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Über dieses Buch

This is the proceedings of the 2nd International Conference on Theoretical, Applied and Experimental Mechanics that was held in Corfu, Greece, June 23-26, 2019.

It presents papers focusing on all aspects of theoretical, applied and experimental mechanics, including biomechanics, composite materials, computational mechanics, constitutive modeling of materials, dynamics, elasticity, experimental mechanics, fracture, mechanical properties of materials, micromechanics, nanomechanics, plasticity, stress analysis, structures, wave propagation.

The papers update the latest research in their field, carried out since the last conference in 2018.

This book is suitable for engineers, students and researchers who want to obtain an up-to-date view of the recent advances in the area of mechanics.



Materials: Properties, Manufacturing, Modelling


Role of Compactness on Hardness and Reduced Modulus of Vaterite Determined with Nanoindentation

The influence of compaction degree of synthetic vaterite, the metastable polymorph of calcium carbonate, on determined mechanical properties was investigated using nanoindentation instrument. Specimens for measurements were prepared as pressed pellets with the application of three different forces—40, 60 and 80 kN. The highest values of reduced modulus and hardness were detected for vateritic pellet pressed at 60 kN. For this specimen, reduced modulus and hardness were found to be in ranges 74–10 and 5.2–0.3 GPa, respectively. Observation with scanning electron microscope showed increase compactness of pellet’s microstructure and an increase in density and length of microcracks within vateritic pellets when higher pressing force was applied.

Radek Ševčík, Vladimír Hrbek

Approximate Mode Shape for Damped Structures

Mode shape is very important in dynamic analysis of the structures. It can be employed to assess dynamic interaction between a structure and its supports to avoid sudden failure. However, unlike undamped structures, exact mode shapes for damped structures are difficult to obtain due to the eigenvectors complexity. In practice, damped structures cannot be shunned and they are available in many engineering applications. Some undamped structures may become damped structures during the operations. Such structures include pipes conveying fluid and because of their roles globally, their dynamic analysis becomes vital to check their integrity to prevent abrupt failures. In this paper, different methods of obtaining approximate mode shapes of composite pipe conveying fluid were investigated. The pipe is modeled using the extended Hamilton’s theory and discretized using wavelet-based finite element method. The pipe complex modal characteristics were obtained by solving the generalized eigenvalue problem and its mode shapes were computed.

Wasiu A. Oke, Oluseyi A. Adeyemi, Kazeem A. Bello, Adewale Adegbenjo

Deformation Behavior of Ferrite/Austenite Duplex Stainless Steel in Hot Compression Processing

The deformation behavior of Cr23 ferrite/austenite duplex stainless steel has been investigated at deformation temperatures from 1173 to 1473 K and strain rates from $$ 0.01 $$ 0.01 to $$ 10\,{\text{s}}^{ - 1} $$ 10 s - 1 at a given total strain of 0.8. The results show that the flow stress is strongly influenced by the deformation temperature, the strain rate and the strain. There is a balance between the working hardening and the softening at strain rate of $$ 1\,{\text{s}}^{ - 1} $$ 1 s - 1 and elevated deformation temperature when the strain is in excess of 0.25. The softening mechanism of the dynamic recovery and dynamic recrystallization is prominent at lower strain rate less than $$ 0.1\,{\text{s}}^{ - 1} $$ 0.1 s - 1 . The Arrhenius-type constitutive model is used to predict the flow stress which is closed to the experimental data.

Hezong Li, Suxia Huang, Qiusheng Li, Xiaopin An, Facai Ren, Simon S. Wang

Material Strength Degradation Experiment and Statistical Expression Under Cyclic Loading

Cyclic loading leads to material strength degradation gradually until fatigue fracture occurs. Material strength degradation path is significant to fatigue life prediction and/or fatigue reliability estimation. Since the stochastic attributes of material strength, fatigue damage and fatigue life, material strength degradation test data are the type of partially left-censored. It makes material strength degradation behavior description difficult. The present paper presents a method to estimate residual strength distribution after n times of cyclic stress application, in which the strength degradation information contained by the early failed specimens is converted to equivalent residual strength at the expected cycle number. The strength degradation information conversion is based on an assumption that the residual strength is normal distributed, and the residual strength data are roughly symmetrical to the median. Such obtained residual strength probability density function and strength degradation path can be applied to predict fatigue life and evaluate reliability.

Liyang Xie, Hongyi Ma, Guoliang Xu

Study of Effect of Phase Separation on Pores Orientation of Electrospun Nanofibre

Nanoporous fibres are advanced materials with wide application in drug delivery, sensor, filtration, membrane, wound dressing, encapsulation and catalysis. Known mechanisms for pore formation in electrospun are temperature-induced phase separation (TIPS) and vapour induced phase separation (VIPS), these are crucial to application and classification. The underestimated factor electrospinning parameter (polymer concentration) resulted in polymer and solvent rich phases which are capable of manipulating orientation in the jet. In view of this, expanded polystyrene was electrospun at various concentration and voltage. The morphology of resultant fibres were examined with Secondary Electron (SE) and Back Scattering Electron (BSE) detectors, both revealed clear porous micrographs. The resultant phases formed during elongation override popular mechanism in the science of pore formation in electrospun fibre. Finally, pathway for polymer re-use in membrane science is presented.

S. O. Alayande, E. O. Dare, J. N. Edokpayi, O. A. Adeyemi, Adewale Adegbenjo, T. A. M. Msagati

Deformation Model of [±45]S Cross-Ply Fiber Reinforced Plastics Under Tension

A series of experiments on tensile testing of specimens from cross-ply reinforced plastics made from unidirectional tape ELUR-P and cold-curing binder XT-118 and stacking sequence [±45°] were carried out. Tests were carried out on different specimens at three maximum stress values. It was established that the total axial strain can be represented as a sum of four components, including: reversible strain, residual (irreversible) strain, irreversible creep deformation and reversible creep strain due to the viscoelastic properties of the epoxy. The questions of the choice of relations for the description of the components of the strains and the identification of their mechanical characteristics are considered. The conclusion is formulated that for a hereditarily elastic model, one can use the Abel creep kernel and determine its parameters from an experiment for long holding times. To determine the parameters included in the irreversible creep relations, we use the results obtained immediately after the start of exposure at maximum stresses, and a method for their determination is proposed. After this is the initial modulus of elasticity. At the last stage, after determining the rheological characteristics and the initial modulus of elasticity, the nonlinear elastic reversible part of the strain can be singled out.

V. N. Paimushin, R. A. Kayumov, D. V. Tarlakovskii, S. A. Kholmogorov

Segregation Resistance, Stiffness and Toughness of CNT Nanomodified Self Compacted Concrete

Self-Compacting Concrete (SCC) reinforced with well dispersed carbon nanotubes (CNTs) was successfully produced. The segregation resistance of fresh CNT-SCC mixture was assessed by conducting a non-destructive electrical resistivity technique. The addition of CNTs resulted in a more homogenous mixture as the CNT-SCC exhibited consistent resistivity values between different electrode pairs along the investigated column. The reinforcing efficiency of the CNTs was also demonstrated by improvements in flexural strength (53%), Young’s modulus (68%), and flexural toughness (38%).

