Advanced Problems in Mechanics

Frontmatter

Influence of the Sperm Velocity on Fertilization Capacity in the Oscillatory Model of Mouse Zona Pellucida

Abstract

Considering the fertilization process as an oscillatory phenomenon, based on mechanotransduction theory of sperm–oocyte interaction, influence of sperm velocity and their specific arrangement on outer surface of oocyte- Zona pellucida (ZP) relative to the oscillatory behavior of ZP was studied using discrete continuum oscillatory spherical net model of mouse ZP. For the calculated favorable impact angles of spermatozoa by using generalized Lissajous curves, a parametric frequency analysis of oscillatory behavior of the knot molecules in the mouse ZP spherical net model is conducted. In order to mimic successful fertilization in physiological conditions in this numerical experiment, velocities of the progressive and hyperactivated spermatozoa were used. The resultant trajectories of knot molecules in mouse ZP (mZP) spherical net model, in the form of generalized Lissajous curves, are presented. Influences of the sperm velocity and its arrangement on the resultant trajectory of the corresponding knot molecules are discussed. Component displacements in the meridian and circular directions of the knot molecules of ZP are in the form of multi-frequency oscillations. Symmetrical arrangements of spermatozoa having effective velocities are more favorable for achieving a favorable oscillatory multi-frequency state of mZP for a successful fertilization. Determining the optimal parameters of spermatozoa impact that will induce a ZP favorable oscillatory state opens the possibilities for more complete explanation of the fertilization process.

Andjelka Hedrih, Ana Mitrovic-Jovanovic, Mihailo Lazarevic

Parameter Determination of Metamaterials in Generalized Mechanics as a Result of Computational Homogenization

Abstract

As the length scale starts decreasing such that the inner substructure of the material becomes dominant in material response, the well-known theory of elasticity shows inadequacies. As a remedy, generalized mechanics is proposed leading to additional, inner substructure related parameters to be determined. In order to acquire them, for a so-called metamaterial with known substructure and material response in the length scale of the substructure, we present how to apply a computational approach based on the finite element method.

Bilen Emek Abali, Hua Yang

A Model of Hydraulic Fractured Horizontal Well for Debit Computation of Slanged Gas and Oil

Abstract

This work presents model of liquid rate and bottomhole pressure computation in multistage hydraulic fractured horizontal well. Model is based on a solution of transient fluid flow equation in porous media with finite volume method. 3D formulation of the problem gives an opportunity to model not only axisymmetric example as it is in 2D models. Results are recorded with a second order time and space accuracy. The most innovate thing that this project can be used for is solution of inverse problem – restoring reservoir parameters on a base of known well production.

Igor Abramov, Maksim Simonov

Double Aging of Heat-Treated Aluminum Alloy of (7075) and (6061) to Increase the Hardness Number

Abstract

The present study is an attempt to study the effect of double-aging process and its relevant parameters (like time, temperature and quenching media) on the mechanical properties of two types of aluminum alloys. AA7075 and AA6061 are selected in this study to examine their responses to the double-aging. Fabricated specimens are heat treated, and tested for hardness using micro-Vickers hardness test. They are then artificially aged at 150 °C for different aging periods. The specimens are then quenched in water and oil. Hardness test are then repeated to determine the optimum time and cooling rate that give the maximum (peak) hardness values. This procedure are repeated on other sets of specimens, but with double aging at 185 °C to find out which alloy has more significant response to double ageing. The outcomes of the study show that the 7075 aluminum alloy demonstrates better results than those obtained for the 6061 aluminum alloys. Increase in hardness from 135.66 HV to 150.61 HV is reported for the 7075 aluminum alloy.

Suleiman E. Al-Lubani, Ahmad I. Ateyat

The Definition of Damage Parameter Changes from the Experimental High-Temperature Creep Curves

Abstract

Under the action of relatively low stresses and high temperatures, metallic materials become brittle and fractured with a small value of residual deformations. This problem is known as a problem of thermal brittleness of metals. To solve this challenge in the mechanics of materials the damage conception was introduced. To describe the brittle region of the experimental long-term strength curve, the system of simple kinetic equations for the damage parameter and creep deformation was proposed, and the long-term strength criterion was formulated.

