# Isoparametric Mapping

#### Peter S

1. Homework Statement
I have an initial configuration and a final configuration for a sample that has been stressed. Both of these are trapezoidal shapes and I have exact coordinates for each point. I know how to use the shape equations as well as deriving the Jacobian. Additionally I have computed the u and v displacement vectors for between the configurations. Now I need to determine the displacement and deformation gradients so I am able to compute strain on the tissue. The issue is that I don't know how a change in configuration affects the shape equations. Relating a single shape to a parent configuration is one thing, but I don't know how to map the two configurations so that I can determine stress and strain. As far as I can find, all examples relate some shape to the double unit square rather than a pre-existing configuration. I would appreciate any sort of help with this quite a bit. For what it's worth the best classification of this problem is a 4 node isoparametric mapping.

2. Homework Equations
x = Σi = 1->4Ni (s,t)xi
N1=¼*(1-s)(1-t)*x1...
y = Σi = 1->4Ni (s,t)yi
N1=¼*(1-s)(1-t)*y1...
u = x - X (lowercase = deformed configuration, uppercase = initial configuration)
v = y - Y
3. The Attempt at a Solution
I have nothing since I can't start the problem without knowing how to relate the configurations. I would prefer having someone point me in the right direction rather than putting up exact values and having my problem solved.

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#### Greg Bernhardt

Thanks for the thread! This is an automated courtesy bump. Sorry you aren't generating responses at the moment. Do you have any further information, come to any new conclusions or is it possible to reword the post? The more details the better.

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