Myrsini Maglogianni, Panagiotis A. Danoglidis, Maria G. Falara, Maria S. Konsta-Gdoutos

High Temperature Creep Properties of Cast Cobalt-Based Superalloys: A Comparison

Cast cobalt-based superalloys have already found applications in the glass industry to construct glass shaping tools. The present study deals with the high temperature characterization of the two cast cobalt-based CoNb and CoTa superalloys which have been developed for precision casting of a rotary fibreglass spinner disc for glass industry. The superalloys have been characterized through constant load creep tests at 1000, 1050 and 1100 °C in a tensile stress range from 20 to 100 MPa, with the aim to simulate the variation of mechanical properties occurring in a rotary fibreglass spinner disc at operational conditions. The results have been compared and discussed, with the aim to link the difference in creep properties to the evolution of creep damage and fracture in superalloys. It was found that the CoNb superalloy possesses longer creep life compared to the CoTa superalloy under the same loading conditions. Fractographic investigations of the creep fractured specimens of the examined superalloys revealed that the dominating creep fracture of the CoTa is of the ductile transgranular dimple fracture mode due to a loss of an external section of specimen (necking). By contrast, the final brittle fracture in the CoNb superalloys occurs via relatively fast propagation of the longest cracks after the ultimate state of creep damage is reach.

Marie Kvapilova, Vaclav Sklenicka, Petr Kral, Jiri Dvorak

Sub-grain Plastic Strain Localization in CoCrNi Medium Entropy Alloy at Cryogenic Temperatures

High and medium entropy alloys are currently attracting significant research interest due to their potential to achieve superior mechanical properties compared to traditional alloys systems. The CoCrNi alloy has been of particular interest owing to the simple single phase structure, superior fracture toughness, and exceptional strength and ductility at cryogenic temperatures. Previous works have been primarily focused on identifying the operative microstructural mechanisms responsible for improved ductility. The activation of deformation twining at low deformation temperatures and high strains has been identified as a primary source for the improved ductility. However, detailed quantitative analysis focused on the deformation heterogeneities in the vicinity of grain boundaries, in particular at cryogenic temperatures, remains limited. Strain heterogeneities across grain boundaries reveal the micro-mechanisms responsible for the alloy strengthening and fracture properties, thus their measurements is of fundamental importance. The current work is dedicated to study the local strain accumulation in the vicinity of grains boundaries of plastically deforming CoCrNi. High resolution digital image correlation was used to measure and quantify the deformation heterogeneities at room temperature (298 K) and cryogenic temperature (77 K). The work aims to further elucidate the role of grain boundaries in improving the strength and ductility at cryogenic deformation temperatures.

Wael Abuzaid, Luca Patriarca

Effects of Treatment on Microstructure and Deformation Behavior of Dissimilar Welded Joint Between Single Crystal and Polycrystalline Superalloy

Dissimilar welding of Al + Ti rich and Nb rich nickel base superalloy has good welding performance. In this work, the tensile behavior of dissimilar Between Single Crystal and Polycrystalline Superalloy welded joint near its service temperatures (600–700 °C) was studied. The results show that the deformation behavior of the welded joint is closely related to the strength difference between difference regions. The yield strength (YS) and ultimate tensile strength (UTS) of the welded joint is dominated by the region with lower YS and UTS, which is Single Crystal Superalloy at 25–650 °C and Polycrystalline Superalloy at 660–700 °C. The plasticity of welded joint depends primarily on the magnitude of strength difference between different regions. Lower strength difference results in higher elongation. Both the UTS and elongation have peak values at 660 °C. The welded joints fail at Single Crystal Superalloy base metal at 25–650 °C while at Polycrystalline Superalloy base metal at 660–700 °C. The FZ has high strength and sufficient plasticity. Soft dendrites are surrounded and constrained by hard interdendrites. Fine discrete MC carbides and Laves phases in the interdendrites can effectively block the movement of dislocations from dendrites.

Yang Liu, Lei Wang, Xiu Song, Taosha Liang, Guo Hua

Improved Post-crack Energy Absorption Capability of Cementitious Composites Reinforced with CNTs and PPs

In this study a thorough investigation of the pre-peak and post-crack mechanical behavior of cement mortars reinforced with carbon nanotubes and polypropylene microfibers, took place. Flexural strength, Young’s modulus, energy absorption capability and energy based dimensionless indices (toughness indices) were investigated. Prismatic specimens of neat mortar and mortars reinforced with 0.1 vol.% CNTs and 1.0 vol.% PPs were subjected to a three point close loop bending test. Combined networks of CNTs and PPs also incorporated in mortar matrix in order to investigate the synergistic effect of hybrid reinforcement on the mechanical properties of mortar composites in comparison to the singly-reinforced mortars. The experimental results showed an exceptional multi scale mechanical behavior of mortars as reflected from the load-deflection curves. Cement-based composites using carbon nanotubes or ladder scale reinforcement of CNTs and PPs are characterized by 1.9 times higher flexural strength and stiffness and 50% increased flexural toughness over the mortars reinforced with micro scale fibers alone. The post-crack energy absorption capability of multiscale reinforced mortars after the formation of the “first crack”, is also outstandingly improved as indicated by the increases of the toughness indices I5, I10, I20.

Panagiotis A. Danoglidis, Maria S. Konsta-Gdoutos, Emmanuel E. Gdoutos

Molecular Dynamics Investigation of Dislocation Slip in Pure Metals and Alloys

Averaged accounting of motion and interaction of dislocations is a natural way to describe plasticity at macroscale in those metals, in which dislocation slip is the main mechanism. This approach describes the inertness of the plasticity development, which is crucial in dynamic problems. On the other hand, such models demand for additional equations and parameters. Molecular dynamics (MD) simulation of elementary processes in the dislocation ensemble at nanoscale is prospective tool for construction of these equations and fitting their parameters. We present MD simulation of the motion of single dislocation lines in pure metals and metals with precipitates. Influence of local stresses on the motion of dislocations in pure metals is discussed. The dislocation motion equation is derived and their parameters are fitted to MD simulations for Al, Cu and Mg. Also we discuss the model for dynamic interaction of dislocation and precipitate intended for description of plasticity in alloys.

Alexander E. Mayer, Vasiliy S. Krasnikov

Development and Validation of 3D DIC Based Residual Stress Testing Method

The paper describes the methodology of residuals stress determination on the basis of displacement fields measurement near drilled holes by means of 3D Digital Image Correlation. Detailed information concerning testing procedure are presented and supplemented by exemplary tests results for steel sample uniaxially loaded to 300 MPa. Determined values of residual stress calculated with inverse method algorithm are compared to the ones obtained with traditional method with near the hole strain measurements by means of tensometric rosette. In both cases 2 mm mill was used to drill the flat bottom hole with 0.25 mm increase steps. The influence of FEM model geometry used to deliver correction terms to the analytical model, necessary in the case of blind holes, is discussed. Determined residual stress from DIC based method agreed reasonably with traditional method.

Tomasz Brynk

Monogenic Filtering Based Automatic Defect Detection from a Single Fringe Pattern

We propose a fringe analysis algorithm for the automatic detection of defects from a single fringe pattern (FP). Typically, the surface defects exhibit high fringe density areas in the FP. Consequently, high fringe density regions can be utilized as a signature for detecting and locating the surface defects. An algorithm based on monogenic filtering of the FP is proposed for an efficient computation of the fringe density. The defect related high density fringe areas are segmented from the defect-free region based on a threshold derived from the fringe density histogram. The algorithm is found to be noise robust and it does not require any pre-processing of the FP. A single FP based analysis approach is suitable in identifying defects using interferometric systems in an industrial environment. Simulation and experimental results are provided to demonstrate the feasibility of the proposed algorithm.

