title: Quantification of nonlinear elasticity for the evaluation of submillimeter crack length in cortical bone.
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 αf and αQ, and Young׳s modulus Eus 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 αf, measured on the intact specimens, were remarkably similar for all the specimens (αf =-5.5±1.5). After crack propagation, the nonlinear elastic coefficient αf increased significantly (p<0.006), with values ranging from -4.0 to -296.7. Conversely, no significant variation was observed for αQ and Eus. 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 αf was found to be significantly 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.
authors.affiliation: Sorbonne Universités, Université Pierre et Marie Curie, CNRS UMR7371 & INSERM U1146, Laboratoire d'Imagerie Biomédicale, Paris FR-75006, France. Electronic address: sylvain.haupert@upmc.fr.
authors.forename: Sylvain
authors.initials: S
authors.lastname: Haupert
authors.affiliation: Arts et Métiers ParisTech, LBM, 151 Boulevard de l'Hôpital, Paris, France.
authors.forename: Sandra
authors.initials: S
authors.lastname: Guérard
authors.affiliation: Université de Lyon, F-69622 Lyon, France; Université Claude Bernard Lyon 1, Villeurbanne, France; IFSTTAR, UMR_T9406, LBMC Laboratoire de Biomécanique et Mécanique des Chocs, F69675 Bron, France.
authors.forename: David
authors.initials: D
authors.lastname: Mitton
authors.affiliation: CREATIS, CNRS UMR 5220, Inserm, U1044, Université de Lyon; Université Lyon 1, INSA-Lyon; 69621, Villeurbanne, France; European Synchrotron Radiation Facility, X-Ray Imaging Group, 38043 Grenoble, France; Université Lyon I, Lyon, France; ESRF, Grenoble, France.
authors.forename: Françoise
authors.initials: F
authors.lastname: Peyrin
authors.affiliation: Sorbonne Universités, Université Pierre et Marie Curie, CNRS UMR7371 & INSERM U1146, Laboratoire d'Imagerie Biomédicale, Paris FR-75006, France.
authors.forename: Pascal
authors.initials: P
authors.lastname: Laugier
mesh_terms: D000368:Aged; D000369:Aged, 80 and over; D001842:Bone and Bones / Q000502:physiology*; D004548:Elasticity; D006801:Humans; D008954:Models, Biological; D013314:Stress, Mechanical
keywords: Cortical bone; Crack; Damage; Elasticity; Nonlinear acoustics; Nonlinear resonant ultrasound spectroscopy; Synchrotron radiation micro-computed tomography