# Mechanics

## On Wave Solutions of Dynamic Equations of Hemitropic Micropolar Thermoelasticity

Coupled equations of hemitropic thermoelastic micropolar continuum formulated in terms of displacement vector, microrotation vector and temperature increment are considered. Thermodiffusion mechanism of heat transport is assumed. Hemitropic thermoelastic constitutive constants are reduced to a minimal set retaining hemitropic constitutive behaviour. Coupled plane waves propagating in thermoelastic media are studied. Spatial polarizations of the coupled plane waves are determined. Bicubic equations for wavenumbers are obtained and then analyzed.

## Axisymmetric Stress Field Near a Circular Cut in a Solid with Stress State Dependent Plastic Properties

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.

## Theory of Vibrations of Carbon Nanotubes Like Flexible Micropolar Mesh Cylindrical Shells Taking into Account Shift

A theory of nonlinear dynamics of a flexible single-layer micropolar cylindrical shell of a network structure is constructed. The geometric nonlinearity is taken into account by the model of Theodor von Karman. We consider a nonclassical continuum shell model based on the Cosserat medium with constrained particle rotation (pseudocontinuum). It is assumed that the displacement and rotation fields are not independent. An additional independent material length parameter associated with the symmetric tensor of the rotation gradient is introduced into consideration.

## Threshold Values of Morphological Parameters Associated with Cerebral Aneurysm Rupture Risk

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.

## Influence of Residual Stresses on Geometric Parameters of Surface-Strengthened Beam

The сomprehensive study of the formation of residual stresses and plastic deformations in prismatic samples of the EP742 alloy after ultrasonic hardening and their influence on the geometric parameters of the beam was conducted. Phenomenological model for the reconstruction of residual stress fields is proposed, and the verification of its adequacy to experimental data with four hardening modes is performed. The correspondence of the calculated and experimental data is observed.

## Extracting Clinically Relevant Data from Biomechanical Modeling of Surgical Treatment Options for Spinal Injury in Damaged Vertebrae Th10, Th11

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.

## Creation of Three-Dimensional Solid-State Models of a Spine with Transpedicular Fixation Using a Specialized Software

Biomechanical experiments are widely used to study the mechanical characteristics of spinal elements under various types of loading. The correct construction of three-dimensional models is especially important for studying the behavior of the spine after surgery, for example, the installation of fixing metal structures. There are several approaches to modeling each anatomical component of the spinal column. It is generally accepted to construct vertebral bodies of a simulated spinal segment based on the results of computed tomography.

## On the Peculiarities of Solving the Coefficient Inverse Problem of Heat Conduction for a Two-Part Layer

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.

## Dynamic Stability of Heated Geometrically Irregular Shallow Shell of Constant Torsion in Supersonic Gas Flow

Heated until invariable temperature, geometrically irregular shallow shell of constant torsion blown by supersonic gas flow from one side of the main surfaces was considered. As the basis, a continual model of thermoelastic system “shell-ribs” was taken. Singular differential equations of dynamical thermostability of geometrically irregular shallow shell had summands containing “stretch-compression” and “shift’’ of the ribs.