Lectures on Continuum Physics

Course Description

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

Copyright Information

This Work, Lectures on Continuum Physics, by Krishna Garikipati is licensed under a Creative Commons Attribution-NonCommercial license.
Lectures on Continuum Physics
Prof. Garikipati answering a student's question using a football.



 

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Video Lectures & Study Materials

Visit the official course website for more study materials: http://open.umich.edu/education/engin/continuum-physics/2013

# Lecture Play Lecture
1 Introduction (18:20) Play Video
2 Response to a question (1:34) Play Video
3 Vectors I (14:56) Play Video
4 Response to a question (2:04) Play Video
5 Vectors II (27:25) Play Video
6 Vectors III (24:41) Play Video
7 Tensors I (15:31) Play Video
8 Tensors II (11:59) Play Video
9 Response to a question (17:18) Play Video
10 Tensors III (21:16) Play Video
11 Tensor properties I (14:04) Play Video
12 Tensor properties I (16:07) Play Video
13 Tensor properties II (15:43) Play Video
14 Tensor properties II (13:55) Play Video
15 Tensor properties III (21:02) Play Video
16 Vector and tensor fields (9:22) Play Video
17 Vector and tensor fields (16:54) Play Video
18 Configurations (14:29) Play Video
19 Configurations (14:31) Play Video
20 Motion (18:32) Play Video
21 Response to a question (2:56) Play Video
22 Response to a follow up question (2:59) Play Video
23 The Lagrangian description of motion (14:32) Play Video
24 The Lagrangian description of motion (15:35) Play Video
25 The Eulerian description of motion (14:10) Play Video
26 The Eulerian description of motion (14:07) Play Video
27 The material time derivative (14:11) Play Video
28 The material time derivative (16:52) Play Video
29 Response to a question (1:21) Play Video
30 The deformation gradient: mapping of curves (23:41) Play Video
31 The deformation gradient: mapping of surfaces and volumes (18:08) Play Video
32 The deformation gradient: mapping of surfaces and volumes (14:26) Play Video
33 The deformation gradient: a first order approximation of the deformation (22:51) Play Video
34 Stretch and strain tensors (21:00) Play Video
35 Stretch and strain tensors (10:14) Play Video
36 The polar decomposition I (22:03) Play Video
37 Response to a question (4:43) Play Video
38 The polar decomposition I (11:31) Play Video
39 The polar decomposition II (14:21) Play Video
40 The polar decomposition II (16:12) Play Video
41 Velocity gradients, and rates of deformation (15:36) Play Video
42 Response to a question (3:00) Play Video
43 Velocity gradients, and rates of deformation (15:46) Play Video
44 Balance of mass I (19:35) Play Video
45 Balance of mass I (8:33) Play Video
46 Balance of mass II (27:08) Play Video
47 Balance of mass II (14:51) Play Video
48 Reynolds' transport theorem I (19:07) Play Video
49 Reynolds' transport theorem I (10:25) Play Video
50 Reynolds' transport theorem II (20:36) Play Video
51 Reynolds' transport theorem III (23:33) Play Video
52 Response to a question (8:47) Play Video
53 Linear and angular momentum I (24:38) Play Video
54 Correction to boardwork (:45) Play Video
55 Response to a question (3:00) Play Video
56 Linear and angular momentum II (18:18) Play Video
57 The moment of inertia tensor (16:41) Play Video
58 The moment of inertia tensor (27:50) Play Video
59 The rate of change of angular momentum (18:37) Play Video
60 The balance of linear and angular momentum for deformable, continuum bodies (26:31) Play Video
61 The balance of linear and angular momentum for deformable, continuum bodies (18:38) Play Video
62 The Cauchy stress tensor (26:17) Play Video
63 Stress-- An Introduction (19:55) Play Video
64 Balance of energy (23:03) Play Video
65 Response to a question (11:13) Play Video
66 Response to a follow up question (6:58) Play Video
67 Additional measures of stress (25:05) Play Video
68 Additional measures of stress (15:54) Play Video
69 Response to a question (6:50) Play Video
70 Response to a follow up question (12:34) Play Video
71 Work conjugate forms (25:57) Play Video
72 Balance of linear momentum in the reference configuration (29:06) Play Video
73 Equations and unknowns--constitutive relations (15:29) Play Video
74 Response to a question (5:35) Play Video
75 Constitutitve equations (27:03) Play Video
76 Elastic solids and fluids--hyperelastic solids (29:16) Play Video