Rishikesh Kulkarni, Pramod Rastogi

Enhanced Post-crack Load Carrying Capacity of Nano and Micro Scale Carbon Fiber Reinforced Mortars

A thorough investigation of the pre-peak, first crack and post-crack flexural response, energy absorption performance and ductility of cement mortar composites with hybrid reinforcement using nano and micro scale carbon fibers took place in this study. Young’s modulus, energy absorption capability and energy based dimensionless indices (toughness indices) were investigated through the Linear Elastic Fracture Mechanics theory. Prismatic notched specimens of neat mortar and mortars reinforced with 0.1 vol.% CNFs and/or 0.5 vol.% CFs were subjected to a three-point close loop bending test, using the crack mouth opening displacement, CMOD. Combined networks of CNFs and CFs were incorporated in mortar matrix in order to investigate the synergistic effect of hybrid reinforcement on the mechanical properties of the single-reinforced mortars. The experimental results showed an exceptional multi scale mechanical performance of nano and micro scale fiber reinforced mortars as reflected from the load-CMOD response of specimens. The energy absorption capability and load carrying capacity of multiscale reinforced mortars after the formation of the initial crack (first crack), are outstandingly improved as indicated by the 138 and 100% increases of the proposed size independent toughness indices, up to the peak load and the ultimate failure, respectively.

Maria G. Falara, Maria S. Konsta-Gdoutos, Emmanuel E. Gdoutos

Two-Point Bending Stress Determination of Ultra-Thin Glass Plates

Based on the large deflection beam theory and the deflection beam profile equation, a two-point bending stress determination method for ultra-thin glass plates was proposed in this paper. The full-profile bending stress distribution as the ultra-thin glass plate is bent with any contact angle and any compression displacement in the two-point bending test can be determined by the proposed method. In experiment, the widths and heights of the profile as well as the compression forces of a 100 μm thickness ultra-thin glass plate bent with different contact angles and compression displacements were measured. Measurement results of the widths and heights of the profiles as well as the compression forces are in good agreement with the theoretical values.

Po-Chi Sung, Wei-Chung Wang, Yu-Wei Kuo

Investigation of Grating Collimation of Coherent Gradient Sensing Technique

In this paper, the grating collimation of coherent gradient sensing (CGS) technique was investigated. Due to the basic principle of the CGS technique, two gratings are used to obtain the interference fringe pattern, therefore, the accuracy of the CGS technique is directly influenced by the collimation of the two gratings. In order to investigate the grating collimation of the CGS technique, a standard specimen was implemented. The measurement results show that the error becomes larger when the rotational misalignment between the gratings was increased.

Po-Yu Chen, Wei-Chung Wang

The Mechanism of Grain Boundary in Hydrogen Embrittlement of Inconel 690 Alloy

The effects of grain boundary on tensile deformation behaviors of Inconel 690 alloy precharged with hydrogen were investigated by changing the grain size, in order to clarify the mechanism of hydrogen embrittlement of the alloy. The results show that tensile strength and elongation of precharged alloy decreases, and the decreasing degree is gradually reduced with the increase of grain size, indicating that the interaction between grain boundary and hydrogen dominate hydrogen embrittlement of Inconel 690 alloy. Hydrogen could easily migrate towards the grain boundaries following the moving dislocations during tensile, and then enrich at grain boundaries, when the strain rate is relatively low. Thus, the accumulation of hydrogen results in dislocations pile-up, and if such dislocations pile-up reaches a critical degree, the hydrogen-induced cracking will initiate at grain boundaries, which leads to the brittle intragranular fracture characteristics. That means hydrogen-enhance dislocation pile-up is the main reason for hydrogen embrittlement of Inconel 690 alloy. Therefore, how to control the ratio of grain boundary could be considered as the key to avoid the hydrogen embrittlement.

Lei Wang, Yang Liu, Cheng He, Xiu Song

Determining Object Motion by Digital Image Correlation Method with Camera-Array Composed Cameras of Normal Frame Rate

In this study, a camera-array constructed by four regular CCD cameras which can provide 20 frames per second output is used for taking images and then analyzed by digital image correlation method to determine the motion route of an object. The object for tracking is prepared by spraying to form artificial random dots on the surface. The camera-array is first calibrated by using black-white chess board to align all image centers of cameras within 2 pixels. No special time-synchronization among cameras is implemented for camera-array, images are taken by a triggering signal and then analyzed by digital image correlation method to obtain whole filed displacement filed with respect to reference frame which is taken before object moved. The test object first is first moved horizontally and then vertical away from and back to the original with maximum 20 mm, the motion at different time interval is then calculated by averaging the displacement field evaluated by DIC. The motion-path determined by DIC matches well to the predefined route but with small zig zag noise can be found from the plot. The result reveals the proposed camera-array can improve temporal resolution and provide motion route, however, the reason for zig zag motion departure is given in the end of this paper which is helpful to improve the proposed method.

Chi-Hung Hwang, Tzu-Yu Kuo, Wei-Chung Wang



Configurational Stability of a Crack Propagating in Mixed-Mode I + II + III

In some previous papers, we presented some linear stability analyses of the coplanar propagation of a crack loaded in mixed-mode I + III, using a propagation criterion combining a Griffith-type energetic condition and Goldstein and Salganik’s “principle of local symmetry”. In the last one, the local value of the fracture energy was no longer considered as a constant but heuristically permitted to depend upon the ratio of the local mode III to mode I stress intensity factors. As a result, a much improved agreement of theory and experimental observations was obtained for the “threshold” value of the ratio of the unperturbed mode III to mode I stress intensity factors, above which coplanar propagation becomes unstable. This analysis is extended here to the situation, of considerable practical significance, where a small additional mode II loading component is present in the initially planar configuration of the crack. This component induces a small, general kink of this crack from the moment it is applied. The main novelty resulting from its application is that the instability modes, present above the threshold, must drift along the crack front during its propagation. It is hoped that this prediction will be useful to theoretically interpret a number of experiments where such a drifting motion was indeed observed but left unexplained.

Jean-Baptiste Leblond, Alain Karma, Laurent Ponson, Aditya Vasudevan

Limiting Equilibrium of Interfacial Shear Cracks at the Corner Point of the Media-Separating Boundary of the Piece-Homogeneous Isotropic Plane

An exact solution of symmetric problem on the elastic equilibrium of piece-homogeneous isotropic plane with the interface of media in the form the sides of angle, which contains the interfacial shear cracks is constructed by the Wiener—Hopf method. The case of smooth contact between sides of cracks is investigated. The stress intensity factor at the end of the shear crack is determined.

V. M. Nazarenko, A. L. Kipnis

An Approach to Analysis of Fracture of Semi-bounded Body Under Compressing Along Interfacial Near-Surface Crack

The problem of compressing a piece-homogeneous half-plane with forces directed along the near-surface crack located in the interface of two materials is considered. The problem relates to non-classical problems of fracture mechanics, since under such a loading scheme the stress-strain state realized in the body is homogeneous and in the corresponding expressions for stresses and displacements near the crack there are no singular components. Due to the fact that the stress intensity factors are equal to zero, the classical Griffiths-Irwin fracture criteria are inapplicable for the problem under consideration. In this situation, the start of crack propagation is associated with the local stability loss of the equilibrium state of a part of the material in the region adjacent to the crack. Using the approaches of the linearized theory of deformed bodies stability, the mathematical formulation of the problem was carried out.

V. L. Bogdanov, A. L. Kipnis

Fracture of Composite Material at Compression Along Near-Surface Crack

Nonclassical problem of fracture mechanics for near-surface crack under the action of compressive loads, directed along crack was investigated. The axisymmetrical problem for penny-shaped crack was considered. There are two approaches that are used to investigate such problems “beam approximation” and three-dimensional linearized theory of stability of deformable bodies for finite and small subcritical strains. Within the limits of the offered in second approach the problem was reduced to the solution of system of integral equations Fredholm with a side condition. Using the Bubnov-Galerkin method and numerically analytic technique, the problem was reduced to system of linear equations. As an example numerical research for a composite material was conducted. Critical loads were obtained for small and large distance between crack and free surface. Results for the composite materials behavior were also present and discussed.

