Viscoelastic properties of bone as a function of water content.

Stress relaxation of bovine femur was investigated as a function of water content, phi. As found for bone and bone collagen [Sasaki et al. (1993) J. Biomech. 26, 1369-1376], all the relaxation curves measured were described by a linear combination of a Kohlrausch-Williams-Watts (KWW) function and a simple exponential decay (Debye) function: G(t)/Gi = A1 exp[- (t/tau 1)beta] + A2 exp(= t/tau 2), A1 + A2 = 1, 0 < or = beta < or = 1, where Gi is an initial value of the relaxation shear modulus G(t), A1 and A2 are portions of KWW and Debye relaxations, respectively, and tau 1 and tau 2 are relaxation times of respective relaxations. Shear modulus values in the relaxation described by the KWW function (KWW relaxation) depend remarkably on phi while those in Debye relaxation are almost constant for increasing phi. phi dependencies of A1, tau 1 and beta are explained by assuming that the elementary process for the KWW relaxation would be a rearranging process of local disorders in the collagen molecular array. The relaxation rate for the Debye relaxation (= 1/tau 2) decreases linearly with phi. This linear relation between tau 2-1 and phi was well described on the basis of the concept of non-elasticity of a solid by the nuclearion of microcracks at the area of stress concentration.

[1]  G. Toulouse,et al.  Random walks on fractal structures and percolation clusters , 1983 .

[2]  J W SMITH,et al.  Factors affecting the elasticity of bone. , 1959, Journal of anatomy.

[3]  J Klafter,et al.  On the relationship among three theories of relaxation in disordered systems. , 1986, Proceedings of the National Academy of Sciences of the United States of America.

[4]  K. Miyasaka,et al.  Effect of water on the mechanical properties of collagen films , 1973 .

[5]  M. Pineri,et al.  Water–collagen interactions: Calorimetric and mechanical experiments , 1978, Biopolymers.

[6]  N. Sasaki,et al.  Stress relaxation in native and EDTA-treated bone as a function of mineral content. , 1993, Journal of biomechanics.

[7]  E W Montroll,et al.  On the Williams-Watts function of dielectric relaxation. , 1984, Proceedings of the National Academy of Sciences of the United States of America.

[8]  J. Woodhead-Galloway,et al.  Modern theories of liquids and the diffuse equatorial X‐ray scattering from collagen , 1976 .

[9]  F. G. Evans,et al.  The mechanical properties of bone. , 1969, Artificial limbs.

[10]  M. Panjabi,et al.  Effects of freezing and freeze‐drying on the biomechanical properties of rat bone , 1984, Journal of orthopaedic research : official publication of the Orthopaedic Research Society.

[11]  H. Mook,et al.  Neutron diffraction studies of collagen in fully mineralized bone. , 1985, Journal of molecular biology.

[12]  C. Hirsch,et al.  Factors affecting the determination of the physical properties of femoral cortical bone. , 1966, Acta orthopaedica Scandinavica.

[13]  J. Crisp,et al.  An interdisciplinary approach to fracture and strength of solids , 1968 .

[14]  J. Currey,et al.  The effects of drying and re-wetting on some mechanical properties of cortical bone. , 1988, Journal of biomechanics.

[15]  R. Lakes,et al.  Viscoelastic properties of wet cortical bone--I. Torsional and biaxial studies. , 1979, Journal of biomechanics.

[16]  N. Sasaki,et al.  Stress relaxation function of bone and bone collagen. , 1993, Journal of biomechanics.

[17]  A. Hiltner,et al.  Interaction of water with native collagen , 1977, Biopolymers.

[18]  John D. Currey,et al.  Stress Concentrations in Bone , 1962 .

[19]  T. Yokobori.  Failure and Fracture of Metals as Nucleation Processes , 1952 .

[20]  John D. Currey,et al.  Anelasticity in Bone and Echinoderm Skeletons , 1965 .

[21]  N. Sasaki,et al.  X‐Ray diffraction studies on the structure of hydrated collagen , 1983, Biopolymers.

[22]  S. Alexander,et al.  Density of states on fractals : « fractons » , 1982 .