Size effects in the elasticity and viscoelasticity of bone

 Size effects of large magnitude are observed in the torsional shear modulus and damping of bovine plexiform bone. Damping increases and stiffness decreases with specimen size over all sizes studied. Measurements were conducted in torsion using a laser-based micromechanics apparatus capable of viscoelastic studies over a range of frequencies up to 100 kHz, upon samples of various size, with no parasitic friction or other errors that could mimic any size effect. Torsional tan δ at 1 Hz varies by about a factor of five over the size range 2.8–6.2 mm thick, and is more dependent on specimen thickness at 1 Hz than it is at higher frequency. The size effects are attributed to compliance and viscoelasticity of the interfaces between laminae. These laminae must be substantially stiffer than whole bone. Observed size effects are likely to play a role in understanding scaling laws of bones in living organisms. Received: 12 February 2002 / Accepted: 22 November 2002 R.S. Lakes is also at the Department of Biomedical Engineering, Department of Engineering Physics, Materials Science Program and Rheology Research Center all at the University of Wisconsin. We thank the Whitaker foundation for their support of this work.