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.

Contenu

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