Phase Field Methods: Application to Bone Remodeling
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Bone remodeling is a dynamic biological process characterized by the ongoing formation of new bone tissue and removal of old bone tissue from skeletal structure. Bone element undergoes continuous deformation due to internal stresses, resulting in the continuous change in its shape. This process mainly comprised of three subprocesses i.e. the evaluation of bone homeostasis, mechanotransduction which is the response of Osteocytes signaling molecules on application of loads and the surface propagation which is ultimately responsible for the change in the shape of bone. In this paper, we are addressing the problem of bone remodeling with the help of the Phase Field Methods. Due to the complexity of the geometry of bone structures, the phase field method can be a very useful mathematical tool as it defines the entire computational domain as a continuous scalar field on a simple box-like domain. Phase field can capture the evolving state of the bone such as the presence of different phases, interfaces, in a continuous and computationally efficient manner. For this study we consider a two-phase model and linear elasticity constitutive model. Simulations are carried out by utilizing a in-house the finite element code (ICItech), incorporating a monolithic adaptive finite element solver. To validate the results, we considered the simple geometries (Ex.Cylindrical shape) of the bone. The scalability of the code is assessed by conducting simulations on 3D shapes on an HPC cluster environment.