Differences in the mechanical behavior of cortical bone between compression and tension when subjected to progressive loading

Abstract

The hierarchical arrangement of collagen and mineral into bone tissue presumably maximizes fracture resistance with respect to the predominant strain mode in bone. Thus, the ability of cortical bone to dissipate energy may differ between compression and tension for the same anatomical site. To test this notion, we subjected bone specimens from the anterior quadrant of human cadaveric tibiae to a progressive loading scheme in either uniaxial tension or uniaxial compression. One tension (dog-bone shape) and one compression specimen (cylindrical shape) were collected each from tibiae of nine middle aged male donors. At each cycle of loading-dwell-unloading-dwell-reloading, we calculated maximum stress, permanent strain, modulus, stress relaxation, time constant, and three pathways of energy dissipation for both loading modes. In doing so, we found that bone dissipated greater energy through the mechanisms of permanent and viscoelastic deformation in compression than in tension. On the other hand, however, bone dissipated greater energy through the release of surface energy in tension than in compression. Moreover, differences in the plastic and viscoelastic properties after yielding were not reflected in the evolution of modulus loss (an indicator of damage accumulation), which was similar for both loading modes. A possible explanation is that differences in damage morphology between the two loading modes may favor the plastic and viscoelastic energy dissipation in compression, but facilitate the surface energy release in tension. Such detailed information about failure mechanisms of bone at the tissue-level would help explain the underlying causes of bone fractures.

Figure 1

Whether in the compression or tension mode, the cortical bone specimen was subjected to multiple cycles of loading-dwell-unloading-dwell-reloading. The last cycle before failure is only shown here to provide greater clearity in how we calculated the mechanical properties.

Figure 2

The maximum stress of each cycle is plotted against the maximum strain of each cycle. The relationships were similar to that obtained by a monotomic test with bone being stronger in compression than in tension.

Figure 3

Permanent or plastic strain is the amount of unrecoverable deformation after unloading and a period of rest. When plotted against the maximum strain of the cycle, this strain departed from zero at the defined yeild point. Although this departure occurred at a higher yield strain in compression than in tension, the permanent strain generated in compression exceeded that in tension at post-yield strains.

Figure 4

The energy dissipated by plastic deformation linearly increased after yielding as the strain increased with each successive cylce of loading. This pathway of toughness was greater for compression than for tension.

Figure 5

With each cycle of prgoressive loading, the modulus of cortical bone decreased for both modes of loading in a similar fashion. The rate of change with respective to the strain of the cycle was greater through yielding but slowed through the post-yield strains.

Figure 6

The degree to which bone relaxed is plotted against the strain during the dwell period (i.e., maximum strain of each cycle). As damage was introduced into the bone at increasing strains, stress relaxation increased in both modes but reached maximum after yielding. Bone sustained greater stress relaxation in compression than in tension.

Figure 7

The time constant for the period of stress relaxation is plotted against the constant strain of that period for each cycle. For both modes of loading, the rate change in stress to reach equalibrium dropped as the strain increased with each cycle. It remained at a nearly constant value in the post-yield region.

Figure 8

With increasing strain as the cycles progressed, the bone dissipated increasing hysteresis energy in both modes of loading.

Figure 9

Bone dissipated more elastic release energy in tension than in compression as the strain on the bone increased with each cycle.