In this work, we propose to determine the damage parameter changes according to the experimental high-temperature creep curves. Only one kinetic equation for creep rate for compressible medium, recorded using the damage parameter is formulated. From this equation, the damage parameter is determined, depending on the creep rate and the creep deformation. Similarly, the value of the damage parameter is determined according to the Rabotnov solution. To describe the experimental creep curves various empirical dependences in the form of power, exponential, and mixed functions are used. Theoretical damage curves are plotted. The corresponding theoretical long-term strength curves are constructed.

A. R. Arutyunyan, R. A. Arutyunyan, R. R. Saitova

Evaluation Criteria for the Wear Resistance of High-Chromium Steels

Abstract

The paper is devoted to estimation on steels of the type of 12Cr and 8Cr in terms of efficiency. The criteria for wear resistance for these materials have been studied. The quality estimation on basic feature was carried out. The complex indicator of the quality level of investigated steels working under friction conditions has been determined. It was found that materials with a uniform distribution of carbides have the highest level of quality.

S. A. Atroshenko

Moving Web and Dynamic Problem of Aerothermoelastic Vibrations and Instability

Abstract

The paper is devoted to the analysis of the axially travelling web supported by a system of fixed rollers and submerged in axially flowing gas medium. In order to accurately model the dynamics and stability of a lightweight moving web, the interaction between it and the surrounding air is taken into account. The light weight of the moving web leads to the inertial contribution of the surrounding air to the acceleration of the material becoming significant. In the context of this paper we apply a Galerkin method for dynamic stability analysis of the moving web based on developed added-mass model.

Nikolay Banichuk, Svetlana Ivanova, Juha Jeronen

New Ansatzes for Solution of Nonlinear Nonautonomous Klein-Fock-Gordon Equation

Abstract

Methods of finding of exact analytical solutions of nonlinear nonautonomous Klein-Fock-Gordon (KFG) equation are proposed. Solutions U(x, y, z, t) are sought in the form of compound function \(U=f(W)\). The argument W(x, y, z, t) is called ansatz. Function f(W) and ansatz W are sought from the different equations. The function f(W) satisfies to nonlinear ordinary differential equation. Its solution is received in the form of integral. Ansatz W is defined as a root of the special algebraic equation. Different ansatzes W are proposed and different solutions of the nonlinear nonautonomous KFG equation are found.

A. N. Bulygin, Yu. V. Pavlov

Development of the Legs Fixation Mechanism for Lokomat Therapy Training Device

Abstract

This article describes the application of constructive solutions for the modernization and calculation of the effects of loads on structural parts that hold the lower limbs of a person who is undergoing treatment on a robotic walking training device located at the St. Petersburg Research Institute of Phthisiopulmonology of the Ministry of Health of the Russian Federation.

Considering the specifics of the training device that’s main task is to recover walking function, it is important to pay particular attention to the convenience and safety of the structure.

At the end of the research and manufacturing described hereunder, the existing training device will be able to begin its work at the Central Research Institute of Phthisiopulmonology, in particular it will provide free rehabilitation for patients. At the moment, only a few simulators for locomotor therapy are installed in St. Petersburg. Most of the treatment sessions are paid.

Support for solving the problem is provided by specialists of the Research Institute of Phthisiopulmonology.

The project was fully implemented on the basis of the Center for Scientific and Technical Creativity of Youth Fablab Polytech. The work on the project described in the article also demonstrates the competencies of digital production, obtained by the authors at Fablab Polytech helping to solve a wide variety of technical problems. In the process of work, such production methods as computer modeling, generative design, computational operations with the influence of loads and CNC machines were used.

Andrei Dolgirev, Natalia Maltseva

Modeling of the Superelastic Behavior of CuAlNi - Single Crystals Accounting Anisotropy of Elastic Properties

Abstract

The lattice deformation tensor for \(\beta _1\leftrightarrow \beta _1'\) martensitic transformation was found from available crystallographic data. This tensor was used for modeling of the isothermal deformation of CuAlNi shape memory alloys in the frames of a microstructural model. The simulated stress-strain curves obtained for pseudoelastic austenitic and pseudoplastic martensitic CuAlNi are in a good qualitative agreement with literature experimental data for single crystals with different orientations.

