Relevant bibliographies by topics / Macroscopic deformation

Academic literature on the topic 'Macroscopic deformation'

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Published: 22 July 2023

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Journal articles on the topic "Macroscopic deformation"

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Luo, J. J., and I. M. Daniel. "Deformation of Inhomogeneous Elastic Solids With Two-Dimensional Damage." Journal of Applied Mechanics 68, no. 4 (January 1, 2001): 528–36. http://dx.doi.org/10.1115/1.1380384.

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A general correlation is derived between macroscopic stresses/strains and microscopic deformation on the damage surfaces for inhomogeneous elastic solids with two-dimensional damage. Assuming linear elastic behavior for the undamaged materials, the macroscopic deformation associated with nonlinear strains, or damage strains, is shown to be the weighted sum of the microscopic deformations on the damage surfaces. For inhomogeneous materials with periodic structures (laminated composites, for example) and various identifiable damage modes, simple relations are derived between the macroscopic deformation and microscopic damage. When the number of identifiable damage modes is less than or equal to the number of relevant measurable macroscopic strains, the correlation can be used to evaluate the damage progression from simple macroscopic stress and strain measurements. The simple case of a unidirectional fiber-reinforced composite under longitudinal load is used to show how the results can help detect and characterize the damage using macroscopic measurements, without resorting to assumptions of detailed microscopic deformation mechanisms.
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Woodward, Nicholas B. "Competitive macroscopic deformation processes." Journal of Structural Geology 21, no. 8-9 (August 1999): 1209–18. http://dx.doi.org/10.1016/s0191-8141(99)00076-0.

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Aero, E. L. "Essentially nonlinear theory of microdeformations in medium with periodic structure." Theoretical and Applied Mechanics, no. 28-29 (2002): 1–26. http://dx.doi.org/10.2298/tam0229001a.

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Essentially nonlinear theory of micro and macro deformations of a medium with cardinally rearranging periodic structure is presented using a new model of double continuum with variable local topology. In a frame of proposed model there are two deformation modes (macroscopic and microscopic) when some threshold is reached. Some problems such as twin transitions, catastrophic deformation waves, shock and tilting bifurcation waves are considered. An exact solution describing elasto plastic fragmentation of medium is constructed also when double periodic domain superstructure are formed. There are solid rotons of opposite signs with singular defects between them. They appear in a critical field of macroscopic deformations of pure shear. When this bifurcation point is overcome then dimensions of domains are stabilized. The letter depend on value of macroscopic deformations. Some criterion of global stability is established. .
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Speich, Marco, Wolfgang Rimkus, Markus Merkel, and Andreas Öchsner. "Large Deformation of Metallic Hollow Spheres." Materials Science Forum 623 (May 2009): 105–17. http://dx.doi.org/10.4028/www.scientific.net/msf.623.105.

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Hollow sphere structures are a new group of advanced lightweight materials for multifunctional applications. Within the scope of this paper, the uniaxial deformation behaviour in the regime of large deformations is investigated. Appropriate computational models are developed to account for the deformation mechanisms occurring under high deformations. Macroscopic stress-strain curves are derived and the influence of different material parameters is investigated.
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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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Zaiser, Michael. "Random aspects of macroscopic plastic deformation." Philosophical Magazine Letters 73, no. 6 (June 1996): 369–76. http://dx.doi.org/10.1080/095008396180641.

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Taniguchi, Akito, Takatoshi Maeyama, Makoto Uchida, and Yoshihisa Kaneko. "Macroscopic and Microscopic Non-Uniform Deformations of Polycrystalline Pure Copper during Uniaxial Tensile Test with High Stress Gradient." Key Engineering Materials 794 (February 2019): 246–52. http://dx.doi.org/10.4028/www.scientific.net/kem.794.246.

