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1
UBRIACO, MARCELO R. "QUANTUM DEFORMATIONS OF QUANTUM MECHANICS." Modern Physics Letters A 08, no. 01 (January 10, 1993): 89–96. http://dx.doi.org/10.1142/s0217732393000106.
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Based on a deformation of the quantum mechanical phase space we study q-deformations of quantum mechanics for qk=1 and 0<q<1. After defining a q-analog of the scalar product on the function space we discuss and compare the time evolution of operators in both cases. A formulation of quantum mechanics for qk=1 is given and the dynamics for the free Hamiltonian is studied. For 0<q<1 we develop a deformation of quantum mechanics and the cases of the free Hamiltonian and the one with a x2-potential are solved in terms of basic hypergeometric functions.
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Armstrong, Ronald W. "Bertram Hopkinson's pioneering work and the dislocation mechanics of high rate deformations and mechanically induced detonations." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 372, no. 2015 (May 13, 2014): 20130181. http://dx.doi.org/10.1098/rsta.2013.0181.
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Bertram Hopkinson was prescient in writing of the importance of better measuring, albeit better understanding, the nature of high rate deformation of materials in general and, in particular, of the importance of heat in initiating detonation of explosives. This report deals with these subjects in terms of post-Hopkinson crystal dislocation mechanics applied to high rate deformations, including impact tests, Hopkinson pressure bar results, Zerilli–Armstrong-type constitutive relations, shock-induced deformations, isentropic compression experiments, mechanical initiation of explosive crystals and shear banding in metals.
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Liu, Chuanbo, Chengqing Yuan, and Shutian Liu. "The Effect of Intrinsic Mechanical Properties on Reducing the Friction-Induced Ripples of Hard-Filler-Modified HDPE." Polymers 15, no. 2 (January 4, 2023): 268. http://dx.doi.org/10.3390/polym15020268.
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Ripple deformations induced by friction on polymeric materials have negative effects on the entire stability of operating machineries. These deformations are formed as a response to contacting mechanics, caused by the intrinsic mechanical properties. High-density polyethylene (HDPE) with varying silicon nitride (Si3N4) contents is used to investigate different ripple deformation responses by conducting single-asperity scratch tests. The relationship between the intrinsic mechanical properties and the ripple deformations caused by filler modifications is analyzed in this paper. The results show the coupling of the inherent mechanical properties, and the stick-slip motion of HDPE creates ripple deformations during scratching. The addition of the Si3N4 filler changes the frictional response; the filler weakens the ripples and almost smoothens the scratch, particularly at 4 wt.%, but the continued increase in the Si3N4 content produces noticeable ripples and fluctuations. These notable differences can be attributed to the yield and post-yield responses; the high yield stress and strain-hardening at 4 wt.% provide good friction resistance and stress distribution, thus a smooth scratch is observed. In contrast, increasing the filler content weakens both the yield and post-yield responses, leading to deformation. The results herein reveal the mechanism behind the initial ripple deformation, thus providing fundamental insights into universally derived friction-induced ripples.
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Brovko, G. L. "Elements of nonlinear continuum mechanics in the modern theory." Izvestiya MGTU MAMI 9, no. 2-4 (July 20, 2015): 34–43. http://dx.doi.org/10.17816/2074-0530-67114.
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The theoretical advancement in the field of modern nonlinear continuum mechanics is discussed. The paper includes elements of the mathematical apparatus, development of the foundations of a General tensor theory of mechanical processes and their representations, including generalization of concepts of objective derivatives and integrals, concepts of tensor measures of stresses and deformations, new approaches in theory of the resistance of solids to deformation.
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Tsai, M. Y., C. H. Huang, and C. Y. Huang. "Hygrothermal Effect on Deformations of QFN Electronic Packaging." Journal of Mechanics 22, no. 4 (December 2006): 271–79. http://dx.doi.org/10.1017/s1727719100000927.
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AbstractThe hygrothermal-mechanical behavior of a quad flat non-lead (QFN) package without a chip inside is investigated experimentally and numerically. The present study is focused on understanding the effect of the inherent hygrothermal behaviors of epoxy molding compound (EMC) on the deformations of QFN package. Prior to studying the package, the coefficient of moisture expansion for the EMC is measured experimentally. Full-field moiré and Twyman-Green interferometries are used for measuring the real-time in-plane and out-of-plane deformations of the specimen, respectively, under thermal and moisture loading. In addition, the finite element and theoretical analyses are adopted for validating the experimental observations and further understanding the hygrothermal mechanics of the specimen. The coefficient of moisture expansion of the EMC was experimentally obtained to be about 0.2. The experimental results of the full-field deformations of the specimen, due to temperature, moisture and a combination of both, are presented. The experimental observations are validated by the finite element and theoretical analyses. It was observed that the maximum moisture-induced deformation (strain) can be up to as large as 50% of the thermal deformation (strain) caused by ΔT = 50°C for the specimen. As a result, neglecting moisture-induced deformations (strains) would cause the significant amount of error in thermal deformation (strain) measurement of plastic packages. Furthermore, the present study has laid down the fundamental mechanics and approaches for the QFN packaging structural design and analysis in terms of hygrothermal effects.
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Dansereau, Véronique, Jérôme Weiss, Pierre Saramito, and Philippe Lattes. "A Maxwell elasto-brittle rheology for sea ice modelling." Cryosphere 10, no. 3 (July 1, 2016): 1339–59. http://dx.doi.org/10.5194/tc-10-1339-2016.
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Abstract. A new rheological model is developed that builds on an elasto-brittle (EB) framework used for sea ice and rock mechanics, with the intent of representing both the small elastic deformations associated with fracturing processes and the larger deformations occurring along the faults/leads once the material is highly damaged and fragmented. A viscous-like relaxation term is added to the linear-elastic constitutive law together with an effective viscosity that evolves according to the local level of damage of the material, like its elastic modulus. The coupling between the level of damage and both mechanical parameters is such that within an undamaged ice cover the viscosity is infinitely large and deformations are strictly elastic, while along highly damaged zones the elastic modulus vanishes and most of the stress is dissipated through permanent deformations. A healing mechanism is also introduced, counterbalancing the effects of damaging over large timescales. In this new model, named Maxwell-EB after the Maxwell rheology, the irreversible and reversible deformations are solved for simultaneously; hence drift velocities are defined naturally. First idealized simulations without advection show that the model reproduces the main characteristics of sea ice mechanics and deformation: strain localization, anisotropy, intermittency and associated scaling laws.
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Vispute, Devarsh M., Prem K. Solanki, and Yoed Rabin. "Large surface deformation due to thermo-mechanical effects during cryopreservation by vitrification – mathematical model and experimental validation." PLOS ONE 18, no. 3 (March 9, 2023): e0282613. http://dx.doi.org/10.1371/journal.pone.0282613.