Tatiana Y. Chernysheva, Margarita E. Evard, Aleksandr E. Volkov, Fedor S. Belyaev

Experimental Investigations of 3D-Deformations in Additively Manufactured Pantographic Structures

Abstract

In the recent past new experimental techniques have been developed with the objective of linking generalized continuum theories with technology. So-called pantographic structures, which can be characterized as a meta-material, will be presented and investigated experimentally: Samples of different materials and dimensions are subjected to large deformation loading tests (tensile, shearing, and torsion) up to rupture, while their response to loading is recorded by an optical measurement system. 3D-digital image correlation is used to quantify the deformation.

Results show that the deformation behavior is strongly non-linear and that the structures are capable of performing large (elastic) deformations without complete failure. This extraordinary behavior makes pantographic structures very attractive as engineering material in technical applications for lightweight applications and in the medical industry.

Gregor Ganzosch, Emilio Barchiesi, Rafal Drobnicki, Aron Pfaff, Wolfgang H. Müller

Fatigue Reliability of Structures: Methodology of Assessment and Problems

Abstract

Fatigue reliability assessment of metallic structures in various applications according current design codes is based mostly on S-N criteria with uncertain characterization of fatigue properties of a particular material and the assumed damage. In case the crack is detected residual service life as recommended may be estimated by applying the Linear fracture mechanics techniques, again, with incomplete defining conditions of the crack growth and exhaustion of life.

Proposed earlier procedure of simulation the fatigue process based on the due finite element modeling of the affected area of a structure, application of the damage summation technique and appropriate criterion for fatigue failure of material allowed assessment of fatigue life from the onset of service loading up to development of a critical state, e.g. of the through crack in a structural component. Also, it was shown that the simulation scheme was capable of account the heterogeneity of the material structure fatigue resistance, the crack closure effects and elastic-plastic material response when the Strain-life criterion for fatigue failure was applied.

However, selection of the criterion for fatigue failure of material is but a straightforward decision: it is shown that S-N criterion even attributed to the same structural steel class as the Strain-life one does not provide in analysis of the fatigue process even an approximate convergence. This is mostly due to fairly indirect considering the inelastic properties of fatigue damage in S-N criteria and the methodology of fatigue testing specimens aimed at evaluation of S-N and \(\Delta \varepsilon \)-N criteria.

Further, the approach would need in more comparisons of simulated and test data in different structural applications.

Ruslan V. Guchinsky, Sergei V. Petinov

Inhomogeneous Distribution of Thermal Characteristics in Harmonic Crystal

Abstract

In this paper, we consider a model of a uniform harmonic chain of particles for the analysis of non-stationary thermal effects in an ideal crystal system. The exact solution for the particle system is presented and the temperature is calculated as a measure of the average kinetic energy of the particles. The corresponding energy averaging is performed over the initial distribution of the displacements and velocities of the particles, provided that they obey the Boltzmann principle. Simple analytical formulae are presented for all energy derivatives with respect to time at the initial time and for the first derivative with respect to the number of particles. Over a small time interval, the temperature was shown to depend monotonically on the number of particles. This means that the non-uniformity of thermal characteristics distribution, i.e. dependence on the number of particles, occurs in the system without additional assumptions about the structure of the initial conditions on a macroscopic scale. The obtained formula for the distribution of kinetic energy is presented through Bessel functions. The functional dependence on the number of particles was shown to appear in the index of Bessel functions, and the parity of the number of particles affects the temperature distribution. The distribution of the kinetic energy for a large time was asymptotically analyzed as well.

Mikhail A. Guzev, Vladimir M. Sadovskii, Chengzhi Qi

Dynamics of the Microresonator in the Regime of Supercritical Compression

Abstract

In this work we investigate nonlinear dynamics of an electrostatically actuated microbeam resonator, located between two stationary electrodes, in the regime of supercritical compression. Longitudinal movement of the elastic fastening creates a longitudinal force in the elastic element of the microresonator. The equations of motion of the resonator are supplemented by equations of electrical circuits containing sources of electromotive force and capacitors of variable capacitance formed by fixed electrodes and the elastic element of the resonator. Equilibrium positions depending on the longitudinal displacement of the elastic fastening mechanism are obtained for various configurations of the electric field. With different switched on sources of constant electromotive force either two or three critical values of the force are possible, which differ from the Euler force. A numerical experiment demonstrating the possibility of the occurrence of a self-oscillatory regime was performed.