Mykhailo Dovzhyk, Vyacheslav Bogdanov, Vladimir Nazarenko

Statistical Distribution of Pores in Solid and Molten Metals at Dynamic Tensile Fracture

Knowledge about the evolution of the size distribution of pores during fracture of material is essential for formulation and verification of the fracture models. Here we continue our previous study on the size distribution of pores in molten and solid metals in conditions of high-rate tension. We expand the previous molecular dynamics simulations on larger systems and lower strain rates. This simulations show that behaviour of solid metals can be more complex than in the case of melts. Solid metals can exhibit secondary nucleation of voids in intersection of lattice defects created by plastic growth of primary pores. Also we compare the obtained molecular dynamics results with theoretical model that takes into account nucleation of pores due to thermal fluctuations and variation of their sizes, which is governed by viscous flow in the case of melt or plasticity in the case of solid metals.

Polina N. Mayer, Alexander E. Mayer

Fatigue and Deformation of Light Magnesium Alloys

Lightweighting has been deemed as one of the most effective strategies to improve fuel efficiency and reduce human-induced emissions in the automotive and aerospace industry. Magnesium alloy, as an ultra-lightweight metallic material, has recently received significant attention in the transportation industry to reduce the vehicle weight due to its high strength-to-weight ratio, dimensional stability, good machinability and recyclability. However, the hexagonal close-packed (hcp) crystal structure of magnesium alloys gives only limited slip systems and develops sharp deformation textures, leading to strong mechanical anisotropy and tension-compression yield asymmetry caused by the presence of twinning in compression and detwinning in tension when loading along the extrusion or rolling direction. For the vehicle components subjected to dynamic loading, such asymmetry could exert an unfavorable effect on the performance. This issue could be overcome through texture weakening via addition of rare-earth (RE) elements and other alloying elements to refine grains and generate nano-sized precipitates. To ensure the structural integrity, durability, and safety of load-bearing structural components, understanding the characteristics and mechanisms of deformation and fatigue of magnesium alloys is vitally important. In this talk, a few examples on the cyclic deformation behavior of extruded magnesium alloys containing both high and low RE contents will be presented in comparison with RE-free extruded magnesium alloys. Moreover, twinning, twin growth, and twin-twin interactions during uniaxial compression in the extrusion direction and de-twinning in the transverse direction will also be discussed.

Daolun Chen

Miscellaneous (Biomechanics, Computational Mechanics, Dynamics, Nanomechanics, Plasticity, Structures, Wave Propagation)


Research on Contact Pressure of Friction Pair Based on Finite Element Method

The brake is a device that realizes mechanical speed reduction and braking, and its key component is the friction pair. In this paper, the problem of the brake pressure distribution characteristic of the friction pair is studied. The dynamic and static contact pressure of the friction pair is simulated by ABAQUS. Based on MATLAB and statistical moment analysis methods, the simulation results of contact pressure under different working conditions are analyzed.

Changlu Wang, Long Wu, Zichun Xu, Yaping Zhang, Hao Gao, Yanzhong Wang

Noise and Vibration Analysis of a Flux Switching Motor (FSM) with Segmental Rotor

Flux Switching Motor (FSM) with segmental rotor is a new class of electric motor, with both AC and DC windings on the stator. The rotor is devoid of any windings. FSM with its high torque density, compactness, less heat production and high ruggedness can prove to be an ideal motor topology to be used for the propulsion systems of electric vehicles. The objective of this study is to investigate the noise and vibration characteristics of an FSM with segmental rotor due to the electromagnetic forces acting on the motor and optimize the design to reduce noise and vibration levels.

Hedduri Sanket, M. N. Kishore, Nagesh Suresh

Quenching of Non-stationary Wave Due to Structural Transformation of Material

In the present paper a new model for describing structural transformation of solids under external impact is discussed. We suppose that the material consists of two crystalline lattices with close physical properties, connected by nonlinear interaction force. The relative displacement of the components is considered to be an additional degree of freedom responsible for transition of material to a new equilibrium position. Using experimental data on shock-wave loading and analogy between continuous model and its discrete representation allows to evaluate the unknown parameters and to reveal the mechanism of energy transfer from macro to micro level. Also it becomes possible to predict the parameters of external impact, necessary to start the process of transition to another state. The results of analytical investigation are confirmed by numerical solution of the original problem.

D. A. Indeitsev, B. N. Semenov, D. Yu. Skubov, D. S. Vavilov

Algorithms for System Identification

Implementations of different algorithms designed for material constant identification are discussed in this contribution. Identification is performed by varying the input variables (i.e., the material constants) and juxtaposing the results obtained by analysis of the model and some benchmark example. In order to reduce the iterations needed to achieve a good agreement with desired results, different numerical strategies can be employed. One of the possibilities is to use a genetic algorithm. The combination of finite element analysis and identification algorithm is a strong tool but it is time consuming and very demanding in computational resources. A surrogate modeling can be employed to reduce computational time. Generally, it consists in replacing the original model with a simplified one. Two approaches are taken into consideration herein: the polynomial chaos expansion and the artificial neural network. The efficiency of the above-mentioned algorithms is to be assessed in terms of computational resource.

Todor Zhelyazov, Rajesh Ruphakety, Simon Olaffson

Mechanics of Earthquake Source Processes: Insights from Numerical Modeling

Many major faults separate two tectonic plates that slowly move past each other in opposite directions. The relative motion is accommodated by faults by both sudden dramatic rupture events perceived as earthquakes and much slower, quasi-static fault slips. We study the mechanics of these rupture processes using dynamic-fracture ideas and continuum-mechanics modeling that incorporates laboratory-derived fault friction laws [1–3], shear heating, and effects of pore fluids [4–6]. The modeling can reproduce all stages of the past behavior of some fault segments—including locked, slowly moving, and earthquake-producing—with remarkable qualitative, and often quantitative, agreement. In part, it reveals the potential physics behind the unexpected extreme events, such the 2011 Mw 9.0 Tohoku earthquake in Japan [6, 7] that caused up to 40-m tsunami and numerous casualties. The modeling has been used to study situations in which energy-related quantities estimated from seismic shaking based on traditional fracture mechanics theory are valid and when they are not [8]. Such continuum-mechanics-based models, when further developed, will enable us to incorporate our increasing understanding of earthquake source physics into the assessment of seismic hazards and seismicity response to perturbations of natural or anthropogenic origins.

Nadia Lapusta

Strategies to Improve Convergence After Degeneration of the Initial Finite Element Mesh

In some cases, the finite element solution does not converge because of severe distortions in the finite elements of the initially generated mesh. Numerical strategies aimed to overcome such issues are discussed in this contribution. The context is the numerical simulation of concrete/RC beams strengthened with composite material. The structural element is considered as a multiple-component system: constitutive relations and local failure criteria are defined for all components, i.e., for all materials: concrete, steel and composite material. A damage-based constitutive law is retained for concrete. As a result of this procedure application, zones of reduced or of zero or rigidity are formed in the medium which is initially defined as homogeneous and isotropic. A new initial state for the subsequent post-failure solution is defined on the basis of the state at the time preceding the loss of convergence. After homogenization, zones containing distorted finite elements are ‘healed’.