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This study presents a simplified thermal-fluids (TF) mathematical model to analyze large surface deformations in cryoprotective agents (CPA) during cryopreservation by vitrification. The CPA deforms during vitrification due to material flow caused by the combined effects of thermal gradients within the domain, thermal contraction due to temperature, and exponential increase in the viscosity of the CPA as it is cooled towards glass transition. While it is well understood that vitrification is associated with thermo-mechanical stress, which might lead to structural damage, those large deformations can lead to stress concentration, further intensifying the probability to structural failure. The results of the TF model are experimentally validated by means of cryomacroscopy on a cuvette containing 7.05M dimethyl sulfoxide (DMSO) as a representative CPA. The TF model presented in this study is a simplified version of a previously presented thermo-mechanics (TM) model, where the TM model is set to solve the coupled heat transfer, fluid mechanics and solid mechanics problems, while the TF model omits further deformations in the solid state. It is demonstrated in this study that the TF model alone is sufficient to capture large-body deformations during vitrification. However, the TF model alone cannot be used to estimate mechanical stresses, which become significant only when the deformation rates become so small that the deformed body practically behaves as an amorphous solid. This study demonstrates the high sensitivity of deformation predictions to variation in material properties, chief among which are the variations of density and viscosity with temperature. Finally, this study includes a discussion on the possibility of turning on and off the TF and TM models in respective parts of the domain, in order to solve the multiphysics problem in a computationally cost-effective manner.
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Tang, Pengbin, Stelian Coros, and Bernhard Thomaszewski. "Beyond Chainmail: Computational Modeling of Discrete Interlocking Materials." ACM Transactions on Graphics 42, no. 4 (July 26, 2023): 1–12. http://dx.doi.org/10.1145/3592112.
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We present a method for computational modeling, mechanical characterization, and macro-scale simulation of discrete interlocking materials (DIM)---3D-printed chainmail fabrics made of quasi-rigid interlocking elements. Unlike conventional elastic materials for which deformation and restoring force are directly coupled, the mechanics of DIM are governed by contacts between individual elements that give rise to anisotropic deformation constraints. To model the mechanical behavior of these materials, we propose a computational approach that builds on three key components. ( a ): we explore the space of feasible deformations using native-scale simulations at the per-element level. ( b ): based on this simulation data, we introduce the concept of strain-space boundaries to represent deformation limits for in- and out-of-plane deformations, and ( c ): we use the strain-space boundaries to drive an efficient macro-scale simulation model based on homogenized deformation constraints. We evaluate our method on a set of representative discrete interlocking materials and validate our findings against measurements on physical prototypes.
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Fares, N. "Effective Mechanical Properties of Composites at Finite Deformations." Journal of Applied Mechanics 60, no. 1 (March 1, 1993): 8–14. http://dx.doi.org/10.1115/1.2900784.
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A new representation theorem for the deformation gradient rate in the presence of cracks and kinematic constraints is presented. This representation theorem uses an extension of the concept of transformation strains to finite deformations. Based on the representation theorem the overall concentration factor was decomposed into contributions from the opening and sliding of cracks and from material nonhomogeneities. Also, inelastic deformations at the microscale were related to those at the macroscale through elastic concentration factors, where it was found that some of the elastic deformation at the microscale may contribute to the macroscale inelastic deformations.
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Frishter, Ludmila. "INFINITESIMAL AND FINITE DEFORMATIONS IN THE POLAR COORDINATE SYSTEM." International Journal for Computational Civil and Structural Engineering 19, no. 1 (March 29, 2023): 204–11. http://dx.doi.org/10.22337/2587-9618-2023-19-1-204-211.
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The deformation problem of elasticity theory with regard to nonlinear deformations is examined. The expressions of deformations through displacements in the orthogonal curvilinear coordinate system are recorded. The relations for finite deformations in cylindrical and polar coordinate systems are derived. Physical relations for finite deformations and corresponding generalized stresses are recorded.
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Kim, Chun Il, and Zhe Liu. "Mechanics of Lipid Membranes under the Influence of Intramembrane Viscosity." Mathematical Problems in Engineering 2019 (April 7, 2019): 1–13. http://dx.doi.org/10.1155/2019/3412129.
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We discuss a continuum-based model describing the deformations of lipid membranes subjected to intramembrane viscosity. Within the frame work of the theory of an elastic surface, the membrane equilibrium equations and the expressions of viscous stress are obtained. The corresponding deformation energy of the membrane is computed via the first and second fundamental form of surface. A compatible linear model is also formulated within the prescription of superposed incremental deformations through which the deformation profiles of the membrane is obtained. It is shown that the intramembrane viscous flow gives rise to straining effects on the membranes. Further, the corresponding dynamic edge conditions reduce to purely elastic boundary conditions in the limit of vanishing viscous effects. Lastly, admissible sets of velocity fields are also examined and are used to formulate membrane shape equations and the associated dynamic boundary conditions.
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Hou, Hang-sheng. "A Study of Combined Asymmetric and Cavitated Bifurcations in Neo-Hookean Material Under Symmetric Dead Loading." Journal of Applied Mechanics 60, no. 1 (March 1, 1993): 1–7. http://dx.doi.org/10.1115/1.2900746.
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A study is given of the deformations of an incompressible body composed of a neo-Hookean material subjected to a uniform, spherically symmetric, tensile dead load. It is based on the energy minimization method using a constructed kinematically admissible deformation field. It brings together the pure homogeneous asymmetric deformations explored by Rivlin (1948, 1974) and the spherically symmetric cavitated deformations analyzed by Ball (1982) in one setting, and, in addition, Hallows nonsymmetric cavitated deformations to compete for a minimum. Many solutions are found and their stabilities examined; especially, the stabilities of the aforementioned asymmetric and cavitated solutions are reassessed in this work, which shows that a cavitated deformation which is stable against the virtual displacements in the spherical form may lose its stability against a wider class of virtual displacements involving nonspherical forms.
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Nawab, Yasir, Frédéric Jaquemin, Pascal Casari, Nicolas Boyard, and Vincent Sobotka. "Evolution of chemical and thermal curvatures in thermoset-laminated composite plates during the fabrication process." Journal of Composite Materials 47, no. 3 (February 22, 2012): 327–39. http://dx.doi.org/10.1177/0021998312440130.
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Residual deformations and stresses formation in the thermoset-laminated composite is a frequently studied subject in the recent years. During fabrication, the laminated composites undergo chemical deformation during cross-linking and thermal deformation while cooling. In thin laminates, due to large displacements and complex evolution of shape, these deformations can only be explained by using nonlinear strain–displacement relationship. In the present article, we calculated together for the first time, the thermal and chemical deformations occurring in carbon/epoxy laminates by considering a nonlinear geometrical approach to understand the evolution of shape and hence residual stresses induced during fabrication process. The effect of fibre fraction on the chemical and thermal deformations is studied as well.
