1. Introduction
2. Response to a question
3. Vectors I
4. Response to a question
5. Vectors II
6. Vectors III
7. Tensors I
8. Tensors II
9. Response to a question
10. Tensors III
11. Tensor properties I
12. Tensor properties I
13. Tensor properties II
14. Tensor properties II
15. Tensor properties III
16. Vector and tensor fields
17. Vector and tensor fields
18. Configurations
19. Configurations
20. Motion
21. Response to a question
22. Response to a follow up question
23. The Lagrangian description of motion
24. The Lagrangian description of motion
25. The Eulerian description of motion
26. The Eulerian description of motion
27. The material time derivative
28. The material time derivative
29. Response to a question
30. The deformation gradient: mapping of curves
31. The deformation gradient: mapping of surfaces and volumes
32. The deformation gradient: mapping of surfaces and volumes
33. The deformation gradient: a first order approximation of the deformation
34. Stretch and strain tensors
35. Stretch and strain tensors
36. The polar decomposition I
37. Response to a question
38. The polar decomposition I
39. The polar decomposition II
40. The polar decomposition II
41. Velocity gradients, and rates of deformation
42. Response to a question
43. Velocity gradients, and rates of deformation
44. Balance of mass I
45. Balance of mass I
46. Balance of mass II
47. Balance of mass II
48. Reynolds' transport theorem I
49. Reynolds' transport theorem I
50. Reynolds' transport theorem II
51. Reynolds' transport theorem III
52. Response to a question
53. Linear and angular momentum I
54. Correction to boardwork
55. Response to a question
56. Linear and angular momentum II
57. The moment of inertia tensor
58. The moment of inertia tensor
59. The rate of change of angular momentum
60. The balance of linear and angular momentum for deformable, continuum bodies
61. The balance of linear and angular momentum for deformable, continuum bodies
62. The Cauchy stress tensor
63. Stress-- An Introduction
64. Balance of energy
65. Response to a question
66. Response to a follow up question
67. Additional measures of stress
68. Additional measures of stress
69. Response to a question
70. Response to a follow up question
71. Work conjugate forms
72. Balance of linear momentum in the reference configuration
73. Equations and unknowns--constitutive relations
74. Response to a question
75. Constitutitve equations
76. Elastic solids and fluids--hyperelastic solids
77. Response to a question
78. Objectivity--change of observer
79. Objectivity--change of observer
80. Objective tensors, and objective constitutive relations
81. Objective tensors, and objective constitutive relations
82. Objectivity of hyperelastic strain energy density functions
83. Examples of hyperelastic strain energy density functions
84. Examples of hyperelastic strain energy density functions
85. Response to a question
86. The elasticity tensor in the reference configuration
87. Elasticity tensor in the current configuration--objective rates
88. Elasticity tensor in the current configuration--objective rates
89. Objectivity of constitutive relations for viscous fluids
90. Models of viscous fluids
91. Response to a question
92. Summary of initial and boundary value problems of continuum mechanics
93. An initial and boundary value problem of fluid mechanics--the Navier Stokes equations
94. An initial and boundary value problem of fluid mechanics--the Navier Stokes equation
95. An initial and boundary value problem of fluid mechanics II
96. Material symmetry 1--Isotropy
97. Response to a question
98. Material symmetry 2--Isotropy
99. Material symmetry 2--Isotropy
100. Material symmetry 3--Isotropy
101. A boundary value problem in nonlinear elasticity I
102. A boundary value problem in nonlinear elasticity I
103. Response to a question
104. A boundary value problem in nonlinear elasticity II--The inverse method
105. Response to another question
106. Linearized elasticity I
107. Linearized elasticity I
108. Linearized elasticity II
109. Linearized elasticity II
110. Response to a question
111. Classical continuum mechanics: Books, and the road ahead
112. The first law of thermodynamics the balance of energy
113. The first law of thermodynamics the balance of energy
114. The first law of thermodynamics the balance of energy
115. The second law of thermodynamics the entropy inequality
116. Legendre transforms the Helmholtz potential
117. The Clausius Planck inequality
118. The Clausius Duhem inequality
119. Response to a question
120. The heat transport equation
121. Thermoelasticity
122. The heat flux vector in the reference configuration
123. The free energy functional
124. The free energy functional
125. Extremization of the free energy functional variational derivatives
126. Euler Lagrange equations corresponding to the free energy functional
127. The weak form and strong form of nonlinear elasticity
128. The weak form and strong form of nonlinear elasticity
129. The setting for mass transport
130. The setting for mass transport
131. Aside A unified treatment of boundary conditions
132. The chemical potential
133. The chemical potential
134. Phase separation non convex free energy
135. Phase separation non convex free energy
136. The role of interfacial free energy
137. The Cahn Hilliard formulation
138. The Cahn Hilliard formulation