Todor Zhelyazov

Parametric Study of Simulated Randomly Rough Surfaces Used in Contact Mechanics

The study and numerical simulation of randomly rough surfaces is a fundamental topic in contact mechanics. Existing theory permits calculating the distributions of values such as height, slopes and gradients based on the power spectrum of the surface. Determination of derived quantities like summit height or radius distribution tends to become mathematically intractable. An alternative approximation is then to simulate the random surfaces to obtain these distributions empirically. Here, a direct Monte-Carlo approach is presented in which distributions of summit heights and curvatures are obtained directly from the theoretical formulae. Results are compared to distributions calculated from simulated surfaces, over a wide range simulation parameters. The latter approach induces significant statistical dispersion as compared to the former. The summit radius distribution is narrower for the simulated surfaces than predicted by theory.

Rafael Schouwenaars, Miguel Ángel Ramírez, Carlos Gabriel Figueroa, Víctor Hugo Jacobo, Armando Ortiz Prado

Simplified Analysis of the Early Stage Self-loosening of a Shear-Loaded Bolted Joint

The self-loosening of a joint through unscrewing of the bolt is a phenomenon mainly occurring when the assembly is solicited by transverse repeated loads. Previous works highlighted that the transversal sliding of the bearing surfaces, either in the threads or underneath the bearing surfaces of bolts and/or nuts, is its root cause and that this phenomena begins during the first loading cycles. In order to study the early stage of this self-loosening, a simplified numerical model has been developed. The latter factors the bearing surfaces of the bolt, the preload, the friction coefficient, the amplitude of the shear-load and the fastener’s material. Through measurements and interpretation of the results, the shearing of the fastener has been identified as the main deformation leading to the self-loosening of the assembly, while the bending of the fastener shank limits the self-loosening. Moreover, according to the values of preload and shear-load, the behaviors were identified and an interpretation has been proposed.

Vincent Rafik, Alain Daidié, Bertrand Combes, Clément Chirol

Wave Scattering by Arrays of Shear Bands

A plane-strain model of multiple shear bands, arranged in different configurations, is presented in order to investigate the effects of their dynamic interaction. Reference is made to a material stressed to the verge of instability and subject to incoming harmonic waves of small amplitude. It is shown that shear band arrays may be subject to resonance and corresponding shear band growth or, conversely, to shear band annihilation. At the same time, multiple scattering may bring about focusing or, conversely, shielding from waves.

Davide Bigoni, Domenico Capuani, Diana Giarola

Dynamic Failure of Granular Slopes: Due to Unidirectional Stress Transfer or Multi-dimensional Wave Propagation?

In order to numerically study fracture development in solids, models composed of discrete elements are often assumed instead of those based on continuum mechanics. Although realistic results have been obtained through the investigation of discontinua, the real fracture process in discrete media, in particular that under dynamic loading conditions, has not been experimentally scrutinized thoroughly. Here, we employ experimental technique of dynamic photoelasticity in conjunction with high speed cinematography and trace evolution of fracture inside discontinuous media. Especially, we consider dynamics of two-dimensional dry granular slopes consisting of penny-shaped birefringent elastic particles and having some inclination angle. The observations of transient stress and fracture development owing to dynamic impact on the top slope surface indicate that at least two specific failure patterns exist and whichever occurs seems to be governed by force-chain-like unidirectional stress transfer and continua-like multi-dimensional wave propagation.

Koji Uenishi, Tsukasa Goji

Symposium on: “Dynamic Response of Elastic and Viscoelastic Solids Elastostatic and Elastodynamic Problems for Thermosensitive and Nonhomogeneous Solids Dynamic Problems in Mechanics of Coupled Fields,” by Roman Kushnir


Heat-Active Circular Interphase Inclusion in the Conditions of Smooth Contact with Half-Spaces

The method of Singular Integral Relations (SIR) for solving problems of stationary thermoelasticity for a piecewise homogeneous transversely isotropic space is generalized. Using the SIR method, the stationary thermoelasticity problem for interphase circular inclusion that is in smooth contact with piecewise homogeneous transversely isotropic space is reduced directly to a system of two-dimensional singular integral equations (SIE) with nuclei, which are expressed through elementary functions. An exact solution has been built for the said SIS; as a result, dependences of the translational displacement of the inclusion on temperature, the resulting load, the main momentum and the thermomechanical characteristics of transversely isotropic materials have been obtained. The order of the features of stresses and displacements jump is determined. Expressions for the stress intensity factor at the boundary of the inclusion are obtained, as well as numerical dependences of these coefficients on the polar angle, temperature and loads.

Oleksandr Kryvyi, Yurii Morozov

Unsteady Elastic Diffusion Oscillations of a Timoshenko Beam with Considering the Diffusion Relaxation Effects

The unsteady Timoshenko beam oscillations with mass transfer considering are investigated. In general formulation, the beam is under the action of tensile forces, bending moments and shearing forces given at its ends. The densities of diffusion fluxes are also given at ends. All the above factors are in the plane of the beam bend. To solve the obtained problem, the Laplace integral transform on time and Fourier series expansion on spatial coordinate are used.

O. A. Afanasieva, U. S. Gafurov, A. V. Zemskov

Interphase Inclusion and Crack in an Inhomogeneous Anisotropic Plane

In the inhomogeneous anisotropic plane the problem about interaction between interphase crack and inclusion, which is in the conditions of full cohesion, was considered. Using the method of singular integral relations for interphase defects, the problem was reduced to the system of singular integral equations, and the method for its solution is proposed. As a result, the effect of the distance between defects, the loading applied to them and the properties of anisotropic materials on the features of the stress fields in the neighborhood of defects was investigated. In particular, the critical distance between the crack and the inclusion, according to which the mutual influence of the defects is significant, was established. It was also established under what loads it is advisable to remain within the singular statement of the problem without taking into account the contact zones of the crack edges.

Kostyantyn Arkhypenko, Oleksandr Kryvyi

Phenomenological Model of Pseudo-Elastic-Plastic Material Under Nonstationary Combining Loading

The study of the behavior of bodies from pseudo-elastic-plastic materials requires the development of special algorithms for calculating the stress-strain state. When constructing the physical relations, it was assumed that the deformation at a point is represented as a sum of the elastic component, the deformation jump at the phase transition, the plastic deformation and the deformation caused by temperature changes. A numerical method of enhanced accuracy based on the use of two-dimensional spline functions is proposed for solving multidimensional nonstationary problems of thermo-elastic-plastic theory for bodies produced of pseudo-elastic-plastic materials. The basic equations comprising heat conduction, equilibrium or motion equations and geometric relations are written. The boundary and initial conditions are formulated in a general form and numerical examples are considered.

Pavel Steblyanko, Yuri Chernyakov, Aleksandr Petrov, Volodymyr Loboda

Plane Scattering Problem for an Inclusion of Non-classical Shape with a Thin Interphase Layer

The null-field method is applied to two-dimensional problems on P- and SV-waves scattering on an elastic inclusion of non-classical shape with a thin interphase layer of low rigidity. The interaction between the inclusion and its surrounding is modeled by means of the effective conditions imposed on the contour of the inclusion. The amplitudes of the scattering waves are analyzed in a far-wave field.

Roman Kushnir, Yaroslav Kunets, Valeriy Matus, Oleksandr Trofymchuk

Stress State in a Finite Cylinder with Outer Ring-Shaped Crack at Non-stationary Torsion

The axisymmetric dynamic problem of determining the stress state in the vicinity of a ring-shaped crack in a finite cylinder is solved. The source of the loading is the rigid circular plate, which is joined with one of the cylinder ends and loaded by the time-dependent torque. The proposed method consists in the difference approximation of only the time derivative. To do this, specially selected non-equidistant nodes and special representation of the solution in these nodes are used. Such an approach allows the original problem to be reduced to a sequence of boundary value problems for the homogeneous Helmholtz equation. Each such problem is solved by using integral Fourier and Hankel transforms, with their subsequent reversal. As a result, integral representations were obtained for the angular displacement through unknown tangential stresses in the plane of the crack. From boundary condition on a crack, an integral equation is obtained, which, as a result of using the Weber-Sonin integral operator and a series of transformations, is reduced to the Fredholm integral equation of the second kind. The numerical solution found made it possible to obtain an approximate formula for calculating the stress intensity factor (SIF).