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Arora, Hari, Ria Mitchell, Richard Johnston, Marinos Manolesos, David Howells, Joseph Sherwood, Andrew Bodey, and Kaz Wanelik. "Correlating Local Volumetric Tissue Strains with Global Lung Mechanics Measurements." Materials 14, no. 2 (January 18, 2021): 439. http://dx.doi.org/10.3390/ma14020439.
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The mechanics of breathing is a fascinating and vital process. The lung has complexities and subtle heterogeneities in structure across length scales that influence mechanics and function. This study establishes an experimental pipeline for capturing alveolar deformations during a respiratory cycle using synchrotron radiation micro-computed tomography (SR-micro-CT). Rodent lungs were mechanically ventilated and imaged at various time points during the respiratory cycle. Pressure-Volume (P-V) characteristics were recorded to capture any changes in overall lung mechanical behaviour during the experiment. A sequence of tomograms was collected from the lungs within the intact thoracic cavity. Digital volume correlation (DVC) was used to compute the three-dimensional strain field at the alveolar level from the time sequence of reconstructed tomograms. Regional differences in ventilation were highlighted during the respiratory cycle, relating the local strains within the lung tissue to the global ventilation measurements. Strains locally reached approximately 150% compared to the averaged regional deformations of approximately 80–100%. Redistribution of air within the lungs was observed during cycling. Regions which were relatively poorly ventilated (low deformations compared to its neighbouring region) were deforming more uniformly at later stages of the experiment (consistent with its neighbouring region). Such heterogenous phenomena are common in everyday breathing. In pathological lungs, some of these non-uniformities in deformation behaviour can become exaggerated, leading to poor function or further damage. The technique presented can help characterize the multiscale biomechanical nature of a given pathology to improve patient management strategies, considering both the local and global lung mechanics.
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Zahalak, G. I., V. de Laborderie, and J. M. Guccione. "The Effects of Cross-Fiber Deformation on Axial Fiber Stress in Myocardium." Journal of Biomechanical Engineering 121, no. 4 (August 1, 1999): 376–85. http://dx.doi.org/10.1115/1.2798334.
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We incorporated a three-dimensional generalization of the Huxley cross-bridge theory in a finite element model of ventricular mechanics to examine the effect of nonaxial deformations on active stress in myocardium. According to this new theory, which assumes that macroscopic tissue deformations are transmitted to the myofilament lattice, lateral myofilament spacing affects the axial fiber stress. We calculated stresses and deformations at end-systole under the assumption of strictly isometric conditions. Our results suggest that at the end of ejection, nonaxial deformations may significantly reduce active axial fiber stress in the inner half of the wall of the normal left ventricle (18–35 percent at endocardium, depending on location with respect to apex and base). Moreover, this effect is greater in the case of a compliant ischemic region produced by occlusion of the left anterior descending or circumflex coronary artery (26–54 percent at endocardium). On the other hand, stiffening of the remote and ischemic regions (in the case of a two-week-old infarct) lessens the effect of nonaxial deformation on active stress at all locations (9–32 percent endocardial reductions). These calculated effects are sufficiently large to suggest that the influence of nonaxial deformation on active fiber stress may be important, and should be considered in future studies of cardiac mechanics.
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KOLCHUNOV, VL I. "PLASTICITY MODEL OF REINFORCED CONCRETE STRUCTURES." Building and reconstruction 106, no. 2 (2023): 39–58. http://dx.doi.org/10.33979/2073-7416-2023-106-2-39-58.
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A model of plasticity of reinforced concrete structures is considered, based on on the transformations of the intensity of the “stress-strain” connection by projecting the tensors of this connection, using special transitions for the main angle of deformations, total shear deformations, etc.). At the same time, the modulus of plasticity of concrete, the coefficient of transverse deformations are determined, and complex functions are constructed for linear and angular deformations in sections, taking into account deformation, gradients of deformations during the formation of cracks and stiffness changes. The hypotheses adopted for the calculation model determine the distribution of force flows - blocks for compressed and stretched concrete (first object), "main cracks" from the mechanics of destruction of reinforced concrete, complex functions and a two-cantilever element for modeling the deformation effect of reinforced concrete, developed by the author (second object). Tensile concrete resistance is transferred to the working reinforcement and is modeled using the sum of the average values of the longitudinal and transverse forces, as well as the average reduced coefficient of tension concrete. The "pin (nagel)" effect in the reinforcement crossed by a crack was obtained using the model of the second level of structural mechanics for a reinforcing bar with two pinched ends. The opening of the crack and the shift of the crack edges are simulated. The main force vector in the reinforcement is characterized by the values of longitudinal and transverse displacements (the third object).
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Armstrong, Ronald W., and Qizhen Li. "Dislocation Mechanics of High-Rate Deformations." Metallurgical and Materials Transactions A 46, no. 10 (February 18, 2015): 4438–53. http://dx.doi.org/10.1007/s11661-015-2779-6.
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Maji, Kuntal. "Parametric Study and Optimization of Pulsed Laser Thermal Micro-Forming of Thin Sheets." International Journal of Manufacturing, Materials, and Mechanical Engineering 9, no. 2 (April 2019): 47–61. http://dx.doi.org/10.4018/ijmmme.2019040103.
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This article presents the investigations on deformation behavior in precision forming of thin sheet metal by laser pulses using finite element analysis. The temperature and deformation fields were estimated and analyzed in pulsed laser micro-forming of AISI 304 stainless steel sheet of rectangular and circular shape considering the effects of different process parameters such as laser power, spot diameter and pulse on time. Response surface models based on finite element simulation results were developed to study the effects of the process parameters on deformations for the rectangular and circular workpieces. The amount of deformation was increased with the increase in laser power and pulse on time, and it was decreased with the increase in spot diameter. The effects of pulse frequency and sample size on deformations were also explained. Experiments were conducted on pulsed laser micro-forming of stainless-steel sheet to validate the finite element results. The results of finite element simulations were in good agreement with the experimental results.
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Nardinocchi, Paola, and Luciano Teresi. "The Influence of Initial Stresses on Blood Vessel Mechanics." Journal of Mechanics in Medicine and Biology 03, no. 02 (June 2003): 215–29. http://dx.doi.org/10.1142/s0219519403000739.
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In order to account for the in vivo conditions of blood vessels, we investigate the mechanical behavior of a stressed tube-like membrane when small deformations are superimposed on large deformations: the latter simulate the stretches present in the in vivo arteries while the superimposed deformations account for the small — but essential for the blood propagation — deformations due to the pulsatile nature of the blood flow. Our aim is to discuss how a stress state influence the response of the vessel-blood system.
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Cornelissen, Bo, Bert Rietman, Matthijn de Rooij, and Remko Akkerman. "Tow Mechanics: A Contact Mechanics Approach of Friction in Fibrous Tows during Forming." Key Engineering Materials 504-506 (February 2012): 325–30. http://dx.doi.org/10.4028/www.scientific.net/kem.504-506.325.
