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Continuum Mechanics

Index of terms

Every titled definition, theorem, recipe and key idea in the book, alphabetically. Click a name to open it here, or the section number to go to it.

Essential vocabulary

Only these are flagged essential: everything else is built from them.

  1. Deformation Definition 3.1.2, §3.1
  2. Deformation gradient Definition 3.2.1, §3.2
  3. Determinant Definition 2.5.5, §2.5
  4. Dyad (tensor product) Definition 2.1.4, §2.1
  5. Eigenvalue and eigenvector Definition 2.7.1, §2.7
  6. Right Cauchy–Green tensor Definition 3.3.2, §3.3
  7. Second-order tensor Definition 2.1.1, §2.1

Every definition, theorem and recipe

  1. A deformation acts on points Key observation 3.1.3, §3.1
  2. Admissible deformation Definition 3.2.4, §3.2
  3. Axial vector (A3) Theorem 2.3.3, §2.3
  4. Basis, dimension, components Definition 1.1.7, §1.1
  5. Body and placement Definition 3.1.1, §3.1
  6. C forgets the rotation Key observation 3.3.4, §3.3
  7. C is symmetric and positive definite Theorem 3.3.3, §3.3
  8. C is the local change of shape Key observation 3.3.6, §3.3
  9. Change in length Theorem 3.3.1, §3.3
  10. Change in volume Theorem 3.4.4, §3.4
  11. Change of basis Definition 2.8.1, §2.8
  12. Cofactor Theorem 3.4.1, §3.4
  13. Components of a tensor Theorem 2.1.6, §2.1
  14. Components of u × v Recipe 1.3.3, §1.3
  15. Composition (product) Definition 2.2.3, §2.2
  16. Computing F Recipe 3.2.3, §3.2
  17. Deformation Definition 3.1.2, §3.1
  18. Deformation gradient Definition 3.2.1, §3.2
  19. Determinant Definition 2.5.5, §2.5
  20. Determinant from the columns Recipe 2.5.7, §2.5
  21. Displacement and displacement gradient Definition 3.2.5, §3.2
  22. Dyad (tensor product) Definition 2.1.4, §2.1
  23. Eigenvalue and eigenvector Definition 2.7.1, §2.7
  24. Eigenvalues and eigenvectors Recipe 2.7.2, §2.7
  25. Einstein convention Definition 1.2.3, §1.2
  26. Every part deforms in the same way Key observation 3.5.2, §3.5
  27. Every tensor splits uniquely Theorem 2.3.2, §2.3
  28. F is not a strain measure Key observation 3.5.7, §3.5
  29. From W to w and back Recipe 2.3.4, §2.3
  30. Green–Lagrange strain Definition 3.6.7, §3.6
  31. Homogeneous deformation Definition 3.5.1, §3.5
  32. Invariants Key observation 2.8.3, §2.8
  33. Inverse Definition 2.5.1, §2.5
  34. Is w a combination of u and v? Recipe 1.1.4, §1.1
  35. Isochoric Definition 3.4.5, §3.4
  36. Linear combination, span Definition 1.1.3, §1.1
  37. Linear independence Definition 1.1.5, §1.1
  38. More dyad rules Proposition 2.2.7, §2.2
  39. Nanson’s formula Theorem 3.4.2, §3.4
  40. New components Theorem 2.8.2, §2.8
  41. Norm, angle, versor, orthogonality Definition 1.2.1, §1.2
  42. Normals go with F⁻ᵀ, not with F Key observation 3.4.3, §3.4
  43. Order is orientation Key observation 3.2.6, §3.2
  44. Orth and Rot Definition 2.6.4, §2.6
  45. Orthogonal from the columns Recipe 2.6.3, §2.6
  46. Orthogonal means transpose = inverse Theorem 2.6.2, §2.6
  47. Orthogonal tensor Definition 2.6.1, §2.6
  48. Orthonormal basis, Kronecker delta, components Definition 1.2.2, §1.2
  49. Point space and translation space Definition 1.1.1, §1.1
  50. Polar decomposition Theorem 3.6.5, §3.6
  51. Position vector Definition 1.1.2, §1.1
  52. Positive definite Definition 2.7.8, §2.7
  53. Positive definite means positive eigenvalues Theorem 2.7.9, §2.7
  54. Principal invariants Definition 2.7.3, §2.7
  55. Principal stretches and directions Definition 3.6.1, §3.6
  56. Product in components Theorem 2.2.4, §2.2
  57. Project v on the line of a versor e, and on the plane normal to it Recipe 1.2.6, §1.2
  58. Projection tensors Proposition 2.1.7, §2.1
  59. Properties of the determinant Theorem 2.5.8, §2.5
  60. Reading and writing index expressions Recipe 1.2.4, §1.2
  61. Reading C Recipe 3.3.5, §3.3
  62. Ricci symbol (A1) Definition 1.3.2, §1.3
  63. Ricci–Kronecker identity (A2) Theorem 1.3.4, §1.3
  64. Right Cauchy–Green tensor Definition 3.3.2, §3.3
  65. Right stretch tensor Definition 3.6.3, §3.6
  66. Right- and left-handed Definition 1.3.5, §1.3
  67. Rigid deformation Definition 3.5.5, §3.5
  68. Rigid means translation plus rotation Theorem 3.5.6, §3.5
  69. Rules for inverses Theorem 2.5.4, §2.5
  70. Rules for transposes and products Theorem 2.2.6, §2.2
  71. Scalar product and norm of tensors Definition 2.4.3, §2.4
  72. Scalar product of dyads Definition 2.1.5, §2.1
  73. Scalar triple product Definition 1.3.6, §1.3
  74. Second-order tensor Definition 2.1.1, §2.1
  75. Spectral theorem Theorem 2.7.4, §2.7
  76. Square root Theorem 2.7.10, §2.7
  77. Stretch, then turn Key observation 3.6.6, §3.6
  78. Symmetric and skew tensors Definition 2.3.1, §2.3
  79. Taking a square root Recipe 2.7.11, §2.7
  80. The Invertible Tensor Theorem Theorem 2.5.2, §2.5
  81. The matrix of a tensor Recipe 2.1.2, §2.1
  82. The scalar product as a sum over a frame Theorem 2.4.4, §2.4
  83. The trace is the same in every basis Key observation 2.4.2, §2.4
  84. The triple product is a signed volume Key observation 1.3.7, §1.3
  85. Three fibres that stay orthogonal Key observation 3.6.2, §3.6
  86. Three properties of the scalar product Theorem 2.4.5, §2.4
  87. Trace Definition 2.4.1, §2.4
  88. Transpose Definition 2.2.1, §2.2
  89. Transpose in components Theorem 2.2.2, §2.2
  90. U is pure stretch Key observation 3.6.4, §3.6
  91. Vector product Definition 1.3.1, §1.3
  92. What a symmetric tensor does Key observation 2.7.5, §2.7
  93. What F does Key observation 3.2.2, §3.2
  94. What the determinant is Key observation 2.5.6, §2.5