Fall 2006

Due to maturity of FEM package, slip-line field theory is not widely used these days. However, we shall keep in mind that slip-line field analysis can provide analytical solutions to a number of very difficult problem which may involve huge deformations or velocity discontinuities, e.g. many metal forming processes. To evaluate these two analytical and numerical methods for plasticity I will try a simple example, compare these two solutions and finally get into a conclusion of my own.

I guess it's time that I cite some papers that are relevant to what I am looking at.

node/add/imageI propose to investigate an elastic-viscoplastic constitutive model proposed by Anand and Gurtin [1] for the large deformation of amorphous solids.  Specifically, I will present the constitutive framework proposed for elastic-plastic amorphous materials, I will implement the constitutive equations into Abaqus/Explicit, and I will compare numerical results with experimental results for polycarbonate [2]. 

43. Energy loss

44. Zener model and relaxation test

45. Zener model and cyclic-load test

46. Vibration of a viscoelastic rod

Return to the outline of the course.

A word file is attached.

Return to the outline of the course.

Each student completes a term paper of selected topics that (a) addresses a phenomenon in thin film materials, and (b) involves analyses using mechanics. The project contributes 25% of the grade, distributed as follows:

• 5%: November 30 (Thursday). Post your title and abstract in iMechanica, formated as below
  

1. Title (EM 397 Term Paper: e.g., Dislocations in Epitaxial Thin Films).
2. Tags (EM 397, Fall 2006, University of Texas at Austin, thin films, term paper)
3. Body: (i) Describe the phenomenon. (ii) Explain how mechanics is relevant. (iii) Cite at least 1 journal article.

• 10%: December 12 Tuesday (2:00-4:00 pm). 30 minute presentation. Use power point slides.
• 10%: December 18 Monday.

3 Papers that might be useful for Will Adam's final project (attached)

As promised, no homework for Thanksgiving :)

39. A circular transverse wave

40. Creep and recovery

41. Temperature dependence and Mr. Arrhenius

42. A loose nylon bolt

Return to the outline of the course.

We studied in class the phenomenon of resonance in forced, damped oscillators.  The mass and stiffness of a one-dimensional oscillator give rise to a natural frequency of oscillations known as the resonance frequency.  With no damping, energy input at this frequency accumulates and the amplitude of vibrations increases.

The phenomenon of resonance generalizes to linear elastic materials with many more (ie infinite) degrees of freedom: energy input at a natural frequency of vibration will accumulate and result in increasing amplitude of vibration.  The natural frequency in this case is determined by material properties (ie Young's modulus) and the geometry and dimensions of the object (ie a wine glass).  With so many degrees of freedom, the resonance frequency of common objects may be impossible to calculate exactly and it may be necessary to use the finite element method to investigate resonance.