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Composites forming processes involve mechanical interactions on the ply, tow, and filament level. The deformations that occur during forming processes are governed by friction between tows and tooling material on the mesoscopic level and consequently between filaments within the tows on the microscopic level. A thorough understanding of the frictional properties of individual filaments is essential to understand and to predict the macroscopic deformations of a fabric during forming. This paper provides a global description of the experimental and modelling approaches to explain the contact friction between fibrous tows and metal tooling material, focusing on contact mechanics at the tow and filament scale.
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Li, Guodong, Qi An, Sergey I. Morozov, Bo Duan, Pengcheng Zhai, Qingjie Zhang, William A. Goddard III, and G. Jeffrey Snyder. "Determining ideal strength and failure mechanism of thermoelectric CuInTe2 through quantum mechanics." Journal of Materials Chemistry A 6, no. 25 (2018): 11743–50. http://dx.doi.org/10.1039/c8ta03837f.
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Agakhanov, Murad, and Elifkhan Agakhanov. "A complex approach to the solution of problems in mechanics of deformable rigid bodies." E3S Web of Conferences 110 (2019): 01071. http://dx.doi.org/10.1051/e3sconf/201911001071.
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There exists an opinion that the modern numerical methods allow to solve practically any problem in mechanics. But it should be noted that both analytical and experimental methods, as before, are urgent, and exactly a complex of methods develops the mechanics of deformable rigid bodies. The statement of a problem in displacements for some possible cases of equivalent substitution of loads allows to formulate necessary and sufficient conditions of existence of an analogy presenting the effect of a forced deformation in the form of the sum of surface and volume forces, the effect of volume forces in the form of the sum of surface forces and forced deformations, the effect of surface forces in the form of the sum of forced deformations and volume forces. The substitution of volume forces for surface loads and forced deformations allows to extend the use of experimental methods and often to solve through an experimental-and theoretical approach the problems, which cannot be solved through other methods. The obtained results are a considerable step in the development of one of the approaches combining experimental, analytical and numerical methods of solution of linear problems in mechanics of deformable rigid bodies.
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Yang, You, Hong Shuai Li, and Yu Xin Huang. "Effect of Cold Rolling on the Microstructure and Mechanical Behaviors of High-Nitrogen and Low-Nickel Alloy." Key Engineering Materials 904 (November 22, 2021): 143–47. http://dx.doi.org/10.4028/www.scientific.net/kem.904.143.
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The effects of different cold rolling deformations on the microstructure and mechanical properties of high nitrogen and low nickel alloys were investigated. The microstructure of high nitrogen alloys with different rolling deformations were characterized by EBSD and TEM. The tensile mechanical properties of the high nitrogen alloys at room temperature were tested. The results showed that the microstructure of the cold rolled high nitrogen alloy with deformation of 0% to 70% shows a twinning process. The twin thickness of the high nitrogen alloy without deformation is micron degree. When the rolling deformation is over 50%, the average thickness of the deformation twin is 23nm. When the rolling deformation increases to 70%, the average thickness of the twin is 14nm. When the rolling deformation increases from 0% to 70%, the cold rolled high nitrogen alloy exhibits high strength (1001-2236 MPa) and excellent plasticity (5.9%-64.1%). It is beneficial to have a good combination of strength and plasticity after rolling deformation.
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Sajadian, Melika, Ana Teixeira, Faraz S. Tehrani, and Mathias Lemmens. "Predicting land deformation by integrating InSAR data and cone penetration testing through machine learning techniques." Proceedings of the International Association of Hydrological Sciences 382 (April 22, 2020): 525–29. http://dx.doi.org/10.5194/piahs-382-525-2020.
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Abstract. Built environments developed on compressible soils are susceptible to land deformation. The spatio-temporal monitoring and analysis of these deformations are necessary for sustainable development of cities. Techniques such as Interferometric Synthetic Aperture Radar (InSAR) or predictions based on soil mechanics using in situ characterization, such as Cone Penetration Testing (CPT) can be used for assessing such land deformations. Despite the combined advantages of these two methods, the relationship between them has not yet been investigated. Therefore, the major objective of this study is to reconcile InSAR measurements and CPT measurements using machine learning techniques in an attempt to better predict land deformation.
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Michaels, T. C. T., R. Kusters, A. J. Dear, C. Storm, J. C. Weaver, and L. Mahadevan. "Geometric localization in supported elastic struts." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 475, no. 2229 (September 2019): 20190370. http://dx.doi.org/10.1098/rspa.2019.0370.
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Localized deformation patterns are a common motif in morphogenesis and are increasingly finding applications in materials science and engineering, in such instances as mechanical memories. Here, we describe the emergence of spatially localized deformations in a minimal mechanical system by exploring the impact of growth and shear on the conformation of a semi-flexible filament connected to a pliable shearable substrate. We combine numerical simulations of a discrete rod model with theoretical analysis of the differential equations recovered in the continuum limit to quantify (in the form of scaling laws) how geometry, mechanics and growth act together to give rise to such localized structures in this system. We find that spatially localized deformations along the filament emerge for intermediate shear modulus and increasing growth. Finally, we use experiments on a 3D-printed multi-material model system to demonstrate that external control of the amount of shear and growth may be used to regulate the spatial extent of the localized strain texture.
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Bagrii, O. V. "Plane problem of discrete environment mechanics." Problems of Tribology 27, no. 2/104 (June 25, 2022): 104–11. http://dx.doi.org/10.31891/2079-1372-2022-104-2-104-111.
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Many engineering problems related to the design of structures and machines, the mathematical description of technological processes, etc., are reduced to the need to solve a plane problem for materials with a significant effect of internal friction on their deformation. Such materials include a large class of materials in which the compressive strength is greater than tensile. These are composite materials, concretes, rocks, soils, granular, loose, highly fractured materials, as well as structurally heterogeneous materials in which rigid and strong particles are interconnected by weaker layers. The laws of deformation and destruction of such materials differ significantly from elastic ones. A feature of these laws is an increase in resistance to shear deformations and an increase in the strength of materials with an increase in the magnitude of compressive stresses. This is associated with the influence of internal Coulomb friction on the process of their deformation in the limiting and boundary stages.
The need to formulate and solve a special boundary value problem for materials with significant internal friction is because the results of solving problems using models of elasticity and plasticity differ significantly from experimental data. The difference increases when approaching the limiting state of discrete materials and depends significantly on the structure of the material and operating conditions.
The boundary value problem of the mechanics of a deformable solid is formulated as a system of equations of three types: static, geometric, and physical. For all linear and physically nonlinear problems, provided the deformations are small, the first two groups of equations remain the same. Thus, these differences can be attributed to the inconsistency of the accepted in the calculations of physical relations "stress - strain" and the real laws of deformation of these materials, which are more complex rheological objects than structurally homogeneous solids, liquids or gases.
