Mechanics

The paper analyzes the properties of the constitutive relations of the theory of plasticity for a continuum, which plastic properties depend on the type of stress state. The plasticity condition presented in the corresponding generalized form is used, where the parameter of the type of stress state is introduced, which is the ratio of the hydrostatic stress component to the equivalent von Mises stress, named in the literature the stress triaxiality.

Numerous studies have shown that morphological parameters of aneurysms are associated with their rupture. However, literature data on the values of these parameters vary significantly. The objective of this study is to identify image-based morphological parameter values which correlate with cerebral aneurysm rupture and can be used during preoperative planning to detect aneurysms prone to rupture. Mean values of the morphological factors such as aspect ratio and size ratio were chosen from the literature.

Two three-dimensional geometric solid-state models of the Th7-L1 spinal segment (Model 1, Model 2) with metal construction were built. Models include the vertebrae Th7, Th8, Th9, Th10, Th11, Th12, L1, intervertebral discs, facet joints and ligaments, and metal construction elements. In Model 1, the cortical and spongy layers are constructed by three-dimensional solids, facet joints and intervertebral discs by three-dimensional bodies, ligaments by one-dimensional objects.

The coefficient inverse problem of thermal conductivity about the determination of the thermophysical characteristics of the functional-gradient part of a two-component layer is posed. The input information is the temperature measurement data on the top face of the layer. After the Laplace transform and dimensioning, the direct problem of heat conduction is solved on the basis of Galerkin projection method. Conversion of transformant on the basis of the theory of residues is carried out.