Analytical Solution of Stationary Coupled Thermoelasticity Problem for Inhomogeneous Structures

A mathematical statement for the coupled stationary thermoelasticity is given on the basis of a variational approach and the contact boundary problem is formulated to consider inhomogeneous materials. The structure of general representation of the solution from the set of the auxiliary potentials is established. The potentials are analyzed depending on the parameters of the model, taking into account the restrictions associated with additional requirements for the positive definiteness of the potential energy density for the coupled problem in the one-dimensional case. The novelty of this work lies in the fact that it attempts to take into account the effects of higher order coupling between the gradients of the temperature fields and the gradients of the deformation fields. From a mathematical point of view, this leads to a change in the roots of the characteristic equation and affects the structure of the solution. Contact boundary value problems are formulated for modeling inhomogeneous materials and a solution for a layered structure is constructed. The analysis of the influence of the model parameters on the structure of the solution is given. The features of the distribution of mechanical and thermal fields in the region of phase contact with a change in the parameters, which are characteristic only for gradient theories of coupled thermoelasticity and stationary thermal conductivity, are discussed. It is shown, for example, that taking into account the additional parameter of connectivity of gradient fields of deformations and temperatures predicts the appearance of rapidly changing temperature fields and significant localization of heat fluxes in the vicinity of phase contact in inhomogeneous materials.

Realistic Reference for Evaluation of Vehicle Safety Focusing on Pedestrian Head Protection Observed From Kinematic Reconstruction of Real-World Collisions

Head-to-vehicle contact boundary condition and criteria and corresponding thresholds of head injuries are crucial in evaluation of vehicle safety performance for pedestrian protection, which need a constantly updated understanding of pedestrian head kinematic response and injury risk in real-world collisions. Thus, the purpose of the current study is to investigate the characteristics of pedestrian head-to-vehicle contact boundary condition and pedestrian AIS3+ (Abbreviated Injury Scale) head injury risk as functions of kinematic-based criteria, including HIC (Head Injury Criterion), HIP (Head Impact Power), GAMBIT (Generalized Acceleration Model for Brain Injury Threshold), RIC (Rotational Injury Criterion), and BrIC (Brain Injury Criteria), in real-world collisions. To achieve this, 57 vehicle-to-pedestrian collision cases were employed, and a multi-body modeling approach was applied to reconstruct pedestrian kinematics in these real-world collisions. The results show that head-to-windscreen contacts are dominant in pedestrian collisions of the analysis sample and that head WAD (Wrap Around Distance) floats from 1.5 to 2.3 m, with a mean value of 1.84 m; 80% of cases have a head linear contact velocity below 45 km/h or an angular contact velocity less than 40 rad/s; pedestrian head linear contact velocity is on average 83 ± 23% of the vehicle impact velocity, while the head angular contact velocity (in rad/s) is on average 75 ± 25% of the vehicle impact velocity in km/h; 77% of cases have a head contact time in the range 50–140 ms, and negative and positive linear correlations are observed for the relationships between pedestrian head contact time and WAD/height ratio and vehicle impact velocity, respectively; 70% of cases have a head contact angle floating from 40° to 70°, with an average value of 53°; the pedestrian head contact angles on windscreens (average = 48°) are significantly lower than those on bonnets (average = 60°); the predicted thresholds of HIC, HIP, GAMBIT, RIC, BrIC2011, and BrIC2013 for a 50% probability of AIS3+ head injury risk are 1,300, 60 kW, 0.74, 1,470 × 104, 0.56, and 0.57, respectively. The findings of the current work could provide realistic reference for evaluation of vehicle safety performance focusing on pedestrian protection.