Vasilisa Igumnova, Lev Shtukin, Alexey Lukin, Ivan Popov

Design and Simulation of an Acoustic Metamaterial Plate Incorporating Tunable Shape Memory Cantilever Absorbers

Abstract

Metamaterials are materials having artificially tailored internal structure and unusual physical and mechanical properties. Due to their unique characteristics, metamaterials possess great potential in engineering applications. This study proposes a tunable metamaterial for the applications in vibration or acoustic isolation. For the state-of-the-art structural configurations in metamaterial, the geometry and mass distribution of the crafted internal structure is employed to induce the local resonance inside the material. Therefore, a stopband in the dispersion curve can be created because of the energy gap. For the conventional metamaterial, the stopband is fixed and unable to be adjusted in real-time once the design is completed. Although the metamaterial with distributed resonance characteristics has been proposed in the literature to extend its working stopband, the efficacy is usually compromised. In this study, the incorporation of tunable shape memory materials (SMM) via phase transformation into the metamaterial plate is proposed. Its theoretical finite element formulation for determining the dynamic characteristics is established. The effect of the configuration of the SMM cantilever absorbers on the metamaterial plate for the desired stopband in wave propagation is simulated by using finite element model. The result demonstrates the tunable capability on the stopband of the metamaterial plate under different activation controls of the SMM absorbers. The result of this study should be beneficial to precision machinery and defense industries which have desperate need in vibration and noise isolation.

Hua-Liang Hu, Yi-Ting Wu, Ji-Wei Peng, Chun-Ying Lee

A New Class of Optimization Problems Related to Structural Control by Contact Interaction

Abstract

For some structures under service loads there is a need of precise control of local boundary displacement and/or its tangential gradient by an additional loading of one or two punches. Such problems exist in design of robot grippers or mechanical tools used in element assembling or in other mechanical processes. The punch interaction is assumed to be executed by a discrete set of pins or by a continuously distributed contact pressure. The optimal contact force and pressure distribution are defined in terms of assumed control function, for which contact shape is specified for both discrete and continuous punch action. For beam or plate structures three classes of control are considered. First, requiring by punch action the fixed load \(F_{Q}\) and displacement \(u_{Q}^{*}\) at a specified position, second, requiring the load-displacement \(F_{Q}=F_{Q}(u_{Q}^{*})\) evolution by the varying punch load and third, provide deflection and slope control at a specified position by a coordinated action of two punches. The reciprocal motion of a transverse pin attached to the beam is induced by varying punch forces. The punch position is specified by satisfying constraints on maximum punch pressure and equivalent Mises stress on the contact interface. Several illustrative examples are presented to illustrate punch control for different boundary supports and three control classes.

István Páczelt, Zenon Mróz

On Crack Propagation in a Two-Component Thermally Reinforced Pipe

Abstract

One of the effective approaches to the retardation of cracks in pipes is based on thermal reinforcement of rolled sheet. For the manufacture of pipes it was proposed to use thermally reinforced steel sheet with periodic strengthened strips. These barriers in the crack path reduce the rate of its propagation and change its trajectory. The direction of crack propagation may be controlled by the configuration of these barriers. This paper presents experimental and theoretical results concerning the direction of crack propagation near the boundary of a strengthened part of a steel sheet depending on the angles of inclination of this boundary with respect to the initial crack trajectory. The competition between deflection and penetration at the interface is investigated for different ratios of the strength limits of the strengthened material and the matrix. The problem is studied using known expressions for the stress components in the vicinity of crack tips with non-singular terms associated with load biaxiality, and the generalised maximum tensile stress criterion.

