Quantification of nonlinear elasticity for the evaluation of submillimeter crack length in cortical bone. (August 2015) - Haupert, Sylvain; Guérard, Sandra; Mitton, David; Peyrin, Françoise; Laugier, Pascal
Abstract: The objective of this study was to investigate the sensitivity of the nonlinear elastic properties of cortical bone to the presence of a single submillimetric crack. Nonlinear elasticity was measured by nonlinear resonant ultrasound spectroscopy (NRUS) in 14 human cortical bone specimens. The specimens were parallelepiped beams (50×2×2 mm 3 ). A central notch of 500 µm was made to control crack initiation and propagation during four-point bending. The nonlinear hysteretic elastic and dissipative parameters α f and α Q, and Young׳s modulus E us were measured in dry condition for undamaged (control) specimens and in dry and wet conditions for damaged specimens. The length of the crack was assessed using synchrotron radiation micro-computed tomography (SR-μCT) with a voxel size of 1.4 μm. The initial values of α f, measured on the intact specimens, were remarkably similar for all the specimens ( α f =−5.5±1.5). After crack propagation, the nonlinear elastic coefficient α f increased significantly ( p <0.006), with values ranging from −4.0 to –296.7. Conversely, no significant variation was observed for α Q and E us . A more pronounced nonlinear elastic behavior was observed in hydrated specimens compared to dry specimens ( p <0.001) after propagation of a single submillimetric crack. The nonlinear elastic parameter α f was found to be signi f icantly correlated to the crack length both in dry ( R =0.79, p <0.01) and wet ( R =0.84, p <0.005) conditions. Altogether these results show that nonlinear elasticity assessed by NRUS is sensitive to a single submillimetric crack induced mechanically and suggest that the humidity must be strictly controlled during measurements. Highlights: Nonlinear elasticity in cortical bone, measured by resonant ultrasound spectroscopy is sensitive to the presence of a single submillimetric crack. A significant correlation exists between the nonlinear elastic parameters and the length of the crack, while the elastic modulus remains unchanged after crack initiation and propagation. Nonlinear elastic behavior of cracked cortical bone depends on the degree of hydration.