Strain rate, cortical bone

The stress-strain curves for cortical bones at various strain rates are shown in Figure 5.130. The mechanical behavior is as expected from a composite of linear elastic ceramic reinforcement (HA) and a compliant, ductile polymer matrix (collagen). In fact, the tensile modulus values for bone can be modeled to within a factor of two by a rule-of-mixtures calculation on the basis of a 0.5 volume fraction HA-reinforced... 

Figure 5.130 Stress-strain curves at various strain rates for cortical bone. Reprinted, by permission, from F. H. Silver and D. L. Christiansen, Biomaterials Science and Biocompatibility, p. 208. Copyright 1999 by Springer-Verlag.

There are two basic structural types of bone cancellous (trabecular, spongy) and cortical (dense) bones. Cancellous bone matter is less dense than that of cortical bone and is found across the ends of the long bones. Owing to its lower density, cancellous bone has also a much lower modulus of elasticity but higher strain-to-failure rate compared to cortical bone (Table 3.1). Bone has higher moduli of elasticity than soft connective tissues, such as tendons and ligaments. The difference in stiffness (elastic modulus) between the various types of connective tissues ensures a smooth gradient in mechanical stress across a bone, between bones and between muscles and bones (Hench, 2014). 

Although bone is a viscoelastic material, at the quasi-static strain rates in mechanical testing and even at the ultrasonic frequencies used experimentally, it is a reasonable first approximation to model cortical bone as an anisotropic, linear elastic solid with Hooke s law as the appropriate constitutive equation. Tensor notation for the equation is written as ... 

Aging also affects the mechanical properties of cortical bone. Tensile ultimate stress decreases at a rate of approximately 2 percent per decade (Fig. 8.7a). Perhaps most important, tensile ultimate strain decreases by about 10 percent of its young value per decade, from a high of almost 5 percent... 

FIGURE 8.7 Reductions of human cortical bone mechanical properties with age. (a) Modulus is not reduced much, if at all, whereas strength is reduced more, at a rate of about 2 percent per decade. (From Ref. 25.) (b) Ultimate strain decreases markedly with age, at a rate of about 10 percent of its young value per decade. (From Ref. 10.)... 

In this paper we use a mechanical model to study the behavior the interstitial flows in cortical bone tissues under cyclic loading. The proposed model allows investigating the influence of different factors like strain rate, load s frequency, permeability and possibly presence of a microcrack on the interstitial fluid velocity which strictly related to shear stress acting on osteon cells. 

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