Page 12 - Introduction to Continuum Mechanics

Contents xi

Part B Nonlinear Viscoelastic Fluid 476

8.5 Current Configuration as Reference Configuration 476
8.6 Relative Deformation Gradient 477
8.7 Relative Deformation Tensors 478
8.8 Calculations of the Relative Deformation Tensor 480
8.9 History of Deformation Tensor. Rivlin-Ericksen Tensors 486
8.10 Rivlin-Ericksen Tensor in Terms of Velocity Gradients -
The Recursive Formulas 491
8.11 Relation Between Velocity Gradient and Deformation Gradient 493
8.12 Transformation Laws for the Relative Deformation Tensors under a
Change of Frame 494
8.13 Transformation law for the Rivlin-Ericksen Tensors under a
Change of Frame 496
8.14 Incompressible Simple Fluid 497
8.15 Special Single Integral Type Nonlinear Constitutive Equations 498
8.16 General Single Integral Type Nonlinear Constitutive Equations 503
8.17 Differential Type Constitutive Equations 503
8.18 Objective Rate of Stress 506
8.19 The Rate Type Constitutive Equations 511

Part C Viscometric Flow Of Simple Fluid 516

8.20 Viscometric Flow 516
8.21 Stresses in Viscometric Flow of an Incompressible Simple Fluid 520
8.22 Channel Flow 523
8.23 Couette Flow 526
Problems 532

Appendix: Matrices 537

Answer to Problems 543

References 550

Index 552