Body Tensor Fields in Continuum Mechanics

With Applications to Polymer Rheology

Arthur S. Lodge

• Publisher: Academic Press
• Year: 2014
• Print ISBN: 9780124549500
• eBook ISBN: 9781483262994
• Topic: Physical Sciences
• Subtopic: Mechanics

Body Tensor Fields in Continuum Mechanics: With Applications to Polymer Rheology aims to define body tensor fields and to show how they can be used to advantage in continuum mechanics, which has hitherto been treated with space tensor fields. General tensor analysis is developed from first principles, using a novel approach that also lays the foundations for other applications, e.g., to differential geometry and relativity theory. The applications given lie in the field of polymer rheology, treated on the macroscopic level, in which relations between stress and finite-strain histories are of central interest. The book begins with a review of mathematical prerequisites, namely primitive concepts, linear spaces, matrices and determinants, and functionals. This is followed by separate chapters on body tensor and general space tensor fields; the kinematics of shear flow and shear-free flow; Cartesian vector and tensor fields; and relative tensors, field transfer, and the body stress tensor field. Subsequent chapters deal with constitutive equations for viscoelastic materials; reduced constitutive equations for shear flow and shear-free flow; covariant differentiation and the stress equations of motion; and stress measurements in unidirectional shear flow.

Table of contents

• Cover image
• Title page
• Table of Contents
• Copyright
• PREFACE
• ACKNOWLEDGMENTS
• LIST OF NOTATION
• Chapter 1: SOME MATHEMATICAL PREREQUISITES
• Chapter 2: THE BODY METRIC TENSOR FIELD
• Chapter 3: THE KINEMATICS OF SHEAR FLOW AND SHEAR-FREE FLOW
• Chapter 4: CARTESIAN VECTOR AND TENSOR FIELDS
• Chapter 5: RELATIVE TENSORS, FIELD TRANSFER, AND THE BODY STRESS TENSOR FIELD
• Chapter 6: CONSTITUTIVE EQUATIONS FOR VISCOELASTIC MATERIALS
• Chapter 7: REDUCED CONSTITUTIVE EQUATIONS FOR SHEAR FLOW AND SHEAR-FREE FLOW
• Chapter 8: COVARIANT DIFFERENTIATION AND THE STRESS EQUATIONS OF MOTION
• Chapter 9: STRESS MEASUREMENTS IN UNIDIRECTIONAL SHEAR FLOW; THEORY
• Chapter 10: CONSTITUTIVE PREDICTIONS AND EXPERIMENTAL DATA
• Chapter 11: RELATIONS BETWEEN BODY- AND SPACE-TENSOR FORMALISMS
• APPENDIX A: EQUATIONS IN CYLINDRICAL POLAR COORDINATES
• APPENDIX B: EQUATIONS IN SPHERICAL POLAR COORDINATE SYSTEMS
• APPENDIX C: EQUATIONS IN ORTHOGONAL COORDINATE SYSTEMS
• APPENDIX D: SUMMARY OF DEFINITIONS FOR UNIDIRECTIONAL SHEAR FLOW
• APPENDIX E: CALCULATIONS FOR VISCOELASTIC LIQUIDS
• REFERENCES
• SOLUTIONS TO PROBLEMS
• AUTHOR INDEX
• SUBJECT INDEX