The Cahn Hilliard formulation 
The Cahn Hilliard formulation
by U. Michigan / Krishna Garikipati
Video Lecture 138 of 138
Copyright Information: This Work, Lectures on Continuum Physics, by Krishna Garikipati is licensed under a Creative Commons Attribution-NonCommercial license.
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Date Added: January 24, 2015

Lecture Description

This video lecture, part of the series Lectures on Continuum Physics by Prof. Krishna Garikipati, does not currently have a detailed description and video lecture title. If you have watched this lecture and know what it is about, particularly what Physics topics are discussed, please help us by commenting on this video with your suggested description and title. Many thanks from,

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Course Index

  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

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

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