The article uses an approach where the material is immediately considered as quasi-continuous, and the physical equations are based on the experimentally obtained relationships between the invariants of the stress and strain tensors, which consider the influence of both molecular connectivity and internal Coulomb friction.
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Bakushev, Sergey V. "Differential equations of continuum equilibrium for plane deformation in cartesian axials at biquadratic approximation of closing equations." Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mekhanika, no. 76 (2022): 70–86. http://dx.doi.org/10.17223/19988621/76/6.
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The subject under analysis is construction of differential equations of equilibrium in displacements for plane deformation of physically and geometrically nonlinear continuous media when the closing equations are biquadratically approximated in a Cartesian rectangular coordinate system. Proceeding from the assumption that, generally speaking, the diagrams of volume and shear deformation are independent from each other, six main cases of physical dependences are considered, depending on the relative position of the break points of biquadratic diagrams of volume and shear deformation. Construction of physical dependencies is based on the calculation of the secant module of volume and shear deformation. When approximating the graphs of volume and shear deformation diagrams using two segments of parabolas, the secant shear modulus in the first segment is a linear function of the intensity of shear deformations; the secant modulus of volume expansion-contraction is a linear function of the first invariant of the strain tensor. In the second section of the diagrams of both volume and shear deformation, the secant shear modulus is a fractional (rational) function of the intensity of shear deformations; the secant modulus of volume expansion-contraction is a fractional (rational) function of the first invariant of the strain tensor. The obtained differential equations of equilibrium in displacements can be applied in determining the stress-strain state of physically and geometrically nonlinear continuous media under plane deformation the closing equations of physical relations for which are approximated by biquadratic functions.
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SHALYT-MARGOLIN, A. E. "NON-UNITARY AND UNITARY TRANSITIONS IN GENERALIZED QUANTUM MECHANICS, NEW SMALL PARAMETER AND INFORMATION PROBLEM SOLVING." Modern Physics Letters A 19, no. 05 (February 20, 2004): 391–403. http://dx.doi.org/10.1142/s0217732304013155.
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Quantum Mechanics of the Early Universe is considered as deformation of a well-known Quantum Mechanics. Similar to previous works of the author, the principal approach is based on deformation of the density matrix with concurrent development of the wave function deformation in the respective Schrödinger picture, the associated deformation parameter being interpreted as a new small parameter. It is demonstrated that the existence of black holes in the suggested approach in the end twice causes non-unitary transitions resulting in the unitarity. In parallel this problem is considered in other terms: entropy density, Heisenberg algebra deformation terms, respective deformations of Statistical Mechanics — all showing the identity of the basic results. From this an explicit solution for Hawking's information paradox has been derived.
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Cherepanov, G. P. "Supercritical deformations." Strength of Materials 17, no. 8 (August 1985): 1029–36. http://dx.doi.org/10.1007/bf01533779.
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Xiao, H., O. T. Bruhns, and A. Meyers. "Elastoplasticity beyond small deformations." Acta Mechanica 182, no. 1-2 (March 2006): 31–111. http://dx.doi.org/10.1007/s00707-005-0282-7.
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Delhaye, Benoit, Philippe Lefèvre, and Jean-Louis Thonnard. "Dynamics of fingertip contact during the onset of tangential slip." Journal of The Royal Society Interface 11, no. 100 (November 6, 2014): 20140698. http://dx.doi.org/10.1098/rsif.2014.0698.
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Through highly precise perceptual and sensorimotor activities, the human tactile system continuously acquires information about the environment. Mechanical interactions between the skin at the point of contact and a touched surface serve as the source of this tactile information. Using a dedicated custom robotic platform, we imaged skin deformation at the contact area between the finger and a flat surface during the onset of tangential sliding movements in four different directions (proximal, distal, radial and ulnar) and with varying normal force and tangential speeds. This simple tactile event evidenced complex mechanics. We observed a reduction of the contact area while increasing the tangential force and proposed to explain this phenomenon by nonlinear stiffening of the skin. The deformation's shape and amplitude were highly dependent on stimulation direction. We conclude that the complex, but highly patterned and reproducible, deformations measured in this study are a potential source of information for the central nervous system and that further mechanical measurement are needed to better understand tactile perceptual and motor performances.
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Chen, Jingrun, and Pingbing Ming. "An Efficient Multigrid Method for Molecular Mechanics Modeling in Atomic Solids." Communications in Computational Physics 10, no. 1 (July 2011): 70–89. http://dx.doi.org/10.4208/cicp.270910.131110a.
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AbstractWe propose a multigrid method to solve the molecular mechanics model (molecular dynamics at zero temperature). The Cauchy-Born elasticity model is employed as the coarse grid operator and the elastically deformed state as the initial guess of the molecular mechanics model. The efficiency of the algorithm is demonstrated by three examples with homogeneous deformation, namely, one dimensional chain under tensile deformation and aluminum under tension and shear deformations. The method exhibits linear-scaling computational complexity, and is insensitive to parameters arising from iterative solvers. In addition, we study two examples with inhomogeneous deformation: vacancy and nanoindentation of aluminum. The results are still satisfactory while the linear-scaling property is lost for the latter example.
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Travush, Vladimir, and Vasily Murashkin. "CONCRETE DEFORMATION MODEL FOR RECONSTRUCTED REINFORCED CONCRETE." International Journal for Computational Civil and Structural Engineering 18, no. 4 (December 28, 2022): 132–37. http://dx.doi.org/10.22337/2587-9618-2022-18-4-132-137.
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During the reconstruction, or upon expiration of the service life, as well as after external impact, reinforced concrete structures require examination and verification calculations. Existing diagrams of concrete deformation are focused on designing new structures and are not adapted to the concretes of the reconstructed structures. Using the world experience in describing alloy deformation, the concrete deformation model based on using the Arrhenius equation is proposed in this article. A technique for creating an individual deformations model during the reconstruction is demonstrated on a specific example. The physical meaning of the coefficients used in the proposed model is illustrated. Examples confirming the adequacy of the proposed concrete deformations model during the reconstruction are given.
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Chandra, Names. "Mechanics of Superplastic Deformations at Atomic Scale." Materials Science Forum 304-306 (February 1999): 411–20. http://dx.doi.org/10.4028/www.scientific.net/msf.304-306.411.
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Potluri, Prasad, Raj Ramgulam, Marco Chilo, and Haseeb Arshad. "Tow-Scale Mechanics for Composite Forming Simulations." Key Engineering Materials 504-506 (February 2012): 255–60. http://dx.doi.org/10.4028/www.scientific.net/kem.504-506.255.