Alexander Maksimov, Yulia Pronina

Rock Fracture During Oil Well Perforation

Abstract

Rock stress fields in the near wellbore of an oil well during perforation are modelled and studied numerically. The main parameters that influence the stress field of rocks during perforation are identified. The dynamic stress field formed in the near wellbore zone causes degradation of reservoir properties and annular zones of rock fracture formed around a production wellbore. The model of porous and permeable reservoir was built considering mechanical parameters such as Poisson’s ratio, Young’s modulus, coupling along the crack system, uniaxial compression strength and compressibility of cracks. The dynamics of rock fracture and stress state change were simulated using Finite Element Method. It is shown in the simulation that the type of perforation has a strong influence on the mechanism of rock fracture and distance of fracturing zone from the well. It is investigated in experiments that pressure drawdown between reservoir and bottomhole zones affects the formation stress state and as a result distribution of permeability and cracks opening.

Evgenii Riabokon, Mikhail Turbakov, Evgenii Kozhevnikov, Vladimir Poplygin, Marian Wiercigroch

Cavity Flow of Nematic Liquid Crystals – A Parameter Study

Abstract

This paper presents a parameter study of the flow of nematic liquid crystals which possess both viscous and elastic properties. The well-known Ericksen–Leslie theory is used. The underlying general equations are stated and subsequently simplified for non-isothermal and steady state conditions. The flow situation of a two-dimensional lid-driven cavity is analyzed. Hence, the equations are specialized for the case of two-dimensional flow. For numerical calculations, the complete boundary value problem is formulated and then expressed in dimensionless form. Several dimensionless parameters are identified and their impact on the solution is analyzed. Furthermore, the temperature rise due to viscous dissipation is studied, which is frequently ignored in the mechanics community. The finite element method is employed using the software package FEniCS. In particular, the numerical treatment of the constraints required in the theory, is analyzed. A convergence analysis is performed based on the constraints for rigid and incompressible nematic liquid crystals.

Wilhelm Rickert, Wolfgang H. Müller

HEDE Model vs Inner Pressure Model in Calculating the Strength of Hydrogenated Metals

Abstract

The degrading effect of hydrogen on high strength steels is well recognized, but this problem still does not have an exact solution. In the present paper, we analyze two models that describe the mechanism of hydrogen embrittlement: HEDE and inner pressure models. We considered the effects of pre-stress load level and initial hydrogen concentration on the initiation time of cracking instigated by hydrogen in the steel bar and on the critical load level. We realized two important facts: (1) the HEDE model has several significant drawbacks such as the distribution of hydrogen in the sample and the place of initiation of the crack, as well as the ratio describing the relationship of stress and hydrogen concentration; (2) the coefficient of diffusion expansion needs research for the possible study of many phenomena in nature.

Julia Sedova, Vladimir Polyansky, Ivan Popov

The Influence of Balcony Greening of High-Rise Buildings on Urban Wind and Thermal Environment: A Case of an Ideal City

Abstract

The balcony greening of high-rise buildings is one of the vertical greening strategies that have been tried in recent years due to the lack of green space in urban areas. In this study, the influence of balcony greening of high-rise building on wind speed and air temperature at different heights (1.75 m and 50 m) through two different variables including “balcony depth” (none, 3 m) and “green cover ratio” (0%, 50%, 100%) of 3 m-balcony are discussed. The key findings can be summarized as follows: 1. There are some differences in wind speeds and air temperatures between the buildings with 3 m-balcony and no balcony. 2. When the 3 m-balcony increased their green cover ratio (up to 50% or 100%), it was found to simultaneously achieve the effect of slowing down the urban wind speed and reducing the urban temperature.

Ying-Ming Su, Chiao-Jou Hsieh

Contour Convergence Regularities for Openings in Coal

Abstract

The article is devoted to the applied problem solution of a continuous medium inelastic deformation as applied to the description of the heaving of rocks in the workings. This is the ubiquitous manifestation of rock pressure in workings, both in coal and ore deposits. It is expressed in raising the soil, which value reaches significant values compared with the size of mining working and lead to the loss of its functional purpose. Heaving is a process stretched in time for weeks, months, or even years.

