title: Multi-phonon scattering processes in one-dimensional anharmonic biological superlattices: understanding the dissipation of mechanical waves in mineralized tissues.
abstract: The scattering of elastic waves in a one dimensional phononic (PnC) crystal composed of alternate collagen and hydroxy-apatite constituent layers is studied. These superlattices are metaphors for mineralized tissues present in bones and teeth. The collagen is treated as an open system elastic medium with water content which can vary depending on the level of stress applied. The open system nature of the collagen-water system leads to a non-linear stress-strain response. The finite difference time domain method is employed to investigate the propagation of non-linear mechanical waves through the superlattice. The spectral energy density method enables the calculation of the non-linear vibrational wave band structure. The non-linearity in the mechanical response of the collagen-water system enables a variety of multi-phonon scattering processes resulting in an increase in the number of channels for the dissipation of elastic waves and therefore for the dissipation of mechanical energy. These results provide an explanation for the relationship between bone fragility and decreased hydration.
authors.affiliation: Department of Materials Science and Engineering, University of Arizona, Tucson, AZ 85721, USA; International Associated Laboratory LEMAC: IEMN, UMR CNRS 8520, PRES Lille Nord de France, ECLille, 59652 Villeneuve d'Ascq, France. Electronic address: pierre-yves.guerder@centraliens-lille.org.
authors.forename: Pierre-Yves
authors.initials: PY
authors.lastname: Guerder
authors.affiliation: Department of Orthopaedic Surgery, Washington University in St. Louis, St. Louis, MO 63110, USA.
authors.forename: Alix C
authors.initials: AC
authors.lastname: Deymier-Black
authors.affiliation: Department of Materials Science and Engineering, University of Arizona, Tucson, AZ 85721, USA.
authors.forename: Nichlas Z
authors.initials: NZ
authors.lastname: Swinteck
authors.affiliation: Institut d'Electronique, de Microélectronique et de Nanotechnologie (IEMN, UMR CNRS 8520), PRES Lille Nord de France, 59652 Villeneuve d'Ascq, France.
authors.forename: Jérôme O
authors.initials: JO
authors.lastname: Vasseur
authors.affiliation: International Associated Laboratory LEMAC: IEMN, UMR CNRS 8520, PRES Lille Nord de France, ECLille, 59652 Villeneuve d'Ascq, France.
authors.forename: Olivier
authors.initials: O
authors.lastname: Bou-Matar
authors.affiliation: Department of Materials Science and Engineering, University of Arizona, Tucson, AZ 85721, USA.
authors.forename: Krishna
authors.initials: K
authors.lastname: Muralidharan
authors.affiliation: Department of Materials Science and Engineering, University of Arizona, Tucson, AZ 85721, USA.
authors.forename: Pierre A
authors.initials: PA
authors.lastname: Deymier
mesh_terms: D001696:Biomechanical Phenomena; D001842:Bone and Bones / Q000378:metabolism*; D003094:Collagen / Q000378:metabolism; D017886:Durapatite / Q000378:metabolism; D004548:Elasticity; D055595:Mechanical Phenomena; D008903:Minerals / Q000378:metabolism*; D008954:Models, Biological; D060739:Phonons; D013314:Stress, Mechanical; D013816:Thermodynamics; D013997:Time Factors; D014070:Tooth / Q000378:metabolism*; D014867:Water / Q000378:metabolism
chemical_list: D008903:Minerals; D014867:Water; D003094:Collagen; D017886:Durapatite
keywords: Biological mineralized tissue; Mechanical energy dissipation; Multiphonon scattering Hydroxyapatite/collagen; Superlattice