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e 4: Fractal Tree to Provide Inspiration
Multiscale Biomechanics TakeHome 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 emails for clarifications, etc.
The
latest
handin time is 5:00 PM – Thursday, May 28, 2009.
Total Recall
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.
Describe what
they are below, and be sure to include the primary positive and negative aspects of each.
Bounding Methods
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
ε
level responses.
The Rule of Mixtures is applied here, where effective properties are determined
by volume fractions, and then a range of
E’s and
’s are found.
ν
+ Effecting macrolevel properties – averaging (range)
+ Simple! (E’s,
’s)
ν
 No way to relate micro to macro (not both ways)
Standard Mechanics
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View Full DocumentA means of determining effective properties for both micro and macro scale.
By selecting a
repeating microstructural unit, and assuming a set of boundary conditions, one can obtain a
micro “solution” and effective macro properties.
Similar to “tiling” the entire macro body with
the same solution.
The downside is that if you make a mistake, it is applied everywhere.
+ Only have to analyze one microstructure
+ Receive effective properties (an actual answer, not just a range)
+ Able to relate micro to macro
 Assumed boundary conditions
 Periodic Error / One micro solution
Cellular Solids
A means of determining effective properties for both micro and macro scale.
By treating the
material as an interconnected network of solid struts or plates that form faces or walls of cells,
one can solve for effective properties.
This is done by assuming macro boundary conditions,
determining forces applied to the microstructure, determining total micro deflection, and then
using that to solve for macro effective properties.
This is different than the standard mechanics
approach because here you assume boundary conditions to obtain general material behavior,
whereas in the standard mechanic approach you assume boundary conditions and solve for one
micro effective property.
+ Only have to analyze one microstructure
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 Spring '10
 WEINER

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