77 Response to a question (5:54) Play Video
78 Objectivity--change of observer (17:44) Play Video
79 Objectivity--change of observer (14:47) Play Video
80 Objective tensors, and objective constitutive relations (20:10) Play Video
81 Objective tensors, and objective constitutive relations (11:06) Play Video
82 Objectivity of hyperelastic strain energy density functions (29:18) Play Video
83 Examples of hyperelastic strain energy density functions (23:21) Play Video
84 Examples of hyperelastic strain energy density functions (10:08) Play Video
85 Response to a question (4:36) Play Video
86 The elasticity tensor in the reference configuration (14:27) Play Video
87 Elasticity tensor in the current configuration--objective rates (25:00) Play Video
88 Elasticity tensor in the current configuration--objective rates (11:40) Play Video
89 Objectivity of constitutive relations for viscous fluids (19:06) Play Video
90 Models of viscous fluids (28:15) Play Video
91 Response to a question (3:50) Play Video
92 Summary of initial and boundary value problems of continuum mechanics (25:21) Play Video
93 An initial and boundary value problem of fluid mechanics--the Navier Stokes equations (18:23) Play Video
94 An initial and boundary value problem of fluid mechanics--the Navier Stokes equation (14:58) Play Video
95 An initial and boundary value problem of fluid mechanics II (20:38) Play Video
96 Material symmetry 1--Isotropy (28:26) Play Video
97 Response to a question (3:18) Play Video
98 Material symmetry 2--Isotropy (11:04) Play Video
99 Material symmetry 2--Isotropy (23:16) Play Video
100 Material symmetry 3--Isotropy (23:54) Play Video
101 A boundary value problem in nonlinear elasticity I (17:16) Play Video
102 A boundary value problem in nonlinear elasticity I (13:25) Play Video
103 Response to a question (7:15) Play Video
104 A boundary value problem in nonlinear elasticity II--The inverse method (17:43) Play Video
105 Response to another question (12:02) Play Video
106 Linearized elasticity I (12:19) Play Video
107 Linearized elasticity I (18:36) Play Video
108 Linearized elasticity II (16:03) Play Video
109 Linearized elasticity II (16:24) Play Video
110 Response to a question (3:44) Play Video
111 Classical continuum mechanics: Books, and the road ahead (22:26) Play Video
112 The first law of thermodynamics the balance of energy (15:57) Play Video
113 The first law of thermodynamics the balance of energy (12:30) Play Video
114 The first law of thermodynamics the balance of energy (16:41) Play Video
115 The second law of thermodynamics the entropy inequality (14:48) Play Video
116 Legendre transforms the Helmholtz potential (20:23) Play Video
117 The Clausius Planck inequality (17:24) Play Video
118 The Clausius Duhem inequality (22:57) Play Video
119 Response to a question (5:33) Play Video
120 The heat transport equation (19:11) Play Video
121 Thermoelasticity (25:23) Play Video
122 The heat flux vector in the reference configuration (22:53) Play Video
123 The free energy functional (12:37) Play Video
124 The free energy functional (19:59) Play Video
125 Extremization of the free energy functional variational derivatives (26:44) Play Video
126 Euler Lagrange equations corresponding to the free energy functional (27:36) Play Video
127 The weak form and strong form of nonlinear elasticity (23:42) Play Video
128 The weak form and strong form of nonlinear elasticity (20:17) Play Video
129 The setting for mass transport (19:20) Play Video
130 The setting for mass transport (11:38) Play Video
131 Aside A unified treatment of boundary conditions (20:25) Play Video
132 The chemical potential (20:19) Play Video
133 The chemical potential (14:52) Play Video
134 Phase separation non convex free energy (16:05) Play Video
135 Phase separation non convex free energy (17:31) Play Video
136 The role of interfacial free energy (27:07) Play Video
137 The Cahn Hilliard formulation (23:27) Play Video
138 The Cahn Hilliard formulation (18:22) Play Video

Comments

Displaying 1 comment:

Ashish Bhatt wrote 1 year ago. - Delete
Hello Professor,

I want to know more about the weak and strong form of
nonlinear elasticity. I looked through the course webpage
and the introduction video but could not find any references
anywhere. Could you suggest one or two good references which
explain the weak and strong form of nonlinear elasticity in
greater detail?

Thanks
Ashish


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