Oleksandr Demydov, Vsevolod Popov

Determination by Iterative Method of Diffraction Field at the Interaction Longitudinal Shear Wave with the System of Thin Rigid Inclusions

The problem of the diffraction field determination is arising as a result of the longitudinal shear wave interaction with the thin rigid inclusions system arbitrarily situated in an infinity body was solved. Inclusions are considered to be fully coupled to the elastic medium and are moving. Unknown amplitudes of inclusions are determined from the equations of motion. The solution method is based on the submission diffraction field displacement as sum of discontinuous solutions to the Helmholtz equation, the constructed for each inclusion. As result the original problem is reduced to the system of the singular integral equations for unknown jumps of stresses on the inclusions surface, The iterative method of this system solving, where the zero approximation are the solutions of the integral equations for the single inclusions, is proposed. This integral equation for single inclusions are numerical solved the mechanical quadrature method. The final result is the approximate formulas for calculating stress intensity factors and the amplitudes of the oscillations.

Vsevolod Popov

Stress State Near Arbitrarily Oriented Cracks on the Continuation of a Rigid Inclusion Under Action of Longitudinal Shear Wave

The problem about determining of the dynamic stress intensity factors (SIF) for the cracks that are located at an angle from the ends of the inclusion is solved. The inclusion is located in an unbounded elastic body, in which the longitudinal shear harmonic waves are propagated. Unknown amplitude of inclusions are determined from the equations of motion. Boundary conditions are formed in the assumption that the inclusion is fully coupled with the medium (matrix), and the surface of cracks are not loaded. The method of the solution is based on the presentation of displacements in the body as a superposition of three discontinuous solutions which are built respectively to the cracks and the inclusion. As result the original problem is reduced to the system of the singular integral equations for unknown jumps of stresses and displacements to the defect. For the numerical solution of the system the method is developed. It takes into consider the real asymptotic of the unknown functions and uses the special quadrature formulas for singular integrals.

А. S. Misharin, V. G. Popov

Stress State of a Hollow Cylindrical Body with a System of Cracks Under Oscillations of Longitudinal Shear

The problem of determining the stress state near the through-cracks in an infinite hollow cylinder of arbitrary cross-section under oscillations of longitudinal shear is solved. The method allows satisfying the conditions separately on the surface of cracks and on the borders of the cylinder. The solution scheme is based on the use of discontinuous solutions of equations of motion of elastic medium with jumps of displacements on the surface of defects. For this displacement are represented by the sums of discontinuous solutions, built for each defect, and an unknown characteristic function. Designed presentation enables fulfilling separately the boundary conditions on the surface of defects that leads to the set of systems of integral equations, which don’t depend from the shape of the boundaries of the body. Then the unknown coefficients of represented characteristic function are determined from the conditions on the boundaries of the body by the collocation method.

Olga Kyrylova, Vsevolod Popov

The Wave Field of a Twice-Truncated Elastic Cone Under Torsion Moment Impact

The problem of an elastic twice-truncated cone wave field estimation is considered for a steady state torsional oscillations. The G. Ya. Popov integral transformation with regard to an angular coordinate is applied. It allows the reduction of the original problem to a one-dimensional boundary value problem in the transformation’s domain. The solution of this boundary value problem is derived in an explicit form. The dependence of the eigenfrequencies on the cone’s geometric parameters is investigated.

K. Mysov, N. Vaysfel’d

To the Solving of the Nonstationary Spatial Lamb—Cerutti Problem

The nonstationary Lamb-Cerutti problem was solved in the spatial statement for the elastic half-plane. Explicit formulae in the Laplace transform domain were derived. The solution was provided in detail for the case of steady state tangential and normal loads. Explicit formulae for the stresses and displacements of the half-space for both normal and tangent load were obtained.

D. Prikazchikov, Yu. Protserov, N. Vaysfeld

The Model of Thin Electromagnetoelastic Shells Dynamics

Interacting with electromagnetic field, thin linear elastic homogeneous anisotropic shell with a smooth median surface is exploring. The equations of its movement are used, taking into account the rotation of the normal fiber and compression. The components of the electromagnetic field together with the Maxwell equations and the generalized Ohm’s law are linearized along the transverse coordinate. In the surface pressure on the shell and the momentum per unit area, electromagnetic components are distinguished, they are found using the expression for the Lorentz force. Physical law for the shell, taking into account piezoelectric effects, closes the system of equations. A special case of equations for an isotropic shell is given.

V. A. Vestyak, D. V. Tarlakovskii

Unsteady Electro-Magneto-Elastic Axisymmetric Oscillations of a Continuous Cylinder of Infinite Length

In the present work is considered an axisymmetric time-dependent waves of an infinite cylindrical body. The body material is taken to be isotropic and electro magneto elastic. Piezoelectric effects are not taken into account. The deformation process is described by a system of equation with respect to radial and angular components of deformation of the body points in cylindrical coordinate system. In additional, it takes into account the effect of current density, surface charges, electric and magnetic fields. All parameters and ratios are reduced to dimensionless form. To solve the problem, are used the Fourier transformation of angles and the Laplace transformation of time. Then, the resulting expressions expansion in series in terms of a small parameter. The small parameter characterizes the relationship between mechanic and electro-magnetic fields. To move into the space of the originals using the inverse Laplace transformation via residue theorem.

Vladimir Vestyak, Vasily Scherbakov

Transient Spatial Motion of Cylindrical Shell Under Influence of Non-stationary Pressure

This paper investigates a transient spatial problem for cylindrical shell of a Tymoshenko-type subjected to external pressure distributed over some area belonging to a lateral surface. The approach to the solution is based on the Influence Function Method. There has been constructed an integral representation of the solution with a kernel in form of a spatial influence function for a cylindrical shell which is found analytically by expansion in Fourier series and Laplace and Fourier integral transformations. This paper proposes and implements an original algorithm of analytical reversion of Fourier and Laplace integral transforms based on connection of Fourier integral with an expansion in Fourier series based on connection of Fourier integral with expansion in Fourier series at variable interval with examples of calculations.

Grigory V. Fedotenkov, Dmitry V. Tarlakovskii, Andrey Yu Mitin

Nonstationary Dynamic Problems for Elastic and Viscoelastic Piecewise Homogeneous Bodies

The problems of transient wave processes in linearly viscoelastic piecewise homogeneous bodies with small deformations, boundedness of the disturbances propagation region, and creep boundedness of the material of homogeneous components of the bodies are considered The issues related to the construction of solutions of such problems by the method of the integral Laplace transform with respect to time and subsequent reversal are touched upon. The statements about the properties of the Laplace transform simplifying the construction of the originals are formulated. The case when all homogeneous components of the body are linearly elastic is considered.

Pshenichnov Sergey

The Wave Field of a Layer with a Cylindrical Cavity

The wave field of an infinite elastic layer weakened by a cylindrical cavity is constructed in this paper. The ideal contact conditions are given on the upper and bottom faces of the layer. The normal dynamic tensile load is applied to a cylindrical cavity’s surface at the initial moment of time. The Laplace and finite sin- and cos- Fourier integral transformations are applied successively directly to axisymmetric equations of motion and to the boundary conditions, on the contrary to the traditional approaches, when integral transformations are applied to solutions’ representation through harmonic and biharmonic functions. This operation leads to a one-dimensional vector inhomogeneous boundary value problem with respect to unknown transformations of displacements. The problem is solved using matrix differential calculus. The field of initial displacements is derived after application of inverse integral transformations. The normal stress on the faces of the elastic layer are constructed and investigated depending on the mechanical and dynamic parameters.

