Study of convergence by finite element analysis in cortical bone tissue

Abstract

In recent decades research has been published on bone simulations in which the finite element method is used to estimate the mechanical properties or behavior of the tissue before certain loads. In all these investigations it is essential to know with the greatest possible accuracy the mechanical behavior of this biological material. This research analyzed the convergence of numerical results obtained from simulations of digital bone structures using the finite element method, in order to provide an efficient methodology. Bovine cortical tissue specimens were constructed, which were performed computed tomography for the generation of geometry and the assignment of mechanical properties. Simulations were developed varying the size of the mesh in order to describe the convergence by stress, load and strain energy versus number of elements. The convergence of the tensile simulations behave independently of the properties assigned as isotropic or orthotropic material. Compression simulations of complete structures with medullary channel and the use of hexahedral elements in cubic samples, significantly reduced the number of elements required to achieve convergence, compared to the use of complete structures without medullary channel and the use of tetrahedral elements in cubic samples, respectively. The convergence of the different bone models is slower by stress and deformation energy versus number of elements. We suggest an efficient methodology for the simulation of computational bone structures using the finite element method to obtain reliable results.