Continuum Mechanics is a branch of physical mechanics that describes the macroscopic mechanical behavior of solid or fluid materials considered to be continuously distributed. It is fundamental to the fields of civil, mechanical, chemical and bioengineering. This time-tested text has been used for over 35 years to introduce junior and senior-level undergraduate engineering students, as well as graduate students, to the basic principles of continuum mechanics and their applications to real engineering problems. The text begins with a detailed presentation of the coordinate invariant quantity, the tensor, introduced as a linear transformation. This is then followed by the formulation of the kinematics of deformation, large as well as very small, the description of stresses and the basic laws of continuum mechanics. As applications of these laws, the behaviors of certain material idealizations (models) including the elastic, viscous and viscoelastic materials, are presented.
This new edition offers expanded coverage of the subject matter both in terms of details and contents, providing greater flexibility for either a one or two-semester course in either continuum mechanics or elasticity. Although this current edition has expanded the coverage of the subject matter, it nevertheless uses the same approach as that in the earlier editions - that one can cover advanced topics in an elementary way that go from simple to complex, using a wealth of illustrative examples and problems. It is, and will remain, one of the most accessible textbooks on this challenging engineering subject.
1. Chapter 1: Introduction 2. Chapter 2: Tensors 3. Chapter 3: Kinematics of a Continuum 4. 3.1 DESCRIPTION OF MOTIONS OF A CONTINUUM 5. 3.2 MATERIAL DESCRIPTION AND SPATIAL DESCRIPTION 6. 3.3 MATERIAL DERIVATIVE 7. 3.4 ACCELERATION OF A PARTICLE 8. 3.5 DISPLACEMENT FIELD 9. 3.6 KINEMATIC EQUATION FOR RIGID BODY MOTION 10. 3.7 INFINITESIMAL DEFORMATION 11. 3.8 GEOMETRICAL MEANING OF THE COMPONENTS OF THE INFINITESIMAL STRAIN TENSOR 12. 3.9 PRINCIPAL STRAIN 13. 3.10 DILATATION 14. 3.11 THE INFINITESIMAL ROTATION TENSOR 15. 3.12 TIME RATE OF CHANGE OF A MATERIAL ELEMENT 16. 3.13 THE RATE OF DEFORMATION TENSOR 17. 3.14 THE SPIN TENSOR AND THE ANGULAR VELOCITY VECTOR 18. 3.15 EQUATION OF CONSERVATION OF MASS 19. 3.16 COMPATIBILITY CONDITIONS FOR INFINITESIMAL STRAIN COMPONENTS 20. 3.17 COMPATIBILITY CONDITION FOR RATE OF DEFORMATION COMPONENTS 21. 3.18 DEFORMATION GRADIENT 22. 3.19 LOCAL RIGID BODY MOTION 23. 3.20 FINITE DEFORMATION 24. 3.21 POLAR DECOMPOSITION THEOREM 25. 3.22 CALCULATION OF STRETCH AND ROTATION TENSORS FROM THE DEFORMATION GRADIENT 26. 3.23 RIGHT CAUCHY-GREEN DEFORMATION TENSOR 27. 3.24 LAGRANGIAN STRAIN TENSOR 28. 3.25 LEFT CAUCHY-GREEN DEFORMATION TENSOR 29. 3.26 EULERIAN STRAIN TENSOR 30. 3.27 CHANGE OF AREA DUE TO DEFORMATION 31. 3.28 CHANGE OF VOLUME DUE TO DEFORMATION 32. 3.29 COMPONENTS OF DEFORMATION TENSORS IN OTHER COORDINATES 33. 3.30 CURRENT CONFIGURATION AS THE REFERENCE CONFIGURATION 34. APPENDIX 3.1: NECESSARY AND SUFFICIENT CONDITIONS FOR STRAIN COMPATIBILITY 35. APPENDIX 3.2: POSITIVE DEFINITE SYMMETRIC TENSORS 36. APPENDIX 3.3: THE POSITIVE DEFINITE ROOT OF U2 = D 37. PROBLEMS FOR CHAPTER 3 38. Chapter 4: Stress and Integral Formulations of General Principles 39. Chapter 5: The Elastic Solid 40. 5.1 MECHANICAL PROPERTIES 41. 5.2 LINEARLY ELASTIC SOLID 42. PART A ISOTROPIC LINEARLY ELASTIC SOLID 43. PART B ANISOTROPIC LINEARLY ELASTIC SOLID 44. PART C ISOTROPIC ELASTIC SOLID UNDER LARGE DEFORMATION 45. APPENDIX 5C.1 REPRESENTATION OF ISOTROPIC TENSOR-VALUED FUNCTIONS 46. Chapter 6: Newtonian Viscous Fluid 47. Chapter 7: The Reynolds Transport Theorem and Applications 48. Chapter 8: Non-Newtonian Fluids 49. References 50. Index 51. Answers to Problems
Continuum Mechanics is a branch of physical mechanics that describes the macroscopic mechanical behavior of solid or fluid materials considered to be continuously distributed. It is fundamental to the fields of civil, mechanical, chemical and bioengineering. This time-tested text has been used for over 35 years to introduce junior and senior-level undergraduate engineering students, as well as graduate students, to the basic principles of continuum mechanics and their applications to real engineering problems. The text begins with a detailed presentation of the coordinate invariant quantity, the tensor, introduced as a linear transformation. This is then followed by the formulation of the kinematics of deformation, large as well as very small, the description of stresses and the basic laws of continuum mechanics. As applications of these laws, the behaviors of certain material idealizations (models) including the elastic, viscous and viscoelastic materials, are presented.