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Abstract. Composites are processed by a variety of forming techniques at both preforming and consolidation stages; ranging from hand draping, diaphragm forming, vacuum infusion to Resin Transfer Molding. During these processes, individual fabric or prepreg layers are subjected to inplane tension and shear, inter-ply shear, transverse compression and out-of-plane bending forces. These forming forces are translated into individual tow-level forces leading to tow deformations. Each tow is subjected to tension, transverse compaction (in the plane of the fabric due to shear and normal to the fabric plane due to consolidation force), bending and torsion. The resulting tow geometry and local fibre volume fractions (within a tow) would have a significant impact on resin flow as well as mechanical properties of the composite. In this paper, we present computational as well as experimental approaches to predicting tow deformations, when subjected to various loading conditions. The test rigs, shown in figure 1, can measure stress-strain behaviour of a tow in bending, torsion and transverse compression respectively. Figure shows buckling of carbon tow – bending stiffness can be computed from the post-buckling behavior. Torsional moments at monotonically increased twist angle were measured using a very sensitive torque sensor. An anvil, nearly same size as a tow, is used to compress a tow (under controlled axial tension) and the cross-sectional shape is computed from the flattened image (recorded using a high resolution camera). A mechanics-based model has been developed to predict tow-scale deformations under transverse compression, tension, bending and torsion modes of deformation. Individual fibres in a tow are modeled as ‘3D elastica’ and a simple inter-fibre friction model has been incorporated. Initially developed for twisted fibre bundles, the elastic-based model works reasonably well for untwisted fibre tows (by assuming an extremely small twist level for convergence). Full paper will present comparison between experimental and theoretical results.
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Kirby, JM, and BG Blunden. "Interaction of soil deformations, structure and permeability." Soil Research 29, no. 6 (1991): 891. http://dx.doi.org/10.1071/sr9910891.
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Soil deformations, structure and permeability are linked in consistent and qualitatively predictable ways. The critical state concept of soil mechanics provides a useful framework for the description of deformations and the changes in structure and permeability in agricultural operations. Changes in structure are limited until yield (the onset of permanent deformation) occurs either in uniaxial compression or shear. Following yield, changes are more pronounced and may be expansive or compressive. Expansion during shear is accompanied by localised zones of aligned fabric, while compression during shear results in more general rearrangement of structure. Uniaxial compression and compression during shear both result in decreases to permeability. Expansion during shear leads to increases or decreases in permeability, depending on the initial structure. In all cases, shearing appears to cause a change in permeability towards a unique set of relationships among the stresses, void ratio and permeability. Quantitative predictions of changes in structure and permeability resulting from soil deformation cannot be made using current information. Systematic studies of the interaction between soil deformations and structure are required, together with further systematic studies of the interaction between soil deformations and permeability. The critical state concept suggests useful directions in which to explore these interactions.
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Seyed Bolouri, Seyed Ehsan, Chun IL Kim, and Seunghwa Yang. "Linear theory for the mechanics of third-gradient continua reinforced with fibers resistance to flexure." Mathematics and Mechanics of Solids 25, no. 4 (December 16, 2019): 937–60. http://dx.doi.org/10.1177/1081286519893408.
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A linear model, framed in the setting of the second strain gradient theory, is presented for the mechanics of an elastic solid reinforced with fibers resistant to flexure. The kinematics and bending resistance of the fibers are formulated via the second and third gradient of the continuum deformation. The corresponding Euler equations and admissible boundary conditions are then obtained by means of iterated integration by parts and variational principles arising in the third gradient of virtual displacement. In particular, within the prescription of superposed incremental deformations, we derive a compatible linear model from which a complete analytical solution describing the deformations of fiber composites is obtained. The proposed linear model predicts smooth and dilatational shear angle distributions over the domain of interest, which are also aligned with the results obtained from the corresponding nonlinear theory.
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Dursunkaya, Zafer, Rifat Keribar, and Venkatesh Ganapathy. "A Model of Piston Secondary Motion and Elastohydrodynamic Skirt Lubrication." Journal of Tribology 116, no. 4 (October 1, 1994): 777–85. http://dx.doi.org/10.1115/1.2927332.
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A model of elastohydrodynamic lubrication of piston skirts in reciprocating engines was developed in the context of a simulation of piston secondary motions. The piston secondary dynamics, skirt lubrication and skirt elastic deformation problems are simultaneously solved in the calculation. The model can represent both conventional and two-piece articulated pistons and also includes a treatment of wristpin lubrication. Skirt deformations are calculated using a skirt compliance matrix derived from a finite element model of the piston. The model was exercised by calculating piston secondary motions and skirt deformations for a heavy-duty truck diesel piston at various operating conditions. Results show that peak skirt radial deformations can exceed the skirt-liner radial clearance and strongly depend on load. Articulated piston skirt deformations were shown to be significantly larger than those in conventional piston skirts. Consideration of skirt elastic deformations significantly affected (rigid piston) motion and skirt friction predictions, highlighting the importance of an elastohydrodynamic model.
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Harlanov, V. L., and S. V. Harlanova. "INCREMENTAL METHODS FOR SOLVING GEOMETRICALLY NONLINEAR PROBLEMS." STRUCTURAL MECHANICS AND ANALYSIS OF CONSTRUCTIONS, no. 5 (October 30, 2023): 64–69. http://dx.doi.org/10.37538/0039-2383.2023.5.64.69.
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In the sequence of displacement – deformation – stress, two types of nonlinear dependence are possible: geometric and physical. Physically related, mainly with the plastic properties of the material. Geometric nonlinearity is due to a wider range of reasons. Both nonlinearities create a nonlinear displacement-load relationship, which, in most cases, can be expressed by some integral function. In this case, the solution can be obtained by incremental (step) methods. Two incremental methods are considered: the tangential stiffness method and the calculation method using a deformed scheme. The methods are applied to three problems of geometric nonlinearity: 1) small deformations with large displacements, 2) displacements and deformations occur in different directions, 3) large deformations with small displacements. The studies considered both uniaxial stress-strain bars and bars modeled by volumetric elements. Conclusions are drawn about the universality and accuracy of the methods considered.
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Dawson, P. R., and P. S. Follansbee. "The Variable Threshold Rod Experiment: A Comparison of Measured and Computed Deformations." Journal of Engineering Materials and Technology 115, no. 2 (April 1, 1993): 211–19. http://dx.doi.org/10.1115/1.2904209.
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A novel experiment has been developed to induce inhomogeneous deformations under simple extension boundary conditions. By appropriate prior cold working of stock material and fabrication of test specimens with tailored dimensions, the location of the deformation zones along the gage length of tensile specimens was controlled. By design, the deformations were chosen to concentrate either toward the harder or softer ends of the specimens. The experiment provides a sensitive test to judge the ability of constitutive models to replicate the behavior of metals undergoing inhomogeneous deformation. A comparison of experimental results with simulated response using an isotropic state variable model is presented.