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Metallic materials usually have microscopically heterogeneous structures, such as polycrystalline structures, affecting macroscopic mechanical characteristics. Both macroscopic and microscopic non-uniform deformations of polycrystalline pure copper under a moderate stress gradient were investigated. In this study, macroscopic and microscopic non-uniform deformations under higher stress gradients are investigated. Uniaxial tensile tests using three-curve specimens with different curvatures and grain sizes were performed. In order to evaluate the heterogeneous strain field in the specimen surface, the development of the displacement field was measured using the digital image correlation method (DIC). The stress field was evaluated by coupling the DIC and finite-element methods. In smaller-grain specimens, a strong strain concentration was generated in the minimum cross-section area. Although a strong strain concentration was also confirmed in a larger-grain specimen, the strain field depended not only on the specimen shape but also on the microscopic heterogeneity. This microstructure-driven non-uniform deformation was also observed in the specimen with a larger curvature radius. These results indicated that the macroscopic non-uniform deformation should be estimated by the material parameter related to the microscopic heterogeneity.
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MOHAMMED-AZIZI, B. "NUMERICAL APPROACH OF THE MICROSCOPIC–MACROSCOPIC METHOD." International Journal of Modern Physics C 21, no. 05 (May 2010): 681–94. http://dx.doi.org/10.1142/s0129183110015415.

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A numerical method close to the Strutinsky procedure (but better) is proposed to calculate the deformation energy of nuclei. Quadrupole (triaxial) deformations are considered. Theoretical as well as practical aspects of the method are reviewed in this paper. A complete FORTRAN program illustrates the feasibility of the method. The numerical method employed in this paper avoids the main drawback of the Strutinsky method, that is to say the well known dependency of the results on the inherent two free parameters.
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Xu, Jiankun, Rui Zhou, Dazhao Song, Nan Li, Kai Zhang, and Danyang Xi. "Deformation and damage dynamic characteristics of coal–rock materials in deep coal mines." International Journal of Damage Mechanics 28, no. 1 (November 15, 2017): 58–78. http://dx.doi.org/10.1177/1056789517741950.

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The deformation and damage characteristics of surrounding rock grow gradually with the increase of mining depth, and the mechanical behavior and damage mechanism of coal–rock materials vary greatly. In order to reveal the deformation and damage dynamic characteristics of coal–rock materials in deep mines, the macroscopic deformation characteristics of coal, rock, and concrete samples under uniaxial compression were studied. The macroscopic deformation amount, velocity, and acceleration of different samples were analyzed. The coal and rock samples exhibit regular dynamic characteristics before they lose stability and fail. The axial strain response of the coal samples changes significantly during the compact and elastic deformation stages. Besides, the relationship between the surface damage and the macroscopic deformation of sample was studied by means of visualization and image processing. The macroscopic deformation index of coal–rock materials changes significantly before and after the destabilization and failure. Based on the deformation and failure dynamic characteristics of coal and rock, the evolution rule of deformation critical values was taken as the deformation and destruction stages, which revealed the dynamic characteristics during the deformation and failure process of coal–rock materials in deep mines. The deformation critical values can be used to realize early warning of deformation and fracture of coal and rock materials in deep mines.
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GHERGHESCU, R. A., D. N. POENARU, M. RAPORTARU, B. POPOVICI, and W. GREINER. "CHARGE DENSITY INFLUENCE ON MACROSCOPIC DEFORMATION ENERGY." International Journal of Modern Physics E 19, no. 07 (July 2010): 1411–23. http://dx.doi.org/10.1142/s0218301310015825.

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A formula describing the proton density dependence on macroscopic deformation energy for different fusion-like shape configurations is derived. As a consequence, the influence of intermediary atomic numbers of fusioning nuclei on the macroscopic deformation-dependent terms of the potential energy in the Yukawa-plus-exponential model is studied. For the same target–projectile pair, at the same distance between their centers, macroscopic fusion barriers differ by energy amounts up to 5 MeV.
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Dissertations / Theses on the topic "Macroscopic deformation"

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Beveridge, A. J. "Novel computational methods to predict the deformation of macroscopic heterogeneous materials." Thesis, University of Strathclyde, 2011. http://oleg.lib.strath.ac.uk:80/R/?func=dbin-jump-full&object_id=15972.