This new edition offers expanded coverage of the subject matter both in terms of details and contents, providing greater flexibility for either a one or two-semester course in either continuum mechanics or elasticity. Although this current edition has expanded the coverage of the subject matter, it nevertheless uses the same approach as that in the earlier editions - that one can cover advanced topics in an elementary way that go from simple to complex, using a wealth of illustrative examples and problems. It is, and will remain, one of the most accessible textbooks on this challenging engineering subject.
1. Chapter 1: Introduction 2. Chapter 2: Tensors 3. Chapter 3: Kinematics of a Continuum 4. 3.1 DESCRIPTION OF MOTIONS OF A CONTINUUM 5. 3.2 MATERIAL DESCRIPTION AND SPATIAL DESCRIPTION 6. 3.3 MATERIAL DERIVATIVE 7. 3.4 ACCELERATION OF A PARTICLE 8. 3.5 DISPLACEMENT FIELD 9. 3.6 KINEMATIC EQUATION FOR RIGID BODY MOTION 10. 3.7 INFINITESIMAL DEFORMATION 11. 3.8 GEOMETRICAL MEANING OF THE COMPONENTS OF THE INFINITESIMAL STRAIN TENSOR 12. 3.9 PRINCIPAL STRAIN 13. 3.10 DILATATION 14. 3.11 THE INFINITESIMAL ROTATION TENSOR 15. 3.12 TIME RATE OF CHANGE OF A MATERIAL ELEMENT 16. 3.13 THE RATE OF DEFORMATION TENSOR 17. 3.14 THE SPIN TENSOR AND THE ANGULAR VELOCITY VECTOR 18. 3.15 EQUATION OF CONSERVATION OF MASS 19. 3.16 COMPATIBILITY CONDITIONS FOR INFINITESIMAL STRAIN COMPONENTS 20. 3.17 COMPATIBILITY CONDITION FOR RATE OF DEFORMATION COMPONENTS 21. 3.18 DEFORMATION GRADIENT 22. 3.19 LOCAL RIGID BODY MOTION 23. 3.20 FINITE DEFORMATION 24. 3.21 POLAR DECOMPOSITION THEOREM 25. 3.22 CALCULATION OF STRETCH AND ROTATION TENSORS FROM THE DEFORMATION GRADIENT 26. 3.23 RIGHT CAUCHY-GREEN DEFORMATION TENSOR 27. 3.24 LAGRANGIAN STRAIN TENSOR 28. 3.25 LEFT CAUCHY-GREEN DEFORMATION TENSOR 29. 3.26 EULERIAN STRAIN TENSOR 30. 3.27 CHANGE OF AREA DUE TO DEFORMATION 31. 3.28 CHANGE OF VOLUME DUE TO DEFORMATION 32. 3.29 COMPONENTS OF DEFORMATION TENSORS IN OTHER COORDINATES 33. 3.30 CURRENT CONFIGURATION AS THE REFERENCE CONFIGURATION 34. APPENDIX 3.1: NECESSARY AND SUFFICIENT CONDITIONS FOR STRAIN COMPATIBILITY 35. APPENDIX 3.2: POSITIVE DEFINITE SYMMETRIC TENSORS 36. APPENDIX 3.3: THE POSITIVE DEFINITE ROOT OF U2 = D 37. PROBLEMS FOR CHAPTER 3 38. Chapter 4: Stress and Integral Formulations of General Principles 39. Chapter 5: The Elastic Solid 40. 5.1 MECHANICAL PROPERTIES 41. 5.2 LINEARLY ELASTIC SOLID 42. PART A ISOTROPIC LINEARLY ELASTIC SOLID 43. PART B ANISOTROPIC LINEARLY ELASTIC SOLID 44. PART C ISOTROPIC ELASTIC SOLID UNDER LARGE DEFORMATION 45. APPENDIX 5C.1 REPRESENTATION OF ISOTROPIC TENSOR-VALUED FUNCTIONS 46. Chapter 6: Newtonian Viscous Fluid 47. Chapter 7: The Reynolds Transport Theorem and Applications 48. Chapter 8: Non-Newtonian Fluids 49. References 50. Index 51. Answers to Problems