In the article, the construction of the heaving problem solution is carried out within the framework of the viscoplasticity theory. This approach can reflect the time dependence of the deformation process, since the equations of state are formulated in increments or strain rates. Creep strain is characterized by the strain rate, which is generally a function of the stresses, time, and possibly temperature.

The form of this function can be constructed for each particular material experimentally as a result of numerous experiments on samples with subsequent statistical processing of the results obtained. However, theoretical studies use a variety of simplified analytical dependencies, mostly of a power type.

The article discusses options for the numerical calculation of viscoplastic deformation both with a constant in time deformation rate, and with a decreasing rate, when the total deformation after a certain period of time reaches a constant level.

To preserve the excavation working capacity after a certain time, a “undermining” of the soil is produced, removing the layer of rock extruded into the mining working. It is known that such actions are performed 2–4 times, after which the heaving on this place completely stops. In addition, from the practice is known such a phenomenon as a gap of the soil; a situation where, in addition to raising the soil, a tension crack is formed in it, which runs along the workings along its center line. Within the framework of the developed approach with the use of a viscoplastic model, the main regularities of the course of such processes are considered.

Vitaly A. Trofimov, Yury A. Filippov

On Finite Element Analysis in Generalized Mechanics

Abstract

Different numerical implementations have been proposed in the literature for computation in generalized mechanics. A computational benchmark problem is beneficial to highlight the differences or even validate an approach. We briefly present the strain gradient elasticity theory and its weak form. A relatively simple analytic solution in strain gradient elasticity theory is shown. The closed-form solutions for a plate under simple shearing in plane strain are investigated for different boundary conditions. Moreover, IsoGeometric Analysis (IGA) within the finite element method is used. By employing open source packages developed under the FEniCS project, we develop a general framework and use the analytical solution to verify the numerical implementation. Comparison of the computation to the closed-form solutions shows that the numerical implementation is accurate and reliable.

Hua Yang, Bilen Emek Abali, Wolfgang H. Müller

Model of the Effect of Low Natural Concentrations of Hydrogen on Cylindrical Steel Samples

Abstract

Small amount of hydrogen concentration impact appears significantly in material fatigue and cracks propagation. To simulate a significant deterioration of the physicomechanical properties of the model, similar to what is happening in the experiments, a model with varying bilinear elastic-plastic properties is proposed, corresponding to the saturation of hydrogen after its accumulation in the actual structure for several years. The finite element method used to simulate the effect of degradation of the mechanical characteristics of the entire sample caused by hydrogen saturation. The simulation carried out for the case of cylindrical corset samples, for which there are extensive experimental data. Analysis of the calculation results shows that the behavior of the material under the influence of hydrogen occurs not only in the zone of elastic deformations. It is noticed that the degradation of the mechanical characteristics of the metal under the influence of hydrogen leads to a significant change in deformation and strength. The material model used for the entire sample allows one to describe experimentally observed effects.

Aleksandr Zegzhda, Vladimir Polyansky

Calculation of the Activation Energies of Hydrogen in Titanium Manufactured with 3D Printing Technology by Means of a Multichannel Diffusion Model

Abstract

The most popular method for calculating activation energies of hydrogen is the method of thermo-desorption spectra (TDS). The disadvantage of this method is that it does not consider diffusion inside the metal. Essentially, only surface sorption and desorption can be adequately studied using this method. All this leads to large variations of experimentally evaluated activation energies for the same materials.

The present paper proposes a method for calculation of the activation energies of hydrogen based on experimental data. Measurements were carried out using the industrial mass-spectrometric hydrogen analyzer AV-1, which uses the hot vacuum extraction method. The authors of the paper realize a gradual heating in a vacuum to measure the activation energies of hydrogen in titanium. The mathematical model is based on the model of multichannel diffusion of hydrogen. Calculation of hydrogen flows and their time integrals, which characterize the integral experimental results on every temperature step, were performed using a Fortran program. The parameters of the sample and the experiment conditions were entered into the program. As a result, the activation energies of hydrogen diffusion were calculated. Using these activation energies, a graph of discrete thermo-diffusion spectrum was plotted, which was then compared to the graph obtained during the experiment.

P. A. Zumberov, Yu. A. Yakovlev, V. A. Polyanskiy

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