External bone remodeling through boundary elements and damage mechanics

  • Authors:

  • Gabriela Martínez;José Manuel García Aznar;Manuel Doblaré;Miguel Cerrolaza

  • Affiliations:

  • Centro de Bioingeniería, Facultad de Ingeniería (U.C.V.), I.M.M.E. Ciudad Universitaria, U.C.V., Caracas, Venezuela;Grupo de Estructuras y Modelado de Materiales, Instituto de Ingeniería de Aragón, Universidad de Zaragoza, Spain;Grupo de Estructuras y Modelado de Materiales, Instituto de Ingeniería de Aragón, Universidad de Zaragoza, Spain;Centro de Bioingeniería, Facultad de Ingeniería (U.C.V.), I.M.M.E. Ciudad Universitaria, U.C.V., Caracas, Venezuela

  • Venue:
  • Mathematics and Computers in Simulation - Special issue: Applied and computational mathematics - selected papers of the fifth PanAmerican workshop - June 21-25, 2004, Tegucigalpa, Honduras
  • Year:
  • 2006

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Abstract

The most recent advances in external bone remodeling are shown using strain energy density (SED) and damage mechanics variables as stimulus functions. The Boundary Element Method (BEM) is used to obtain the tractions and displacements in each iteration.In this paper it is assumed that the level of damage and the strain energy near the periosteum and endosteum control the external bone remodeling response in the cortical of long bones. The boundary is modified as a function of time and the numerical analysis is solved through the method before mentioned for each variation of the boundary coordinates, then the geometry is evaluated and adapted. Smoothing techniques are used ([β-spline surfaces) to prevent sudden variations in the boundary that may hinder a solution convergence. To validate this model a numerical example is shown with previously validated experimental data from other authors.