Progressive post-yield behavior of human cortical bone in compression for middle-aged and elderly groups

Abstract

In this study, a progressive loading regimen (load-dwell-unloading-dwell-reloading) was applied on bone samples to examine the compressive post-yield response of bone at increasing strain levels. Cortical bone specimens from human tibiae of two age groups (middle-aged group: 53±2 years, 4 females and 4 males, elderly group: 83±6 years, 4 females and 4 males) were loaded in compression using the progressive loading scheme. Modulus degradation, plastic deformation, viscous response, and energy dissipation of bone during post-yield deformation were assessed. Although initial modulus was not significantly different between the two age groups, the degradation of modulus with the applied strain in the elderly group was faster than in the middleaged group. The modulus loss (or microdamage accumulation) of bone occurred prior to plastic deformation. Plastic strain had a similar linear relationship with the applied strain for both middleaged and the elderly group although middle-aged bone yielded at a greater strain. The viscoelastic time constant changed similarly with increasing strain for the two groups, whereas a higher magnitude of stress relaxation was observed in the middle-aged group. Energy dissipation was investigated through three pathways: elastic release strain energy, hysteresis energy, and plastic strain energy. The middle-aged group had significantly greater capacity of energy dissipation than the elderly group in all three pathways. The information obtained may provide important insights in age-related effects on bone fragility.

Progressive Post-Yield Behavior of Human Cortical Bone in Shear

“…At 3% of applied strain, the shear modulus degrades to about 56% of the initial shear modulus in this study, but the elastic modulus under tension [4] and compression modes [6] falls further to about 15% of the initial values. In addition, the damage sensitivity constant (m) of bone is much smaller (m = 19.6) in shear than in tension and compression (m = 64.3) for agematched human cortical bone specimens [6,7]. The above results imply that it is more difficult for microdamage to accumulate in bone specimens under shear load than under tension and compression load.…”

“…However, the slope of the linear relationship (0.53) is in between the values obtained in tension (0.45) and compression (0.61) tests [6,7]. Considering the cross-hatch damages in human cortical bone associated with the compression mode [21], it is presumable that shear failure is the major mode in compression tests.…”

“…The shear modulus of bone sustains about 82% of initial modulus at 1% of applied strain, whereas the elastic modulus of bone in tension [4] and compression tests [6] drops almost in half (50%) of the initial elastic modulus at the same strain level. At 3% of applied strain, the shear modulus degrades to about 56% of the initial shear modulus in this study, but the elastic modulus under tension [4] and compression modes [6] falls further to about 15% of the initial values. In addition, the damage sensitivity constant (m) of bone is much smaller (m = 19.6) in shear than in tension and compression (m = 64.3) for agematched human cortical bone specimens [6,7].…”

“…The applied strain (γ i ) at each cycle was defined as the strain at the beginning of stress relaxation. For ease of comparison, an exponential decay of shear modulus (G i ) was assumed with respect to applied shear strain (γ i ) during the progressive loading as seen in tension and compression tests [3,[5][6][7]. The following equation was used for curve fitting to express the relationship: (2) where, m could be used to estimate the sensitivity of bone to damage accumulation.…”

“…In previous studies, we have utilized a novel progressive loading protocol to study progressive changes in the post-yield behavior of human cortical bone in tension [3][4][5] and in compression [6,7]. It was observed that the post-yield behavior of human cortical bone exhibited similar trends in both tension and compression tests, showing an exponential decay of elastic modulus, quasi-linear increase in plastic deformation, and bimodal viscous responses with increasing applied strain.…”