BackgroundThe 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.ResultsThe 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.ConclusionThe results are consistent with the existing literature which shows that the bone stiffness drops in damaged bone structure under mechanical loading.

BackgroundBone tissue is the main element of the human skeleton and is a dynamic tissue that is continuously renewed by bone-resorbing osteoclasts and bone-forming osteoblasts.The bone is also capable of repairing itself and adapting its structure to changes in its load environment through the process of bone remodeling.Therefore, this phenomenon has been gaining increasing interest in the last years and many laws have been developed in order to simulate this process.ResultsIn this paper, we develop a new law of bone remodeling in the context of damaged elastic by applying the thermodynamic approach in the case of small perturbations.The model is solved numerically by a finite difference method in the one-dimensional bone structure of a n-unit elements model.ConclusionIn addition, several numerical simulations are presented that confirm the accuracy and effectiveness of the model.