Mechanical model of a heterogeneous continuum based on numerical-digital algorithm processing computer

Abstract

The paper considers one of the possible numerical approachs for describing mechanical behavior of heterogeneous media based on modelling of the structure using computed tomograghy data. The proposed approach allows us to model the mechanical behavior of a porous medium taking into account the structure properties. At the first stage of the study, sample is scanned by computed tomography, then the data is digitized and digital prototype is built. This prototype with corresponding weights is used in the forming the local stiffness matrices for finite element method. The integration of stiffness matrices carried out by the central rectangles method. The effect of tomographic data density on the convergence of the proposed numerical method was investigated. The results of solving a typical problem for the diaphysis of the femur are given. The obtained numerical results reflect the influence of the accuracy of approximation of the sample geometry, and also illustrate the dependence of the displacement field on the structure of the material.