title: Computational simulation of the bone remodeling using the finite element method: an elastic-damage theory for small displacements.
abstract: BACKGROUND
  The resistance of the bone against damage by repairing itself and adapting to environmental conditions is its most important property. These adaptive changes are regulated by physiological process commonly called the bone remodeling. Better understanding this process requires that we apply the theory of elastic-damage under the hypothesis of small displacements to a bone structure and see its mechanical behavior.
  
  
  RESULTS
  The purpose of the present study is to simulate a two dimensional model of a proximal femur by taking into consideration elastic-damage and mechanical stimulus. Here, we present a mathematical model based on a system of nonlinear ordinary differential equations and we develop the variational formulation for the mechanical problem. Then, we implement our mathematical model into the finite element method algorithm to investigate the effect of the damage.
  
  
  CONCLUSIONS
  The results are consistent with the existing literature which shows that the bone stiffness drops in damaged bone structure under mechanical loading.
authors.affiliation: Laboratory of Applied Mathematics and Computer Science (LAMAI), Faculty of Sciences and Technics, Cadi Ayyad University, Abdelkrim El Khattabi Avenue, Marrakech, Morocco. a.idhammad@gmail.com
authors.forename: Ahmed
authors.initials: A
authors.lastname: Idhammad
authors.forename: Abdelmounaïm
authors.initials: A
authors.lastname: Abdali
authors.forename: Noureddine
authors.initials: N
authors.lastname: Alaa
mesh_terms: D016723:Bone Remodeling; D003198:Computer Simulation; D004548:Elasticity; D020342:Finite Element Analysis