# Mechanics

## Investigation of surface roughness at micro-scale and mechanical response in the contemporary bio-polimer sutures by the nanoindentation

An investigation of properties of contemporary suture materials (surgical threads) is the state-of-art challenge in biomechanics. To improve an effectiveness of sutures application, an analysis of structure and elastic properties by the atomic force microscopy and scanning electron microscopy is necessary to be performed.

## Covariant field equations and d-tensors of hyperbolic thermoelastic continuum with fine microstructure

A non-linear mathematical model of hyperbolic thermoelastic continuum with fine microstructure is proposed. The model is described in terms of 4-covariant field theoretical formalism. Fine microstructure is represented by d-tensors, playing role of extra field variables. A Lagrangian density for hyperbolic thermoelastic continuum with fine microstructure is given and the corresponding least action principle is formulated. 4-covariant field equations of hyperbolic thermoelasticity are obtained.

## Modeling of the shock system motion with impacts about hard barriers

Abstract: We have developed a model of a shock system with a resilient member under periodic force action including impacts about hard barriers. In order to model the shock system we have developed a program providing a computational solution for differential equations of a subject motion taking into account conditions of periodicity and collision, graphical and numerical reproduction of motion parameters in the simulation process. We have performed simulation of modes of the shock system.

## The equilibrium equations of shells in the coordinates of the general form

A mathematical model of homogeneous elastic shells is consider under kinematics Reissner–Mindlin type. Through direct (coordinateless) methods of the tensor calculus equations of equilibrium are obtained in terms of displacements in an arbitrary (not necessarily orthogonal) coordinate system, taking into account the asymmetry of the location of the front surface.

## The asymptotic separation of variables in thermoelastic problem for anisotropic layer with inhomogeneous boundary conditions

A method for resolving a thermoelasticity problem with inhomogeneous boundary conditions is presented. Boundary conditions represent uneven surface heating of the layer. An asymptotic procedure for separation of variables based on introduction of additional dimensional scales is used. With an additional assumption that the unevenness of the heating is small enough this procedure makes it possible to obtain the solution. The method is shown for periodic heating case. After the separation of variables the solution is obtained using Fourier series.

## Calculation plainly loaded geometrically nonlinear designs on the basis of mixed FEM with tenzorno-vector approximation requires sizes

The algorithm of reception on a step of loading designs matrixes of deformation of a volume final element with cross-section section in the form of any quadrangle with central unknown persons in the form of increments of movings and increments of deformations is stated in mixed formulation FEM. For numerical realization of algorithm it is used functional, received of a condition of equality of possible and valid works of external and internal forces on a step loading.

## 3-dimentional mathematical model of blood flow with secondary heart theory

This paper presents haemodynamics of blood vessels mathematical model. There is 3-dimentional system of equations describes blood flow, where vessel motions are taking in account.

## Determination of elastic characteristics of polymeric covers by results of tests of flat specimens at tension and bending

The results of experimental identification of elastic modulus and Poisson's ratio of thin polymeric covers on the surface of the flat specimens of steel 08-OP are presented. The values of elastic modulus were determined with the rule of the mixtures by the standard tests of the specimens with the covers at the tension and four-point bending. The values of the Poisson's ratio were obtained on the base of the comparison of the tests results and the computer modeling of the bending process the studied specimens.

## Thermomechanical orthogonality in nonlinear type-III thermoelasticity (GNIII)

The present paper is devoted to formulations of constitutive equations for the non-linear Green–Naghdi type-III thermoelastic continuum consistent with the principle of thermodynamic (or thermomechanical) orthogonality.

## Research of consequences of tether's jamming in the task of payload delivery from an orbit

In article the off-normal situation of tether's jamming at the decision of the task of payload delivery from an orbit by means of a tether is considered. The mathematical model described the space tether system consisting of the basic space vehicle, the tether and the payload is used. At creation of model the mass and damping properties of the tether weren't considered. It is supposed that basic space vehicle moves on a circle orbit.