The idea for these Lectures on Continuum Physics grew out of a short series of talks on materials physics at University of Michigan, in the summer of 2013. Those talks were aimed at advanced graduate students, post-doctoral scholars, and faculty colleagues. From this group the suggestion emerged that a somewhat complete set of lectures on continuum aspects of materials physics would be useful. The lectures that you are about to dive into were recorded over a six-week period at the University. Given their origin, they are meant to be early steps on a path of research in continuum physics for the entrant to this area, and I daresay a second opinion for the more seasoned exponent of the science. The potential use of this series as an enabler of more widespread research in continuum physics is as compelling a motivation for me to record and offer it, as is its potential as an open online class.

This first edition of the lectures appears as a collection of around 130 segments (I confess, I have estimated, but not counted) of between 12 and 30 minutes each. The recommended single dose of online instruction is around 15 minutes. This is a recommendation that I have flouted with impunity, hiding behind the need to tell a detailed and coherent story in each segment. Still, I have been convinced to split a number of the originally longer segments. This is the explanation for the proliferation of Parts I, II and sometimes even III, with the same title. Sprinkled among the lecture segments are responses to questions that arose from a small audience of students and post-doctoral scholars who followed the recordings live. There also are assignments and tests.

The roughly 130 segments have been organized into 13 units, each of which may be a chapter in a book. The first 10 units are standard fare from the continuum mechanics courses I have taught at University of Michigan over the last 14 years. As is my preference, I have placed equal emphasis on solids and fluids, insisting that one cannot fully appreciate the mechanical state of one of these forms of matter without an equal appreciation of the other. At my pace of classroom teaching, this stretch of the subject would take me in the neighborhood of 25 lectures of 80 minutes each. At the end of the tenth of these units, I have attempted, perhaps clumsily, to draw a line by offering a roadmap of what the viewer could hope to do with what she would have learned up to that point. It is there that I acknowledge the modern masters of continuum mechanics by listing the books that, to paraphrase Abraham Lincoln, will enlighten the reader far above my poor power to add or detract.

At this point the proceedings also depart from the script of continuum mechanics, and become qualified for the mantle of Continuum Physics. The next three units are on thermomechanics, variational principles and mass transport--subjects that I have learned from working in these areas, and have been unable to incorporate in regular classes for a sheer want of time. In the months and years to come, new editions of these Lectures on Continuum Physics will feature an enhancement of breadth and depth of these three topics, as well as topics in addition to them.

Finally, a word on the treatment of the subject: it is mathematical. I know of no other way to do continuum physics. While being rigorous (I hope) it is, however, neither abstract nor formal. In every segment I have taken pains to make connections with the physics of the subject. Props, simple but instructive, have been used throughout. A deformable plastic bottle, water and food color have been used--effectively, I trust. The makers of Lego, I believe, will find reason to be pleased. Finally, the time-honored continuum potato has been supplanted by an icon of American life: the continuum football.

Krishna Garikipati
Ann Arbor, December 2013