Construction and analysis of finite-element models of inhomogeneous deformable solids based on scanning

The paper presents a set of mathematical methods and its computer implementation aimed at studying the real change in mechanical characteristics (elastic modulus) and the geometry of deformable solids based on scanning. Later these data will be used in constructing the finite element (FE) models and analyzing the stress-strain state (SSS). The presented research is important for deformable solids of complex (individual) geometric shapes and pronounced properties of inhomogeneity of the material mechanical characteristics. The scanning of the deformable solids is carried out by a computer tomography (CT). As a result of this work we prepared a package of raster images of sections of the investigated body. The further stage of the investigation is determined by analyzing the pixel color characteristics of the resulting raster images for the construction of an individual geometry of deformable solids and the distribution of mechanical characteristics in it. The contour of the external geometry and geometry of the internal structure of deformable solids in the cross-section is constructed based on two stages. The first stage is the preliminary one; and is necessary for the determination in the sections of the domain, both of the body itself and of the regions in it with pronounced changes in the mechanical characteristics. At the second stage, the geometry of the contours is refined, formed based on the method of studying the gradients of the change in the pixel color indices. The determination of the field of the change in mechanical characteristics is carried out by calculating the weight coefficients obtained on the basis of two parameters: the mathematical expectation of a change in the pixel color index in the package of sections of deformable solids; as well as the results of a full-scale test on the tensile (compression) of standard samples, that is, the averaged data on the mechanical properties of the material of deformable solids. We studied the deformable solids from bone tissue, in the form of a fragment of the femur, a human tooth in the jaw and a tooth with a composite seal in the jaw. The presented choice of deformable solids is not principled, but is caused by the following circumstances: a high degree of heterogeneity of bone material and its geometry, as well as a high level of development of CT scanning technology in medicine and engineering. The analysis results of the SSS of the obtained FE models of real deformable solids, obtained taking into account the inhomogeneity of the mechanical characteristics of the material and the individuality of the geometry, allow us to reach a higher level realization of the mathematical finite element model with respect to the real object, and also prove efficiency and accuracy of the presented technology in real working conditions (design and manufacturing) of structures.