Multi-phonon scattering processes in one-dimensional anharmonic biological superlattices: Understanding the dissipation of mechanical waves in mineralized tissues

Pierre Yves Guerder, Alix C. Deymier-Black, Nichlas Z. Swinteck, Jér Ôme O. Vasseur, Olivier Bou-Matar, Krishna Muralidharan, Pierre A. Deymier

Research output: Contribution to journalArticle

3 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)24-32
Number of pages9
JournalJournal of the Mechanical Behavior of Biomedical Materials
StatePublished - Sep 2014



  • Biological mineralized tissue
  • Mechanical energy dissipation
  • Multiphonon scattering Hydroxyapatite/collagen
  • Superlattice

ASJC Scopus subject areas

  • Biomaterials
  • Biomedical Engineering
  • Mechanics of Materials

Cite this