Biomechanics and Modeling in Mechanobiology

, Volume 4, Issue 2–3, pp 178–189 | Cite as

Nonlinear elastic-viscoplastic constitutive equations for aging facial tissues

  • E. Mazza
  • O. Papes
  • M. B. Rubin
  • S. R. Bodner
  • N. S. Binur
Original Paper


This paper reports on the initial stages of a project to simulate the nonlinear mechanical behavior of an aging human face. A cross-section of the facial structure is considered to consist of a multilayered composite of tissues with differing mechanical behavior. The constitutive properties of these tissues are incorporated into a finite element model of the three-dimensional facial geometry. Relatively short time (elastic-viscoplastic) behavior is governed by equations previously developed which are consistent with mechanical tests. The long time response is controlled by the aging elastic components of the tissues. An aging function is introduced which, in a simplified manner, captures the observed loss of stiffness of these aging elastic components due to the history of straining as well as other physiological and environmental influences. Calculations have been performed for 30 years of exposure to gravitational forces. Progressive gravimetric soft tissue descent is simulated, which is regarded as the main indication of facial aging. Results are presented for the deformations and stress distributions in the layers of the soft tissues.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • E. Mazza
    • 1
  • O. Papes
    • 1
  • M. B. Rubin
    • 2
  • S. R. Bodner
    • 2
  • N. S. Binur
    • 3
  1. 1.Institute of Mechanical Systems ETHZurichSwitzerland
  2. 2.Faculty of Mechanical EngineeringTechnion—Israel Institute of TechnologyHaifaIsrael
  3. 3.The Cosmetic Surgery Center of SE Texas Port ArthurTexasUSA

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