Zhigang Suo's blog

Notes are attached.  Return to the outline of the course.

The notes are part of the course on advanced elasticity. 

So, What is Mechanics? It seems that useful answers ought to depend on who you are talking to. If you are persuading your dean to hire a new faculty member in Mechanics, perhaps you’d like to point out promising research in one area or another, and how foundational mechanics is to the education of future scientists and technologists in (almost) all fields.

43. Energy loss
44. Zener model and relaxation test
45. Zener model and cyclic-load test
46. Vibration of a viscoelastic rod

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A word file is attached.

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39. A circular transverse wave
40. Creep and recovery
41. Temperature dependence and Mr. Arrhenius
42. A loose nylon bolt

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Zhen Zhang and Zhigang Suo (Harvard), Jun He (Intel)

Attached is a set of slides presented at ASME Congress, 10 November 2006. Thermal strains and electromigration can cause voids to grow in conductor lines on semiconductor chips. This long-standing failure mode is exacerbated by the recent introduction of low-permittivity dielectrics. We describe a method to calculate the volume of a saturated void (VSV), attained in a steady state when each point in a conductor line is in a state of hydrostatic pressure, and the gradient of the pressure along the conductor line balances the electron wind. We show that the VSV will either increase or decrease when the coefficient of thermal expansion of the dielectric increases, and will increase when the elastic modulus of the dielectric decreases. The VSV will also increase when porous dielectrics and ultrathin liners are used. At operation conditions, both thermal strains and electromigration make significant contributions to the VSV. We discuss these results in the context of interconnect design.

A file on elastic waves is attached.

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Updated on 11 October 2008.  Each student creates a distinct project that (a) addresses a phenomenon, and (b) involves a serious use of ABAQUS.   To get some inspiration, see projects of students who took this course in the past.

The project contributes 25% to the grade, distributed as follows.

34. Surface acoustic wave device
35. Approximate a rod as a 2DOF system
36. Soft tissues: large difference in velocities of longitudinal and transverse waves
37. A general approach to determine body waves
38. Reflection and refraction of a transverse wave

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Notes on the stiffness matrix formulation, used for ES 120, Introduction to the Mechanics of Solids, a sophomore course. This material will not be covered in ES 240, but might provide helpful reading if you do not have this background.

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31. A machine on a cantilever
32.  A beam on simple supports
33. Vibration of piano strings

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A word file is attached.

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26. Stress-strain relations under the plane strain conditions
27. Getting weak: derive weak statements from differential equations
28. Potential energy and Rayleigh -Ritz method
29. Constant strain triangle
30. Gaussian quadrature

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The notes are attached. Return to the outline of the course.

If you have not read them, you might find them interesting.

• The New Yorker article: Manifold Destiny
• The New York Times article: The Emperor of Math

A word file is attached.

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21. A fiber in an infinite matrix
22. Anti-plane shear
23. Saint-Venant's principle for orthotropic materials
24. Plane problems with no length scales
25. More scaling relations: a half space filled with a power-law material

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• 16. Recommend a textbook that you think will help students in this course.  See recommendations from students who took this course before.
• 17. Disclination (the cut-and-weld problem)
• 18. Design a rotating disk to avert plastic deformation
• 19. A half space of an elastic material subject to a periodic traction on the surface
• 20. Orthotropy rescaling

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• A small system in thermal contact with a large system
• The Boltzmann factor
• Partition function
• The probability for a system in thermal equilibrium with a reservoir to be in a specific state
• The probability for a system in thermal equilibrium with a reservoir to be in a configuration
• Thermal fluctuation of an RNA molecule
• A matter of words
  

Return to the outline of Statistical Mechanics.