Anna Fesenko, Nataly Vaysfel’d

Features of Subsonic Stage of Contact Interaction of Viscoelastic Half-Plane and Absolutely Rigid Striker

Non-stationary dynamic contact problem for viscoelastic half-plane and absolutely rigid striker at subsonic stage of interaction is considered. Viscoelastic properties of half-plane material are described by exponential relaxation kernel. Free slipping is considered as contact boundary condition. Green function for normal displacement at the boundary of the half-plane is obtained using generalized convolution method. The resolving equation system consists of the striker motion equation, integral representation of half-plane boundary normal displacement, contact area boundary equation and the relation connecting half-plane boundary normal displacement and striker displacement. Equation system is solved numerically by meshing integration area and constructing equations difference scheme. The solution of the problem is obtained for the case of three types of surfaces constraining the striker: parabolic, circular and hyperbolic cylinders. Time dependencies of the striker velocity, resulting force for contact stresses and radius and contact area expansion velocity are obtained. The influence of relaxation kernel parameters on the mentioned contact interaction characteristics is analyzed.

Ekaterina Korovaytseva, Dmitry Tarlakovskii

The Unsteady Contact Interaction Problem of an Absolutely Rigid Body and a Membrane

This article investigates the vertical impact of an absolutely rigid body (indenter) on a membrane. The supersonic (initial) and subsonic stages of unsteady interaction are considered. The solution at the initial stage of contact interaction is reduced to solving a differential equation. A resolving system of equations was obtained for the problem at subsonic stage. The Green’s function for the membrane is found and a numerical-analytical algorithm is constructed to solve the system. The unknown functions calculation results are presented in the graph form.

Elena Yu Mikhailova, Grigory V. Fedotenkov, Dmitry V. Tarlakovskii

Static and Dynamic Models of Bending for Elastic Sandwich Plates

This work is an attempt to solve the problem how to describe static and dynamic bending deformations of elastic sandwich plates in the frame of two–dimensional theories. We focus here on the case of so-called hard-skin plates, i.e. the sandwich plates the faces of which are very hard. We consider only the hard-skin plates of symmetric structure on thickness. In this case the any static and dynamic problem can be represented as a superposition of two problems: one considers the deformations “in plane of the plate” (tension deformations) and the other considers deformations “out of plane of the plate” (bending deformations). It is proposed to solve the problem of static and dynamic bending for hard-skin plates on the basis of governing two- dimensional models derived from linear three-dimensional elasticity with the help of variational asymptotic method [1]. We show in which cases the bending problem must be solved on the basis the equations considering transverse shear effects both in statics and dynamics.

M. Yu. Ryazantseva, E. I. Starovoitov

Analysis of Vibration Insulation Properties of a Plate in an Elastic Medium Under the Influence of Different Types of Waves

The vibration-absorbing properties of the plate under the action of the flat, cylindrical and spherical harmonic wave in the soil are studied. In the soil model, an elastic isotropic medium is used. The motion of the plate is described by the system of equations of Paimushin V.N. The mathematical formulation of the problem includes the assignment of the incident wave, the equations of motion of the soil and the plates, the boundary conditions for the slab and the soil, the conditions at infinity, and the conditions of contact of the earth with the obstacle, where we neglect the connection of the plate to the ground. The kinematic parameters of the plate and the parameters of the disturbed stress-strain state of the soil are represented in the form of double trigonometric series satisfying the boundary conditions. After that, the constants of integration, displacement and vibration acceleration are determined. The main goal is to determine the total vector field of acceleration for each type of waves.

N. A. Lokteva, D. V. Tarlakovskii

Studying of Influence of the Material Anisotropy on the Limit State of an Orthotropic Plate Weakened by a Periodic System of Collinear Cracks Under Biaxial Loading

On the basis of a modified Dugdale model, we investigate the influence of the anisotropy of the material, in particular, differences between the ultimate tensile strength and ultimate compressive strength, on the limit state of an orthotropic plate weakened by a periodic system of periodic collinear cracks under biaxial external loading. As a strength criterion, the Hoffman strength criterion is considered. Strength diagrams of an orthotropic plate with a crack for different strength and crack resistance parameters are obtained.

Olga Bogdanova

The Boundary-Element Approach to Modeling the Dynamics of Poroelastic Bodies

The present paper is dedicated to dynamic behavior of poroelastic solids. Biot’s model of poroelastic media with four base functions is employed in order to describe wave propagation process, base functions are skeleton displacements and pore pressure of the fluid filler. In order to study the boundary-value problem boundary integral equations (BIE) method is applied, and to find their solutions boundary element method (BEM) for obtaining numerical solutions. The solution of the original problem is constructed in Laplace transforms, with the subsequent application of the algorithm for numerical inversion. The numerical scheme is based on the Green-Betty-Somigliana formula. To introduce BE-discretization, we consider the regularized boundary-integral equation. The collocation method is applied. As a result, systems of linear algebraic equations will be formed and can be solved with the parallel calculations usage. Modified Durbin’s algorithm of numerical inversion of Laplace transform is applied to perform solution in time domain. A problem of the three-dimensional poroelastic prismatic solid clamped at one end, and subjected to uniaxial and uniform impact loading and a problem of poroelastic cube with cavity subjected to a normal internal pressure are considered.

Leonid Igumnov, Svetlana Litvinchuk, Aleksandr Ipatov, Tatiana Iuzhina

Modeling Surface Waves on a Partially Saturated Poroelastic Half-Space

Defining relations for a partially saturated porous Biot medium, written in the variables of displacements of the skeleton and pore pressures of the fillers, are considered. The initial system of partial differential equations includes five functions (a displacement vector and two pore pressures). The model of the material corresponds to a three-component medium. A system of equations in partial derivatives and boundary-value conditions are written in Laplace transform for time variable and in direct time with initial conditions. The boundary-value problem is analyzed using the method of boundary integral equations, their solutions being sought with the boundary-element method. The numerical scheme is based on using the Green-Bettie-Somigliana formula. Quadratic interpolation polynoms are taken as form functions in describing the boundary of the body. Unknown boundary fields are sought through nodal values in interpolation nodes. The element-by-element numerical integration uses Gauss method and an adaptive integration algorithm. The boundary-element schemes are constructed, based on the consistent approximation of the boundary functions and the collocation method. The solution of the formulated system of linear algebraic equations is sought using the block-type Gauss method. The boundary integral equation method in combination with the technique of searching a boundary-element solution is oriented at a dynamic problem of an isotropic homogeneous partially saturated poroelastic half-space. The time-stepping method for numerical inverting the Laplace transform is used to obtain the solution in the time domain.

Leonid Igumnov, Svetlana Litvinchuk, Andrey Petrov, Igor Vorobtsov

Symposium on: “Elastostatic and Elastodynamic Problems for Thermosensitive and Nonhomogeneous Solids” by Roman Kushnir


Residual Strength and Reliability of Corroded Pipelines—Monte-Carlo Approach for Consideration of Spatially Nonuniform Material Properties

Assessment of the residual strength and workability of pipelines with detected corrosion defects assumes implementation of the limiting state criteria, which relate the parameters of pipe material and actual geometry of structure with the system of operating loading. Since the finite-element modeling is widely used for the expert analysis of the results of technical diagnostics and gives the opportunity to decrease the conservativeness of reliability determination, development of corresponding numerical techniques with regard to specific pipeline element are actual. This work proposes the numerical approach of statistical analysis of corroded pipelines limiting state. It consists in consideration of natural nonuniformity of the material properties within the limits of the finite-element description of the combined development of stress-strain state and ductile subcritical damage up to the limiting state using Monte-Carlo procedure. It allows taking into account of spatial stochastic distribution of such material characteristics as yield stress, microcleavage stress, initial concentration of nucleated porosity of ductile fracture, critical value of plastic strain, etc. It is shown, that this approach has lower conservativeness, than conventional ones, those presuppose the consideration of uniform material properties, but remains responsive enough for solution of typical engineering problems.