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Dawson, P. R., and P. S. Follansbee. "The Variable Threshold Rod Experiment: A Comparison of Measured and Computed Deformations." Journal of Engineering Materials and Technology 115, no. 4 (October 1, 1993): 446–54. http://dx.doi.org/10.1115/1.2904244.
Full textAbstract:
A novel experiment has been developed to induce inhomogeneous deformations under simple extension boundary conditions. By appropriate prior cold working of stock material and fabrication of test specimens with tailored dimensions, the location of the deformation zones along the gage length of tensile specimens was controlled. By design, the deformations were chosen to concentrate either toward the harder or softer ends of the specimens. The experiment provides a sensitive test to judge the ability of constitutive models to replicate the behavior of metals undergoing inhomogeneous deformation. A comparison of experimental results with simulated response using an isotropic state variable model is presented.
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de Loubens, C., J. Deschamps, F. Edwards-Levy, and M. Leonetti. "Tank-treading of microcapsules in shear flow." Journal of Fluid Mechanics 789 (January 26, 2016): 750–67. http://dx.doi.org/10.1017/jfm.2015.758.
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We investigated experimentally the deformation of soft microcapsules and the dynamics of their membrane in simple shear flows. Firstly, the tank-treading motion, i.e. the rotation of the membrane, was visualized and quantified by tracking particles included in the membrane by a new protocol. The period of membrane rotation increased quadratically with the extension of the long axis. The tracking of the distance between two close microparticles showed membrane contraction at the tips and stretching on the sides, a specific property of soft particles such as capsules. The present experimental results are discussed in regard to previous numerical simulations. This analysis showed that the variation of the tank-treading period with the Taylor parameter (deformation) cannot be explained by purely elastic membrane models. It suggests a strong effect of membrane viscosity whose order of magnitude is determined. Secondly, two distinct shapes of sheared microcapsules were observed. For moderate deformations, the shape was a steady ellipsoid in the shear plane. For larger deformations, the capsule became asymmetric and presented an S-like shape. When the viscous shear stress increased by three orders of magnitude, the short axis decreased by 70 % whereas the long axis increased by 100 % before any break-up. The inclination angle decreased from 40° to 8°, almost aligned with the flow direction as expected by theory and numerics on capsules and from experiments, theory and numerics on drops and vesicles. Whatever the microcapsule size and the concentration of proteins, the characteristic lengths of the shape, the Taylor parameter and the inclination angle satisfy master curves versus the long axis or the normalized shear stress or the capillary number in agreement with theory for non-negligible membrane viscosity in the regime of moderate deformations. Finally, we observed that very small deviation from sphericity gave rise to swinging motion, i.e. shape oscillations, in the small-deformation regime. In conclusion, this study of tank-treading motion supports the role of membrane viscosity on the dynamics of microcapsules in shear flow by independent methods that compare experimental data both with numerical results in the regime of large deformations and with theory in the regime of moderate deformations.
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Vershina, G. A., and L. E. Reut. "Influence of Elastic Core on Size of Ring Product under Bending of Fluoroplastic Band." Science & Technique 18, no. 1 (February 12, 2019): 21–31. http://dx.doi.org/10.21122/2227-1031-2019-18-1-21-31.
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The paper is devoted to study of a possibility to manufacture fluoroplastic products while using method of cold deformation of pressed blanks and research of peculiar features in mechanical behavior of fluoroplastic which are revealed during deformation that affects quality and accuracy of the manufactured parts. Manufacturing technique of fluoroplastic sealing rings which are obtained while using method of coiling a band blank on a cylindrical mandrel with further endurance in a wound state and subsequent cutting of a spiral on rings has been considered in the paper. An important stage in the development of the technological process is a calculation and a design of a tool (mandrel caliber) that ensure obtaining of ring products with the required size and shape. Deformation behavior of fluoroplastic under conditions of force action is significantly different from the behavior of the known classical materials and it has a number of specific features and manifestations. Therefore the problem for creation of a calculation methodology for tool development looks as a complicated one and it requires a justified approach while selecting a mechanical model of polymer. Considering the fact that fluoroplastic has a structure with a high degree of crystallinity, a mechanism and sequence of deformations in it due to load are largely similar to the behavior of metals and other low-molecular materials. It allows to use methods and approaches adopted in the mechanics of solids for a calculation of fluoroplastic products however it is necessary to take into account the fact that deformation processes in polymers proceed in time and have a different nature of elastic and residual deformations. When bending the fluoroplastic band in case of winding it on the mandrel residual deformations which provide the required size and shape play the most significant role. However elastic deformations which cause springing and change of size in a finished product after removal of loading are also important. It has been proved that an elastic zone of finite width which has a certain influence on accuracy of manufactured products with due account of all accumulated elastic deformations will be present in the field of a neutral layer even at high degrees of deformation. In this case, fluoroplastic is a multi-modulus material having elasticity which at stretching is significantly higher than in compression, and therefore elastic recovery is more associated with the area of stretched fibers. The authors have developed a methodology for calculation of the tool for obtaining rings of the required size on the basis of the analysis pertaining to deformation behavior of the fluoroplastic while taking into account specificity of its mechanical properties. The proposed methodology with a sufficient degree of accuracy is consistent with the results of experimental studies.
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Belyaev, A. K., V. A. Polyanskiy, and D. A. Tretyakov. "Estimating of mechanical stresses, plastic deformations and damage by means of acoustic anisotropy." PNRPU Mechanics Bulletin, no. 4 (December 15, 2020): 130–51. http://dx.doi.org/10.15593/perm.mech/2020.4.12.
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Acoustic anisotropy is a consequence of anisotropy of the mechanical characteristics of a solid. In metals, it is associated with microstructural anisotropy of mechanical characteristics, internal mechanical stresses and strains, including residual stresses and plastic deformations. Sensors measuring acoustic anisotropy do not require complex preparations of a metal surface, therefore it is easy to measure which makes it possible for measurement results to be used to quantify stresses and strains in metals based on the magnitude of phase shifts of the shear wave velocities of the orthogonal polarization. Acoustic anisotropy is one of the manifestations of the phenomenon of changes in the elastic properties of an acoustic medium caused by mechanical stresses and deformation (acoustoelastic effect). This makes it possible to use the effect of acoustic anisotropy for the development of quantitative methods of acoustic tensometric measurements, as well as methods of non-destructive testing, which enables effective quality controls and diagnostics of the residual life of structures and machine parts. The article describes the history of the discovery and theoretical substantiation of the acoustoelastic effect and the quantitative relationship of acoustic anisotropy with stresses and deformations, starting with the pioneering works of the twentieth century. The way of forming the theory based on nonlinear mechanics of continuous media is shown. The third part of the article is concerned with an overview of the current state of research. An analysis is presented of experimental works on the measurement of acoustic anisotropy in low- and high-carbon steels, aluminum alloys, as well as in composites and other structural materials. Special attention is paid to a review of studies on the relationship between acoustic anisotropy and plastic deformations and the applicability limitations of the acoustic method. It also provides a list of the main applied results related to the measurement and use of acoustic anisotropy to control the blades of compressors and gas turbine engines, pipe steels, welded joints, etc. A review is given of the main publications on system analysis and generalization of theoretical and experimental scientific results obtained by domestic and foreign researchers in the field of studying the acoustic anisotropy of metallic structural materials under conditions of uniaxial and complex stress states, plastic deformation, thermomechanical loading and fatigue fracture is given.