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Maßhoff, Philipp [Verfasser], and Stefan U. [Akademischer Betreuer] Egelhaaf. "Colloidal Spheres under Shear: The Interplay between Macroscopic Deformation and Microscopic Properties / Philipp Maßhoff ; Betreuer: Stefan U. Egelhaaf." Düsseldorf : Universitäts- und Landesbibliothek der Heinrich-Heine-Universität Düsseldorf, 2020. http://d-nb.info/1203872372/34.

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Phan, Van Tung [Verfasser], and T. [Akademischer Betreuer] Böhlke. "Modeling the mesoscopic and macroscopic deformation behavior of the ferritic stainless steel DC04 / Tung Phan Van. Betreuer: T. Böhlke." Karlsruhe : KIT-Bibliothek, 2012. http://d-nb.info/1020663561/34.

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Willeman, Héloïse. "Multi-scale characterization of deformation mechanisms of poly-ether-ether-ketone (PEEK) under tensile stretching." Electronic Thesis or Diss., Lyon, INSA, 2023. http://www.theses.fr/2023ISAL0006.

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L’objectif de cette thèse est d’établir le scénario multi-échelles de déformation du PEEK lorsqu’il est sollicité en traction uniaxiale. Préalablement à la mise en oeuvre d’échantillons de deux grades commerciaux de PEEK, les propriétés thermiques et mécaniques de ces matériaux ont été caractérisées. La température d’oubli thermodynamique ainsi que la sensibilité aux vitesses de refroidissement ont été établies. Des éprouvettes de traction ont été obtenues à partir de plaques thermocompressées, procédé choisi pour obtenir des morphologies les plus isotropes possibles. Les propriétés mécaniques en traction ont ensuite été caractérisées au-dessus et au-dessous de la transition vitreuse de la phase amorphe (Tg). Grâce à un dispositif expérimental fabriqué sur mesure, des essais de traction à deux températures distinctes au-dessous et au-dessus de Tg ont été suivis par diffusion des rayons X aux petits (SAXS) et grands angles (WAXS) pour caractériser les déformations à l’échelle des empilements lamellaires et à l’échelle de la maille cristalline. Simultanément, le champ de déformation a été mesurée par corrélation d’images (DIC) afin de comparer la déformation macroscopique et microscopique. Pour les deux températures, les lamelles tendent à s’orienter perpendiculairement à la direction de traction (TD). Ce mécanisme d’orientation local (que nous appelons « modèle de réseau de chaînes ») est induit par la transmission des contraintes par les chaînes amorphes reliant les lamelles cristallines adjacentes. Au-dessus de Tg, l’allongement local est plus faible que l’allongement macroscopique dans les lamelles perpendiculaire à TD, ce qui implique que les lamelles inclinées doivent être cisaillées. L’évolution de la distribution d’orientation des lamelles appuie ce résultat. Une morphologie fortement orientée est finalement obtenue quelle que soit la température. Cependant, le profil d’endommagement est différent. En-dessous de Tg, le profil de diffusion centrale indique l’existence de petites entités (lamelles ou crystallites) orientées aléatoirement. A hautes température, le matériau est fibrillaire et présente des cavités
The aim of this PhD work is accessing the microscopic deformation mechanisms of bulk poly-ether-ether-ketone (PEEK) under tensile stretching. Beforehand, the thermal and mechanical properties of two commercial grades of PEEK were characterized. Tensile specimens were then compression-molded to obtain morphologies as isotropic as possible and characterized below and above the glass transition temperature. Deformations at the scales of lamellar stacks and of the crystalline unit cell have been characterized by small and wide-angle X-ray scattering (SAXS and WAXS) performed in-situ during tensile tests. Simultaneously, the strain field within the samples was followed by digital image correlation (DIC) in order to compare microscopic and macroscopic strains. At both temperatures, lamellae tend to orient perpendicular to the tensile direction (TD). This orientation mechanism (which we denote as ‘Chain Network model’) is driven by the amorphous chains which transmit the stress between adjacent lamellae. The tensile strain in lamellar stacks perpendicular to TD is lower than the macroscopic tensile strain, which must be compensated by increased shear in inclined stacks. Some differences of behavior have been observed depending on the test temperature, especially at high deformation. A highly oriented morphology is ultimately obtained in all cases. However, the central scattering profiles changes with testing temperatures. Below Tg, the presence of small entities randomly oriented is indicated. Above Tg, the material is fibrillar and contains cavities
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Ivaneyko, Dmytro, Vladimir Toshchevikov, Marina Saphiannikova, and Gert Heinrich. "Mechanical properties of magneto-sensitive elastomers: unification of the continuummechanics and microscopic theoretical approaches." Royal Society of Chemistry, 2014. https://tud.qucosa.de/id/qucosa%3A36394.

