Determination of the bones stress-strain state by the computer tomography data

Abstract

Numerical simulation of the inhomogeneous medium elements appears to be one of the current trends in the continuum mechanics. Approaches based on combined application of the non-destructive testing and numerical simulation methods were significantly developed. The paper proposes a technique for numerical simulation of the porous structure elements based on their computer tomography. Calculations were carried out by the finite element method using the eight-node isoparametric finite element of the continuous medium with linear approximation of the geometric parameters and the displacement field. Stiffness matrix of each finite element was integrated by using the weight function; its values corresponded to the material permeability in the current microelement volume. A static calculation technique for the porous structure elements is described based on the material spatial distribution. Simulation was carried out on the example of samples of the pygmy pigs bone organs. The tests corresponded to a three-point bend. Computational grids were constructed by filtering at the threshold value that set fraction of the elastic material content in the volume. Numerical calculations made it possible to determine the displacement field and the stress-strain state. Data reliability was established on the basis of the energy distribution error over the voltages. Results were validated according to the full-scale experiment data. The relative error was of 3...10%; therefore, simulation described the sample mechanical destruction with sufficient degree of reliability. The proposed technique demonstrated its efficiency in solving the problem of describing behavior of the inhomogeneous media elements exposed to the external loads both due to high performance at the numerical model construction stage, and due to excluding the need to accurately restore the sample computational domain.