Tendons stress-strain curves for

Figure 6.5. Typical stress-strain curve for tendon. The diagram illustrates the stress-strain curve for an isolated collagen fiber from tendon. Note that collagen fibers from tendon fail at UTS values above 50 MPa and at strains between 10 and 20%. The slope of the linear portion of the curves at high strains is 2GPa.

Elastic and viscous stress-strain curves for unmineralized and mineralized turkey tendons are plotted in Figure 7.5. In general, the elastic stress-strain curves for tendons with low mineral content (0.029 weight fraction of mineral) are lower than those that are seen for mineralized tendons (mineral content about 0.3). 

FIGURE43.6 A typical stress-strain curve for tendon [Rigby et al., 1959],... 

Elastic and viscous stress-strain curves can be experimentally determined from incremental stress-strain curves measured on samples of different tendons. Typical elastic and viscous stress-strain curves for rat tail and turkey tendons are shown in Figures 7.4 and 7.5. For both types of tendons the curves at high strains are approximately linear. As we discuss in Chapter 8, the elastic modulus can be calculated for collagen, because most of the tendon is composed of collagen and water, by dividing the elastic slope by the collagen content of tendon. When this is done the value of the elastic modulus of collagen in tendon is somewhere between 7 and 9 GPA. 

Figure 7.4. Total, elastic, and viscous stress-strain curves for collagen fibers from rat tail tendon. The total stress-strain curve (open boxes) was obtained by collecting all the initial, instantaneous, force measurements at increasing time intervals and then dividing by the initial cross-sectional area. The elastic stress-strain curve (closed diamonds) was obtained by collecting all the force measurements at equilibrium and then dividing by the initial cross-sectional area. The viscous component curve (closed squares) was obtained as the difference between the total and the elastic stresses. Error bars represent one standard deviation of the mean.

Figure 7.5. Representative total elastic and viscous stress-strain curves for unmineralized and mineralized avian tendons. The curves show the total, elastic, and viscous stress-strain relations for gastrocnemius tendon segments proximal to the bifurcation point, B, in Figure 3.29 for animals after (A) and prior to (B), the onset of mineralization. Note the different scales in A and B and the increased slope of the elastic stress-strain curve and decreased strain to failure for mineralized (A) compared to unmineralized (B) tendons.

Figure 7.6. Effective mechanical fibril length versus fibril segment length. Plot of effective fibril length in pm determined from viscous stress-strain curves for rat tail tendon and self-assembled collagen fibers versus fibril segment length. The correlation coefficient (R2) for the line shown is 0.944 (see Silver et al., 2003).

At low mineral content, the elastic stress-strain curve for turkey tendons has a very long, low modulus region and, as the mineral content increases, the low modulus region is replaced with an almost linear relationship between elastic stress and strain. The slope of the elastic stress-strain curve increases with mineral content and approaches 8GPa. 

Mechanical models of mineralized tendons follow from the analyses done for tendon. The elastic moduli of mineralized turkey tendons have been calculated from the experimental elastic incremental stress-strain curves. For mineralized tendons the stress-strain curves are linear at mineral content of about 0.3 and the elastic modulus is about 8GPa and increases with... 

From the viscous stress-strain curve using Equations (4.1), (4.2), and (8.2) we can calculate the collagen fibril length. The collagen fibril lengths in tendon range from about 20 pm for during tendon development to in excess... 

When the uncrosslinked self-assembled collagen fibers tested above were crosslinked by removal of water (dehydration) the resulting incremental stress-strain curves approached those observed for tendons (see Figure... 

In vivo measurements suggest, at least in vessel wall and perhaps tendon, that under normal conditions ECMs operate in the beginning of the high strain region of the stress-strain curve, therefore we can use the stress obtained in this manner to estimate the unloaded stress on a tissue. The unloaded elastic stress can then be corrected for the applied external elastic loading and the cellular stress can be estimated knowing the tissue... 

The tensile stress-strain curve of frame silk is shown in Fig. 3.7. The curves for a number of different materials, steel, cellulose, tendon, are also included for comparison. Note the high fracture energy (area under the stress-strain curve) of the frame silk fiber. The strain to failure of frame silk can be as high as 30%. 

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