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A new theoretical formalism is developed for the study of the mechanical behaviour of magneto-sensitive elastomers (MSEs) under a uniform external magnetic field. This formalism allows us to combine macroscopic continuum-mechanics and microscopic approaches for complex analysis of MSEs with different shapes and with different particle distributions. It is shown that starting from a model based on an explicit discrete particle distribution one can separate the magnetic field inside the MSE into two contributions: one which depends on the shape of the sample with finite size and the other, which depends on the local spatial particle distribution. The magneto-induced deformation and the change of elastic modulus are found to be either positive or negative, their dependences on the magnetic field being determined by a non-trivial interplay between these two contributions. Mechanical properties are studied for two opposite types of coupling between the particle distribution and the magneto-induced deformation: absence of elastic coupling and presence of strong affine coupling. Predictions of a new formalism are in a qualitative agreement with existing experimental data.
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Orliac, Jean-Guillaume. "Analyse et simulation du comportement anisotrope lors de la mise en forme de renforts tissés interlock." Phd thesis, INSA de Lyon, 2012. http://tel.archives-ouvertes.fr/tel-00823359.

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Afin de pouvoir prédire le comportement des renforts de composites 3D interlock au cours d'un procédé de mise en forme, il est nécessaire de connaitre la position des mèches dans le renfort durant la phase de préformage du procédé. Les travaux présentés ici traitent de la simulation du préformage de renforts 3D épais à l'aide d'un élément fini hexaédrique semi-discret spécifique. En utilisant le principe des travaux virtuels, on distingue le travail interne virtuel dû à la tension des mèches des autres travaux virtuels. La raideur due aux tensions de mèches, qui constitue la contribution principale de la rigidité du matériau, est prise en compte à l'aide de barres incluses dans les éléments. Les rigidités dues aux autres sollicitations, comme la compression transverse, les cisaillements ou les frottements inter-mèches, sont décrites par un matériau continu additionnel. La combinaison de ce modèle discret du premier ordre et d'un matériau continu hyperélastique anisotrope dit du second ordre, pour formuler le comportement du matériau va permettre la simulation du préformage des renforts tissés épais. Conjointement aux travaux sur la simulation, des travaux expérimentaux pour l'identification des paramètres matériau de la loi de comportement ont été définis et réalisés. Ces paramètres concernent les deux parties de la formulation du comportement.
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Lin, Hung-Yi, and 林弘毅. "The Phenomenal Analysis of Overturn,Deformation and Macroscopic with Assemble Cylinders in the Conveyor Belt Experiment." Thesis, 2006. http://ndltd.ncl.edu.tw/handle/jdht3y.

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碩士
國立中央大學
土木工程研究所
94
This study performs experimental work with cylinders on the conveyor belt to simulate the initial process of landslide induced debris flow.The experimental set up consists of three parts: microscopic overturn deformation and macroscopic fluidization. The kinetic of angular velocity and displacement of the overturn process on the top layer of the cylinders is studied. The change of porosity before and after the overturn is analyzed at different velocities (i.e. 5.08cm/s, 10.16cm/s,15.24 cm/s,20.32 cm/s), and slopes (i.e. 0°, 5°, 10°,15°, 20°),respectively. The particle image algorithm is used to study the deformation on the bottom of the assemble cylinders by shearing force. The change of porosity before and after the failure is analyzed at different velocities (i.e. 4.17cm/s, 12.34cm/s), and slopes (i.e. 0°, 20°). We establish a method to measure the deformation, angular velocity and porosity of particles. The experimental results show that region of the shearing zone increases as the velocity of the conveyor belt, increases. Different belt velocities (i.e. 4.17cm/s, 12.34cm/s) affect the thickness of fluidization, and lead to two opposite results on the decay rate of PVC, and steel layers under the same experimental conditions. The sequence of cylinders flowing out the confined zone is strongly related to the gap clearance. When the gap is raised, the leading side of cylinders will flow out first while the gap becomes low, the tailing side and bottom parts of cylinders will flow out first.
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"Multiscale Modeling of Oxygen Impurity Effects on Macroscopic Deformation and Fatigue Behavior of Commercially Pure Titanium." Doctoral diss., 2018. http://hdl.handle.net/2286/R.I.48476.

