Question

8. Imagine that you have been given a large data set of mechanical measurements for the Young’s Modulus of blood vessels, as well as the amount of collagen in each sample.

a.) Assuming the tissue can be well modeled as a fiber-containing two-component composite loaded longitudinally, derive a GRAPHICAL scheme for estimating the Young Modulus of collagen and elastin.

b.) Sketch a graph of what your data would look like if this is a good model. Label all pertinent slopes and intercepts.

c.) Now re-derive the analysis assuming the samples were loaded transversely.

d.) Sketch a graph of what your data would look like if this is a good model. Label all pertinent slopes and intercepts.

e.) Based on your analysis and graphs, how could you qualitatively tell which model is better from a plot of the Young’s modulus and the volume fraction of collagen (Hint: the answer to this question should be self-evident from the graphs).

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Answer 1

Solution

(e) Based on the plots above, the collagen in longitudinal has highest modulus among all other constituents of the composites discussed.Highest modulus with high volume fraction makes it better.