In figures 4 through 6 we plot the invariants as a function of pressure for sample 2. Also, in these figures we plot the variation of these invariants as determined using three different sets of five markers. The configuration of the markers is given in figure 2. If the deformation is axially symmetric and does not vary along the axis, then the value of the invariants would not depend on the choice of markers used to estimate them. However, it is clear from the figures 4 through 6 that the value of the invariants depends upon the choice of markers. Here it is pertinent to observe that the error in the estimated invariants is ±0.02 as is evident from figure 8. This error in the estimated invariants is arrived at by translating a balloon along the horizontal direction as a rigid body and computing the invariants for this motion. Ideally, the invariant I1 C and I 2 C should be 3 nd I C should be 1. Deviation from this value is deemed as error in the estimated invariants. f this happens then the vein should be heterogeneous and/or sidually stressed in the axial and/or circumferential direction. a 3 The observation that the invariants of the Cauchy-Green deformation tensor are not a constant on the surface of the vein is significant for the following reason. Saravanan [8] showed that i re Figure 8: Plot of invariants (a) I1 C – 3 (b) I 2 C – s a rubber balloon is translated as a rigid body horizontally along its axis region occupied between the markers used to estimate the deformation field and ot the overall volume change in the vein. clic loading or an anisotropic viscoelastic aterial with differing viscoelastic properties along the radial and axial directions. 3 (c) I3 C – 1 vs. axial load a It can be seen from figure 6 that I3 C is not 1, as it should be if the vein is incompressible. Thus, we conclude that the vein is compressible. It should be noted that we are checking the compressibility of a small chunk of the solid material that constitute the wall of the vein, namely the n From the figures 4 through 6 and figure 9 it is evident that the loading and unloading paths are not different in the GSV. However, if we look at figure 7, where the axial load required for maintaining the vein at constant length while inflating and deflating is plotted, we find that the axial load required for maintaining the axial length decreases with increasing number of cycles of inflating and deflating pressure. Moreover, this being a displacement controlled set up when the vein is brought back to its original length after eight cycles of pressurization, the axial load becomes negative (see figure 7b and 7c). These suggest the artery has stress relaxed along the axial direction, a viscoelastic phenomenon. Hence, it appears that the vein is a special kind of viscoelastic material that stress relaxes but does not dissipate in cy m Figure 9: Plot of invariants (a) I1 C – 3 (b) I 2 C – 3 (c) I 3 C – 1 vs. inflation pressure for sample 1 her lood vessels [2], the axial load increases with increasing pressure for all stretch ratios at which the vein is held fixed. Figure 4 through 6 also capture the variation in the invariants with increasing axial stretch ratio. Here we find that as the axial stretch ratio increases, the value of I1 C decreases, that of I 2 C increases and I 3 C decreases. However, unlike some of the ot b 84
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