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abstract: Interstitial impurity atoms can significantly alter the chemical and physical properties of the host material. Oxygen impurity in HCP titanium is known to have a considerable strengthening effect mainly through interactions with dislocations. To better understand such an effect, first the role of oxygen on various slip planes in titanium is examined using generalized stacking fault energies (GSFE) computed by the first principles calculations. It is shown that oxygen can significantly increase the energy barrier to dislocation motion on most of the studied slip planes. Then the Peierls-Nabbaro model is utilized in conjunction with the GSFE to estimate the Peierls stress ratios for different slip systems. Using such information along with a set of tension and compression experiments, the parameters of a continuum scale crystal plasticity model, namely CRSS values, are calibrated. Effect of oxygen content on the macroscopic stress-strain response is further investigated through experiments on oxygen-boosted samples at room temperature. It is demonstrated that the crystal plasticity model can very well capture the effect of oxygen content on the global response of the samples. It is also revealed that oxygen promotes the slip activity on the pyramidal planes. The effect of oxygen impurity on titanium is further investigated under high cycle fatigue loading. For that purpose, a two-step hierarchical crystal plasticity for fatigue predictions is presented. Fatigue indicator parameter is used as the main driving force in an energy-based crack nucleation model. To calculate the FIPs, high-resolution full-field crystal plasticity simulations are carried out using a spectral solver. A nucleation model is proposed and calibrated by the fatigue experimental data for notched titanium samples with different oxygen contents and under two load ratios. Overall, it is shown that the presented approach is capable of predicting the high cycle fatigue nucleation time. Moreover, qualitative predictions of microstructurally small crack growth rates are provided. The multi-scale methodology presented here can be extended to other material systems to facilitate a better understanding of the fundamental deformation mechanisms, and to effectively implement such knowledge in mesoscale-macroscale investigations.
Dissertation/Thesis
Doctoral Dissertation Mechanical Engineering 2018
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Schmidt, Oleg [Verfasser]. "Macroscopic and microscopic deformation of the piezoelectric Li2SO4.H2O, Li2SeO4.H2O and BiB3O6 crystals under an external electric field / vorgelegt von Oleg Schmidt." 2010. http://d-nb.info/1010568809/34.

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Palla, Murali *. "Multi-Scale Approaches For Understanding Deformation And Fracture Mechanisms In Amorphous Alloys." Thesis, 2007. http://hdl.handle.net/2005/650.

