Computational or Analytical?
Once you can describe a problem analytically, you should be able to solve the problem straightforward. Moreover, bookkeeping of the related variables is rather easy, enabling you to model your problem in an rather easy fashion. (During my undergraduate courses, I used to check my assignents by Excel). However, implementing such a strategy in software involves a certain amount of problem directed programming - i.e. your code may be valid for a given problem only.
These notes are part of a graduate course on advanced elasticity.
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A couple of years ago a colleague who wanted to simulate high-speed machining asked me: " Which is the best phenomenological flow stress model for metals?" I wasn't able to give an answer right away and decided to look in the literature.
What I found was, every ten years or so, a new model appears in the literature that tries to solve some of the problems of older models. However, a clear ranking of models has not been established yet.
Two Valuable papers on current research areas in computational mechanics:
http://www.tam.northwestern.edu/tb/TBPublications.htm
http://www.nsf.gov/pubs/reports/sbes_final_report.pdf
I am working on my PhD in Biomedical Engineering at the University of Neb. and have enrolled inES 242r because failure modes of many orthopedic implants can be attributed to initial flaws & fractures of material coatings. This course, albeit, focuses on ductile materials, the principles seem relevant.
