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The small dark circles in the human bone are cross sections of Haversian canals. The large circles are cross sections of osteons, which are large fibers about 200 microns across. Bovine plexiform has a laminated structure. Bone has a hierarchical structure in which each structural element itself contains structure.
An interrelation between creep and relaxation is therefore developed for ligament viscoelasticity based on a single-integral nonlinear superposition model. This interrelation differs from the convolution relation obtained by Laplace transforms for linear materials. We demonstrate via continuum concepts of nonlinear viscoelasticity that such a difference in rate between creep and relaxation phenomenologically occurs when the nonlinearity is of a strain-stiffening type, i.e. the stress-strain curve is concave up as observed in ligament. We also show that it is inconsistent to assume a Fung-type constitutive law (Fung, 1972) for both creep and relaxation in ligament viscoelasticity. Using published data of Thornton, et al., the nonlinear interrelation developed herein predicts creep behavior from relaxation data well (R greater than 0.998). Although data are limited and the causal mechanisms associated with viscoelastic tissue behavior are complex, continuum concepts demonstrated here appear capable of interrelating creep and relaxation with fidelity. The image shows ligament structure, after Vanderby.
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The overall hypotheses of this research are that:
The mechanical properties of earlywood compared to latewood are dramatically different in loblolly pine plantation wood.|
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