PHYSIC-CHEMICAL PROPERTIES OF TYPICAL CHERNOZEMS OF PRYDNISTERSK PODILLYA

This article analyzes the physic-chemical properties of typical chernozems. According to the methods, a laboratory study was performed. Physic-chemical parameters that are typodiagnostic for subfacial classification division of typical chernozems of the Prydnistersk Podillya are determined. Typical chernozems of the Prydnistersk Podillya are low-humus (2.78–3.98%). With depth, the humus content decreases by an average of 0.2% for every 10 cm, which indicates a uniformly accumulative type of distribution of organic matter in the profile of chernozems. In the same direction, humus reserves are declining. There is a spatial correlation between the humus content and the amount of physical clay in the fine soil. Humic acids predominate in the humus to a depth of 90–100 cm (Sgk: Sfk is 1.12–1.78). The general tendency of relative “fulvatization” of the arable layer as a result of its agrotechnical depletion is noticed. In relation to SGC to total organic C, chernozems of the study area are characterized by a high and very high degree of humification of organic matter. It is highest (62–70%) in the soils of the key section “Humentsi”, decreasing to 52–62% and 43–63% in the western direction. The humic acids of typical chernozems are dominated by calcium humates (GK-2). The largest number of them (29–35%) is concentrated on the contact boundary of humus and carbonate profiles. The convex nature of the distribution curves of the fraction of 2 humic acids and a sharp decrease in its content deeper than 100 cm, indicates their high migration capacity and the possibility of significant deposition of only a significant excess of calcium carbonates. The intensity of migration processes of the GK-2 fraction decreases in the direction of increasing the stiffness of hydrothermal conditions, due to the pulling of carboxylic acid salts closer to the soil surface, supersaturation of the solution with calcium bicarbonate, and as a consequence, increasing the total alkalinity in the humus horizon. The capacity of cation exchange (ECO) of typical chernozems is quite high (29–32 mmol-eq / 100 g of soil) with the dominance of calcium and magnesium cations in the composition of the soil-absorbing complex (GVC). There is a general tendency to increase these indicators in chernozems with low values ​​of SCC of the territory. The pH of the aqueous extract of typical chernozems of the Prydnistersk Podillya increases with depth from weakly acidic in the arable horizon to weakly and medium-alkaline within the carbonate profile. The reasons for such changes in the increase with the depth of the concentration of Ca2 + bicarbonates, which in their dissociation leads to an increase in the amount of hydroxyl ion and increase the alkalinity of the soil. The carbonate profile of typical chernozems is dominated by migratory forms of carbonate neoplasms - mold, carbonate plaque, veins. The vertical curve of carbonate content has an eluvial-illuvial type of profile structure. The content and reserves of carbonates in the 1.5-meter layer of typical chernozems increase from the west (434–714 t / ha) to the east (979–1847 t / ha). Key words: physic-chemical properties, typical chernozems, humic horizon, humic acids, carbonate profile.

Seiberg–Witten Floer Homotopy Contact Invariant

We introduce a Floer homotopy version of the contact invariant introduced by Kronheimer–Mrowka–Ozsváth–Szabó. Moreover, we prove a gluing formula relating our invariant with the first author’s Bauer–Furuta type invariant, which refines Kronheimer–Mrowka’s invariant for 4-manifolds with contact boundary. As an application, we give a constraint for a certain class of symplectic fillings using equivariant KO-cohomology.

Numerical analysis of shear interaction of an underground structure with soil

A soil layer behaviour under the shear interaction of an underground structure with soil is studied. Structural failure is considered under conditions of strained soil, and complete cohesion is assumed at the underground structure-soil contact boundary. The Finite Difference Method is used to numerically investigate the process of the structure-soil shear interaction under consideration. The main attention is paid to the adequacy of the conditions of soil-structure interaction, and to the strain state of the near-contact soil layer around the underground structure. The results are plotted and analysed. From the results obtained, the existence of a near-contact soil layer is shown; the use of the condition of complete cohesion is justified considering the structural failure of soil under conditions of complex interaction; the possibility to determine the thickness of the near-contact soil layer and of the layers with the respective degrees of structural failure is shown.

