Soft tissue follows an exponential deformation behavior in uniaxial tension while it is in the physiologic a normal range of elongation This can be expressed as Where stress, strain, and E o and are material constants that are determined experimentally To evaluate the two material constants, the ab...

Because the data is equispaced we can use the secondorder finite divided difference formulas from Fi ...

Soft tissue follows an exponential deformation behavior in uniaxial tension while it is in the physiologic a

Question:

Soft tissue follows an exponential deformation behavior in uniaxial tension while it is in the physiologic a normal range of elongation. This can be expressed as

Where σ = stress, ε = strain, and E_o and α are material constants that are determined experimentally. To evaluate the two material constants, the above equation is differentiated with respect to ε, which is a fundamental relationship for soft tissue

To evaluate E_o and α, stress-strain data is used to plot dσ/dε versus σ and the slope and intercept of this plot are the two material constants, respectively. The table contains stress-strain data for heart chordae tendineae (small tendons use to hold heart valves closed during contraction of the heart muscle). This is data from loading the tissue; different curves are produced on unloading.

(a) Calculate the derivative dσ/dε using finite differences that are second-order accurate. Plot the data and eliminate the data points near the zero points that appear not to follow the straight-line relationship. The error in this data comes from the inability of the instrumentation to read the small values in this region. Perform a regression analysis of the remaining data points to determine the values of E_o and α. Plot the stress versus strain data points along with the analytic curve expressed by the first equation. This will indicate how well the analytic curve matches the data.

(b) Often the previous analysis does not work well because the value of E_o is difficult to evaluate. To solve this problem, E_o is not used. A data point is selected (σ, ε) that is in the middle of the range used for the regression analysis. These values are substituted into the first equation, and a value for E_o/α is determined and substituted into the first equation:

Using this approach, experimental date that is well defined will produce a good match of the data points and the analytic curve. Use this new relationship and again plot the stress versus the strain data points and the new analyticcurve.