Alexey Milenin, Elena Velikoivanenko, Galina Rozynka, Nina Pivtorak

Actual Problems of Structural Integrity Assessment of WWER-1000 Pressure Vessel Internals

The problem of numerical prediction of the process of radiation swelling in internal elements for assessment of structural integrity and prolonging the lifetime of the WWER-1000 reactors is quite actual. The critical element is core baffle, which is operating under high gradients of neutron irradiation and temperature. The influence of features of various fuel campaigns and their sequence on the distribution and the maximum value of radiation swelling, as well as, on stresses and distortions in the baffle after long-term service. The consequences of a possible decrease in the efficiency of cooling on the external surface of the baffle in the event of a gap closing between the barrel and the baffle due to radiation swelling or prediction tolerances are reviewed. According to result of modeling the recommendation for numerical assessment of residual life of internal baffle WWER-1000 reactor are formulated.

O. V. Makhnenko, S. M. Kandala

Vibration of Titanium Blades of Turbomachines for Nuclear Power Plants with Erosive Damage

The influence of erosion damages on the vibration features of the working titanium blades of the last stage of the steam turbine with a capacity of 1 GW for a nuclear power plant is considered. Erosion damages of these blades were observed after 180 thousand hours of operation. Morphological and fractographic studies have shown the nature of erosion damages, but did not reveal degradation of the mechanical properties of the material. Such damages cause the stress concentration, that leading to a decrease of fatigue limit and residual life. A finite element model of the blade has been developed, which has a denser mesh in the area of damage. Numerical studies have revealed features of stress concentration in the damages zone. The degree of reduction of blade fatigue and residual life is determined. It is shown that mechanical treatment of the erosion damage zones allows to increase the fatigue limit and residual resource.

Yurii Vorobiov, Oleg Makhnenko, Nataliia Ovcharova, Anton Olkhovskyi

Influence of Residual Stresses in the Cladding Zones of RPV WWER-1000 on Integrity Assessment

One of the current problems of the structural integrity assessment of the reactor pressure vessel WWER-1000 is the determination of resistance to brittle fracture taking into account the residual stresses after cladding of the protective anticorrosion layer and heat treatment. Existing data on the residual stresses do not take into account possible microstructural transformations in the base material steel 2.5Cr-Mo-V (15H2NMFA). Mathematical modeling of residual stresses taking into account microstructural phase transformations determines a compression stress area in the heat affected zone of the base material as result of martensite formation. These results were confirmed by dilatometric analysis and metallography of the steel 15H2NMFA templates. The evaluation of resistance to brittle fracture under the thermal shock load showed, that calculated compression residual stresses in the base material HAZ reduce value SIF for cracks of a depth up to 7 mm.

Oleh Makhnenko, Elena Kostenevich

Symposium on: “Dynamic Problems in Mechanics of Coupled Fields,” by Roman Kushnir


Damping of Hydroelastic Vibrations of the Plate Using Shunted Piezoelectric Element. Part I: Numerical Model

In this work, we investigate the possibility of using a piezoelectric element connected to an external electric RL-circuit for passive vibrations damping of a cantilevered plate interacting with a quiescent fluid. The behavior of piezoelectric elements is described by the equations of electrodynamics of deformable electroelastic media within the framework of quasi-static approximation. The motion of an ideal fluid in the case of small perturbations is considered in the framework of acoustic approximation. Small strains in a thin plate are determined using the Reisner–Mindlin theory. A mathematical formulation of the problem of electroelasticity elastic body with external electric circuits is based on the Lagrange variational principle, which includes the expression for hydrodynamic pressure. The acoustics equations together with the boundary conditions and the impermeability condition are converted to a weak form using the Bubnov–Galerkin method. The numerical implementation of the problem is carried out using an original approach, which is based on the ANSYS finite element package integrated with the program that implements the algorithm for solving the non-classical eigenvalue problem by the Muller method. This allows us to evaluate the values of the parameters of the external RL-circuit, which could provide the most effective damping of vibrations at a certain frequency.

Sergey Lekomtsev, Dmitrii Oshmarin, Natalya Sevodina

Damping of Hydroelastic Vibrations of the Plate Using Shunted Piezoelectric Element. Part II: Experiment

In this work, we explore the possibilities of passive damping the resonance vibrations of a cantilevered duralumin plate located on the free surface of a quiescent fluid. The harmonic excitation with a specified frequency is provided by the electromagnetic field, which is generated under a combined action of a light neodymium magnet attached to the structure and a superposed coil. Passage of the alternating current produced by the generator through the coil generates an electromagnetic force, which oscillates the plate. The oscillations are damped by a piezoelectric element connected to an external passive electric RL-circuit. Measurements of the plate vibrations are taken using a Polytec PDV-100 digital laser vibrometer with a sampling frequency of 48 kHz. The amplitude-frequency characteristics of the plate were obtained from the experimental studies. The values of inductance and resistance parameters of the external RL-circuit were selected in such a way as to ensure the most effective damping of the harmonic vibrations of the plate. It was shown that the peak value of the vibration velocity can be reduced by 20 times in air environment and by 2.5 times in the case of interaction with fluid.

Maksim Iurlov, Alexander Kamenskikh, Sergey Lekomtsev, Dmitrii Oshmarin

Stationary Dynamic Acoustoelasticity Problems of a Thin Plate in a Perfect Compressible Fluid, Taking into Account the Dissipation of Energy in the Plate and Liquid

We propose the refined equations of motion of the plate and the fluid with additional accounting of the energy dissipation in the material of the plate and fluid based on the Thompson–Kelvin–Voight hysteresis model. These equations are used for the formulation of stationary dynamic problems in the field of acoustoelasticity of thin plates surrounded on both sides by acoustic media, which is represented as a perfect compressible fluid. Refinement of fluid behavior is based on the assumption that the pressure increment in fluid is proportional not only to volumetric deformation, but also to its velocity. This assumption allows us to obtain the generalized Helmholtz wave equation by introducing into consideration the complex velocity of sound according to the representation of Skudrzyk to account for energy dissipation. The equations of the plate motion are based on the classical Kirchhoff-Love model.

V. N. Paimushin, R. K. Gazizullin, D. V. Tarlakovskii

Dynamics and Elastic Stability of an Electrostatically Actuated Microbeam Under Ultrafast Laser Pulse

Laser-induced vibrations and elastic stability of a clamped-clamped beam electrostatic transducer are considered under ultrafast laser pulse. It is assumed that laser pulse acts as volume heat generation with Gaussian time-profile localized in near-surface layer of the beam. Temperature load non-stationarity and non-homogeneity through length and thickness lead to appearance of thermal-induced mechanical moment and axial forced acting on the beam, which can result in buckling phenomena. Semi-analytical methods for solution of nonlinear boundary-value problems are used for static equilibrium determination of the beam in the electric field of one stationary electrode. Analytical solution of non-stationary temperature problem in the beam volume is obtained. Finally, areas in parameter space of system geometrical and mechanical properties along with laser pulse characteristics are determined which correspond to elastic stability of initial equilibrium form of the beam subjected to laser pulse.

A. V. Lukin, D. A. Indeitsev, I. A. Popov, O. V. Privalova, L. V. Shtukin


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