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Displacement gradients?

  1. Apr 7, 2009 #1
    displacement gradients?????

    1. The problem statement, all variables and given/known data

    Arrays of markers created on the surface (i.e. 2-D) of a tissue are often used to quantify
    tissue deformations. Find the displacement gradients and calculate the Green strain tensor,
    E, and the infinitessimal strain tensor, ε. Measurement of marker positions are listed below:
    (marker #, before deformation, after deformation)
    1 (0, 0) (0, 0)
    2 (1, 0) (1.02, 0.01)
    3 (2, 0) (2.15, 0.03)
    4 (0, 1) (-0.02, 1.03)
    5 (1, 1) (1.01, 1.05)
    6 (2, 1) (2.19, 1.15)
    7 (0, 2) (-0.04, 2.06)
    8 (1, 2) (1.00, 2.09)
    9 (2, 2) (2.30, 2.22)

    a) Generate images of the marker locations before and after deformation.
    b) Using these data perform linear fits to compute the four displacement gradients, ∂u/∂x for
    each of the areas defined by points 1-2-4-5, 2-3-5-6, 4-5-7-8, and 5-6-8-9.


    2. Relevant equations


    3. The attempt at a solution

    at this point all i can do is part a, i have no idea what to calc for b.
     
  2. jcsd
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