration of other representations, general relations are derived, then expanded to components of stress or strain for special cases. Both constant stress (or strain) and variable states are described, together with methods of determining material constants. Conversion from creep to relaxation, effects of temperature and stress analysis problems in nonlinear materials are also treated here. Finally, Chapter 13 discusses experimental methods for creep and stress relaxation under combined stress. This chapter considers especially those experimental problems which must be solved properly when reliable experimental results of high precision are required. Six appendices present the necessary mathematical background, conversion tables, and more rigorous derivations than employed in the text. An extensive updated bibliography completes the book. |
Contents
INTRODUCTION | 1 |
HISTORICAL SURVEY OF CREEP | 8 |
STATE OF STRESS AND STRAIN | 22 |
MECHANICS OF STRESS AND DEFORMATION ANALYSES | 40 |
LINEAR VISCOELASTIC CONSTITUTIVE EQUATIONS | 50 |
LINEAR VISCOELASTIC STRESS ANALYSIS | 106 |
MULTIPLE INTEGRAL REPRESENTATION | 129 |
NONLINEAR CREEP AT CONSTANT STRESS AND RELAXATION AT CONSTANT STRAIN | 174 |
NONLINEAR CREEP OR RELAXATION UNDER VARIABLE STRESS OR STRAIN | 218 |
CONVERSION AND MIXING OF NONLINEAR CREEP AND RELAXATION | 237 |
EFFECT OF TEMPERATURE ON NONLINEAR V1SCOELASTIC MATERIALS | 247 |
NONLINEAR VISCOELASTIC STRESS ANALYSIS | 266 |
EXPERIMENTAL METHODS | 287 |
Other editions - View all
Creep and Relaxation of Nonlinear Viscoelastic Materials William N. Findley,Francis A. Davis Limited preview - 2013 |
Creep And Relaxation Of Nonlinear Viscoelastic Materials With An ... W.N. Findley Limited preview - 2012 |
Common terms and phrases
applied approximation axial strain axial stress beam biaxial Chapter combined tension complex modulus components of strain constant strain constant stress constitutive equation constitutive relation corresponding creep behavior creep compliance creep strain creep tests dashpot deformation derived described determined deviatoric Dirac Delta Function discussed displacement elastic employed example experimental expressed Findley given incompressible input Inserting Kelvin model kernel functions linear viscoelastic linearly compressible loading material constants mathematical matrix Maxwell model mechanical multiple integral representation nonlinear viscoelastic materials obtained plastics Poisson's ratio Polyurethane prediction prescribed principal stresses problems pure torsion relaxation modulus Rheology Section shear strain shear stress shown in Fig specimen strain components strain rate strain tensor stress analysis stress and strain stress components stress history stress relaxation stress tensor superposition principle t-t₁ t—t₁ t₁ temperature tensile tension and torsion theory time-dependent tion torsion uniaxial stress values variable viscoelastic behavior viscous yields the following zero