e 4: Fractal Tree to Provide Inspiration
Multiscale Biomechanics Take-Home Final Answers
To complete this exam, you can use:
Class notes, class handouts, or any published, written reference (e.g. books
at library, journal articles, etc).
If you end up using a reference (like a
book, a website, or a journal article) to answer a question, go ahead and
provide the complete reference.
This is an individual exam, which means it should be solved by individuals, and not solved in
pairs or teams or worked on/discussed with other class members.
Please feel free to come ask
questions of me, or send e-mails for clarifications, etc.
hand-in time is 5:00 PM – Thursday, May 28, 2009.
Before we start getting into anything too heavy, let us first recall some of the basic
ideologies we have used as tools this quarter.
[A] Throughout the course of this class we discussed four methodologies used to determine
various properties of micro and macro structures in relation to each other.
they are below, and be sure to include the primary positive and negative aspects of each.
A means of determining effective properties at the macro scale based on micro scale constituents
(one but not the other).
By determining (averaging) effective properties, and then applying
loadings to macro level, we are able to determine
, etc at macro level and then determine micro
The Rule of Mixtures is applied here, where effective properties are determined
by volume fractions, and then a range of
’s are found.
+ Effecting macro-level properties – averaging (range)
+ Simple! (E’s,
- No way to relate micro to macro (not both ways)