Chapter 19 Chapter 19 The Mechanical Behavior of Bone Copyright © 2013 Elsevier Inc. All rights reserved.

FIGURE 19.1 Schematic diagram of stress (σ = normal stress, T = shear stress) and strain (ε) on an object. 2

Copyright © 2013 Elsevier Inc. All rights reserved. FIGURE 19.2 Schematic diagram of a typical stress–strain curve. 3

Copyright © 2013 Elsevier Inc. All rights reserved. FIGURE 19.3 Schematic diagrams of the normal and shear stresses acting on a bone tissue specimen during the different strength-of-material approaches used for determining the biomechanical properties of bone. 4

Copyright © 2013 Elsevier Inc. All rights reserved. FIGURE 19.4 Schematic diagram of the three stages of fatigue life. Stage I is the time during which cracks initiate and accumulate, stage II illustrates the time during which the cracks grow, and stage III illustrates the time during which the cracks coalesce. a: crack length; N: number of cycles; K: stress intensity factor. 5

Copyright © 2013 Elsevier Inc. All rights reserved. FIGURE 19.5 Initiation and propagation toughness can be calculated from mechanical testing data of a precracked specimen. Initiation toughness calculations include the initiation load, while propagation toughness can be calculated using either the maximum or instability load. 6

Copyright © 2013 Elsevier Inc. All rights reserved. FIGURE 19.6 Schematic diagram of a single edge notch bend (SENB) test specimen. 7

Copyright © 2013 Elsevier Inc. All rights reserved. FIGURE 19.7 Schematic diagrams of a rising R-curve (left) and flat curve (right). 8

Copyright © 2013 Elsevier Inc. All rights reserved. FIGURE 19.8 Image of (left) a linear microcrack and (right) diffuse damage in cortical bone. Images are shown at 20× magnification. 9

Copyright © 2013 Elsevier Inc. All rights reserved. FIGURE 19.9 Fracture patterns in the diaphysis and associated loading conditions. Fractures are classified as A: transverse; B: oblique; c: spiral; d and E: butterfly. Source: reprinted from Morgan etal. (2008), with permission [132]. 10

Copyright © 2013 Elsevier Inc. All rights reserved. FIGURE Representative force–displacement curve for an isolated thoracic vertebra tested in axial compression. The stiffness and ultimate force, a measure of vertebral strength, are marked on the curve. Source: reprinted from Shore etal. (2012), with permission [140]. 11

Copyright © 2013 Elsevier Inc. All rights reserved. FIGURE The bending stiffness of a structure such as a long bone diaphysis is proportional to the areal moment of inertia. If the diaphyseal cross-section is circular, then the torsional stiffness is proportional to the polar moment of inertia; otherwise, this proportionality is only approximate. These moments of inertia quantify how the tissue is distributed with respect to the axis of bending (shown here as the dotted line on the diaphyseal cross-section) or the axis of torsion (the line that passes through point o and that is directed out of the plane of the figure). Source: reprinted from Morgan etal. (2008), with permission [132]. 12

Copyright © 2013 Elsevier Inc. All rights reserved. FIGURE Illustration of the influence of cross-sectional geometry on the structural strength of circular structures. A cylindrical diaphysical cross-section with bone tissue located closer to the diaphysical axis has lower bending and torsional stiffness than a cross-section with the same amount of bone tissue but with larger inner and outer diameters. Here, the bending and torsional rigidities of Bar c are twice that of Bar A due to its greater moment of inertia. Source: reprinted from Bouxsein etal. (2007), with permission [144]. 13

Copyright © 2013 Elsevier Inc. All rights reserved. FIGURE Age-related changes in distal radius. y: years. Source: reprinted from Orwoll (2009), with permission [196]. 14

Copyright © 2013 Elsevier Inc. All rights reserved. FIGURE Predicted age-related changes in the distal radius in women (left column) and men (right column): (A) bone volume to total volume ratio (BV/TV), (B) trabecular number (Tb.N), (c) trabecular thickness (Tb.Th), and (d) cortical porosity (ct.Po) at the distal radius. The solid line represents the fitted mean from the regression model, and the dashed lines represent the 95% confidence interval of the prediction. Source: reprinted from Macdonald etal. (2011), with permission [221]. 15