NONLINEAR PROBLEM OF FRACTURE MECHANICS OF AN INTERFACE CRACK SUBJECTED TO SHEAR WAVE

Solution for the problem for an interface crack under the action of a harmonic shear wave in normal direction is presented. The contact of the crack faces is put into consideration. The problem is solved by the boundary integral equations method, the vector components in the boundary integral equations are presented by Fourier series. The unilateral Signorini boundary conditions are involved to prevent the interpenetration of the crack faces and the emergence of tensile forces in the contact zone. Amonton-Coulomb Friction Law included allows to put into consideration relative resting of the crack opposite faces or their relative motion when one crack face is slipping or sliding across another face. The contact boundary restrictions are implemented using the iterative correction algorithm. The mathematical model adequacy is checked by comparing with classical model solution for statics problems that takes into account the crack faces contact. Numerical researches of friction influence on the displacement and contact forces distribution, size of contact zone are carried out. Influence of the faces contact and value of the friction coefficient on the distribution of stress intensity coefficients of normal rupture and transverse shear, which are the parameters of the biomaterial fracture, are presented and analyzed. It is shown that the nature of change in the distribution of the stress intensity coefficients for the conditions of tensile and shear waves is fundamentally different. It is concluded that it is possible to extend the approach proposed to the problems of three-dimensional fracture mechanics for composites with interfacial cracks at arbitrary dynamic loading.

Surface Phenomena at the Interface between Silicon Carbide and Iron Alloy

The paper discusses a potential composite produced using the casting method, where the matrix is gray cast iron with flake graphite. The reinforcement is provided by granular carborundum (β-SiC). The article presents model studies aimed at identifying the phenomena at the contact boundary resulting from the interaction of the liquid matrix with solid reinforcement particles. The scope of the research included, primarily, the metallographic analysis of the microstructure of the resulting composite, carried out by using light (LOM) and scanning electron (SEM) microscopy with energy dispersive X-ray spectroscopy (EDS) analysis. The occurrence of metallic phases in the boundary zone was indicated, the contents and morphology of which can be optimized in order to achieve favorable functional properties, mainly the tribological properties of the composite. In addition, the results obtained confirm the possibility of producing similar composites based on selected iron alloys.

The strength of the communication elements of pneumatic tires as composite material

The mechanical properties at the boundary of the distribution of the rubber matrix and metal and fabric fibrous materials as a separate area in the mechanism of crack inhibition and its effect on the durability of pneumatic tires during the accumulation of damage during operation are considered. Experimental studies on the stratification of the elements of the composition of the tire material in samples made from different parts of the car tire. The strength at the contact boundary "rubber matrix-fibers of metal cord" and between the fibers of the cord, which allows to assess the total strength of the tire material as a composition of reinforcing elements and the matrix in the accumulation of damage created during operation, artificial the nature and behavior of the rupture of the samples during the tests, the morphology of fracture on the surface of the interaction of the reinforcing fibers of the wire with the rubber matrix was evaluated.

Effects of TiO2 Nanoparticle Addition on Microstructure and Selected Properties of Ag–xTiO2 Composites

The paper presents the results of a study of the microstructure and selected properties of silver-based composites reinforced with TiO2 nanoparticles, produced by the powder metallurgy method. Pure silver powders were mixed with TiO2 reinforcement (5 and 10 wt%) and 5 mm steel balls (100Cr6) for 270 min in a Turbula T2F mixer to produce a homogeneous mixture. The composites were made in a rigid die with a single-action compaction press under a pressure of 400 MPa and 500 MPa and then sintered under nitrogen atmosphere at 900 °C. Additionally, to improve the density and mechanical properties of the obtained sinters, double pressing and double sintering operations were conducted. As a result, compacts with a density of 90–94% were obtained. The microstructure of the sintered compacts consists of uniform grains, and the TiO2 reinforcement phase particles are located on the grain boundaries. There were no discontinuities at the Ag–TiO2 contact boundary, which was confirmed by SEM and TEM analysis. The use of a higher pressure had a positive effect on the hardness and flexural strength of the tested materials. It was found that the composites with 5 wt% TiO2 pressed under 500 MPa are characterized by the highest level of mechanical properties. The hardness of these composites is 57 HB, while the flexural strength is 163 MPa.