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Gavini, Vikram. "Role of the defect core in energetics of vacancies." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 465, no. 2110 (August 5, 2009): 3239–66. http://dx.doi.org/10.1098/rspa.2009.0136.
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Electronic structure calculations at macroscopic scales are employed to investigate the crucial role of a defect core in the energetics of vacancies in aluminium. We find that vacancy core energy is significantly influenced by the state of deformation at the vacancy core, especially volumetric strains. Insights from the core electronic structure and computed displacement fields show that this dependence on volumetric strains is closely related to the changing nature of the core structure under volumetric deformations. These results are in sharp contrast to mechanics descriptions based on elastic interactions that often consider defect core energies as an inconsequential constant. Calculations suggest that the variation in core energies with changing macroscopic deformations is quantitatively more significant than the corresponding variation in relaxation energies associated with elastic fields. Upon studying the influence of various macroscopic deformations, which include volumetric, uniaxial, biaxial and shear deformations, on the formation energies of vacancies, we show that volumetric deformations play a dominant role in governing the energetics of these defects. Further, by plotting formation energies of vacancies and di-vacancies against the volumetric strain corresponding to any macroscopic deformation, we find that all variations in the formation energies collapse on to a universal curve. This suggests a universal role of volumetric strains in the energetics of vacancies. Implications of these results in the context of dynamic failure in metals through shock-induced spalling are analysed.
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Wu, C. L., Z. R. Wang, and Wen Zhang. "Research of Formation Mechanics on Nanostructured Chips by Multi-Deformations Based on Finite Element Method." Advanced Materials Research 989-994 (July 2014): 352–55. http://dx.doi.org/10.4028/www.scientific.net/amr.989-994.352.
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Formation of chip is a typical severe plastic deformation progress in machining which is only single deformation stage. The rake angle of tool is governing parameter to create large strain imposed in the chip. Effect of rake angle and deformation times on effective strain, mean strain, strain variety and strain rate imposed in the chip are researched respectively. The result of simulation have shown that the chip with large strain and better uniform of strain along the longitudinal section of chip can be produced with negative rake angle at some lower cutting velocity by multi-deformations in large strain machining.
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Chung, K., and O. Richmond. "The Mechanics of Ideal Forming." Journal of Applied Mechanics 61, no. 1 (March 1, 1994): 176–81. http://dx.doi.org/10.1115/1.2901394.
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In this paper, the mechanics of ideal forming theory are summarized for general, three-dimensional, nonsteady processes. This theory has been developed for the initial stages of designing deformation processes. The objectives is to directly determine configurations, both initial and intermediate, that are required to ideally form a specified final shape. In the proposed theory, material elements are prescribed to deform along minimum plastic work paths, assuming that the materials have optimum formabilities in such paths. Then, the ideal forming processes are obtained so as to have the most uniform strain distributions in final products without shear tractions. As solutions, the theory provides the evolution of intermediate shapes of products and external forces as well as optimum strain distributions. Since the requirement of ideal forming to follow minimum work paths involves an over determination of the field equations, the theory places constraints on constitutive and boundary conditions. For example, tool interfaces must be frictionless and yield conditions must have vertices to achieve self-equilibrating three-dimensional deformations in most cases. Despite these constraints, the theory is believed to provide a useful starting point for deformation process design.
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Kadianakis, Nikos, and Fotios I. Travlopanos. "Infinitesimally affine deformations of a hypersurface." Mathematics and Mechanics of Solids 23, no. 2 (December 21, 2016): 209–20. http://dx.doi.org/10.1177/1081286516680261.
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Affine deformations serve as basic examples in the continuum mechanics of deformable three-dimensional bodies (usually referred to as homogeneous deformations). They preserve parallelism of straight lines, and are often used as an approximation to general deformations. However, when the deformable body is a membrane, a shell or an interface modeled by a surface, parallelism is defined by the affine connection of this surface. In this work we study the infinitesimally affine time-dependent deformations (motions) of such a continuum, but in a more general context, by considering that it is modeled by a Riemannian hypersurface. First we prove certain equivalent formulas for the variation of the connection of the hypersurface. Some of these formulas are expressed in terms of geometrical quantities, and others in terms of kinematical quantities of the deforming continuum. The latter is achieved by using an adapted version of the polar decomposition theorem, frequently used in continuum mechanics to analyze motion. We also apply our results to special motions like tangential and normal motions. Further, we find necessary and sufficient conditions for this variation to be zero (infinitesimal affine motions), providing insight on the form of these motions and the kind of hypersurfaces that allow such motions. Finally, we give some specific examples of mechanical interest which demonstrate motions that are infinitesimally affine but not infinitesimally isometric.
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Wilson, J. F., and G. Orgill. "Linear Analysis of Uniformly Stressed, Orthotropic Cylindrical Shells." Journal of Applied Mechanics 53, no. 2 (June 1, 1986): 249–56. http://dx.doi.org/10.1115/1.3171748.
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Within the framework of classical elasticity, the nonbuckled deformations are calculated for orthotropic, right circular, thin-walled cylinders under uniform load conditions. The principle direction of orthotropy follows parallel constant angle helices. Nondimensional system parameters involving four material constants and three loading conditions (internal pressure, longitudinal load, and pure torque) are identified. Through parametric studies deformation patterns are calculated that are unique to orthotropy. Numerical examples illustrate that the proper selection of cylinder orthotropy can lead to designs with optimal deformations or load-carrying capacity. Results may be used for the design of robotic actuators driven by internal pressure.
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Deng, Jie, Shi Jie Zhou, Han Jun Gao, Ming Hui Lin, and Xin Li. "Numerical Simulation Investigation on Machining Deformation of Aviation Thin-Walled Parts Caused by Residual Stress." Materials Science Forum 1032 (May 2021): 186–91. http://dx.doi.org/10.4028/www.scientific.net/msf.1032.186.
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Holistic thin-walled parts are common structural parts of modern aircraft to reduce the weight and increase the stiffness. Over 90% of the materials are removed from the blank, as a result, large machining deformations occur to the parts, which causes the manufacturing discrepancies and even the scrap parts. In this paper, numerical simulation models are established to predict the machining deformation of two typical aviation thin-walled parts. The blank initial and machining induced residual stresses, as well as the cutting parameters, are considered in the model. The deformations and stresses after machining are calculated using the proposed model, and the deformation and stress distributions are analyzed.