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Amorphous alloys possess attractive combinations of mechanical properties (high elastic limit, ~2%, high fracture toughness, 20-50 MPa.m1/2, etc.) and exhibit mechanical behavior that is different, in many ways, from that of the crystalline metals and alloys. However, fundamental understanding of the deformation and fracture mechanisms in amorphous alloys, which would allow for design of better metallic glasses, has not been established on a firm footing yet. The objective of this work is to understand the deformation and fracture mechanisms of amorphous materials at various length scales and make connections with the macroscopic properties of glasses. Various experimental techniques were employed to study the macroscopic behavior and atomistic simulations were conducted to understand the mechanisms at the nano level. Towards achieving these objectives, we first study the toughness of a Zr-based bulk metallic glass (BMG), Vitreloy-1, as a function of the free volume, which was varied by recourse to structural relaxation of the BMG through sub-Tg annealing treatment. Both isothermal annealing at 500 K (0.8Tg) for up to 24 h and isochronal annealing for 24 h in the temperature range of 130 K (0.65Tg) to 530 K (0.85Tg) were conducted and the impact toughness, Γ, values were measured. Results show severe embrittlement, with losses of up to 90% in Γ, with annealing. The variation in Γ with annealing time, ta, was found to be similar to that observed in the enthalpy change at the glass transition, ΔH, with ta, indicating that the reduction of free volume due to annealing is the primary mechanism responsible for the loss in Γ with annealing. Having established the connection between sub-atomic length scales (free volume) and macroscopic response (toughness), we investigated further the affects of relaxation on intermediate length scale behavior, namely deformation induced by shear bands, by employing instrumented indentation techniques. While the Vickers nano-indentation response of the as-cast and annealed glasses do not show any significant difference, spherical indentation response shows reduced shear band activity in the annealed BMG. Further, relatively high indentation strain was observed to be necessary for shear band initiation in the annealed glass, implying an increased resistance for the nucleation of shear bands when the BMG is annealed. In the absence of microstructural features that allow for establishment of correlation between properties and the structure, we resort to atomistic modeling to gain further understanding of the deformation mechanisms in amorphous alloys. In particular, we focus on the micromechanisms of strain accommodation including crystallization and void formation during inelastic deformation of glasses. Molecular dynamics simulations on a single component system with Lennard-Jones-like atoms suggest that a softer short range interaction between atoms favors crystallization. Compressive hydrostatic strain in the presence of a shear strain promotes crystallization whereas a tensile hydrostatic strain was found to induce voids. The deformation subsequent to the onset of crystallization includes partial re-amorphization and recrystallization, suggesting important mechanisms of plastic deformation in glasses. Next, a study of deformation induced crystallization is conducted on two component amorphous alloys through atomistic simulations. The resistance of a binary glass to deformation-induced-crystallization (deformation stability) is found to increase with increasing atomic size ratio. A new parameter called “atomic stiffness” (defined by the curvature of the inter-atomic potential at the equilibrium separation distance) is introduced and examined for its role on deformation stability. The deformation stability of binary glasses is found to increase with increasing atomic stiffness. For a given composition, the internal energies of binary crystals and glasses are compared and it is found that the energy of glass remains approximately constant for a wide range of atomic size ratios unlike crystals in which the energy increases with increasing atomic size ratio. This study uncovers the similarities between deformation and thermal stabilities of glasses and suggests new parameters for predicting highly stable glass compositions.
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Books on the topic "Macroscopic deformation"

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Bayly, Brian. Chemical Change in Deforming Materials. Oxford University Press, 1993. http://dx.doi.org/10.1093/oso/9780195067644.001.0001.

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This book is the first to detail the chemical changes that occur in deforming materials subjected to unequal compressions. While thermodynamics provides, at the macroscopic level, an excellent means of understanding and predicting the behavior of materials in equilibrium and non-equilibrium states, much less is understood about nonhydrostatic stress and interdiffusion at the chemical level. Little is known, for example, about the chemistry of a state resulting from a cylinder of deforming material being more strongly compressed along its length than radially, a state of non-equilibrium that remains no matter how ideal the cylinder's condition in other respects. M. Brian Bayly here provides the outline of a comprehensive approach to gaining a simplified and unified understanding of such phenomena. The author's perspective differs from those commonly found in the technical literature in that he emphasizes two little-used equations that allow for a description and clarification of viscous deformation at the chemical level. Written at a level that will be accessible to many non-specialists, this book requires only a fundamental understanding of elementary mathematics, the nonhydrostatic stress state, and chemical potential. Geochemists, petrologists, structural geologists, and materials scientists will find Chemical Change in Deforming Materials interesting and useful.
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Kravtsov, Vladimir. Heavy-tailed random matrices. Edited by Gernot Akemann, Jinho Baik, and Philippe Di Francesco. Oxford University Press, 2018. http://dx.doi.org/10.1093/oxfordhb/9780198744191.013.13.

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This article considers non-Gaussian random matrices consisting of random variables with heavy-tailed probability distributions. In probability theory heavy tails of distributions describe rare but violent events which usually have a dominant influence on the statistics. Furthermore, they completely change the universal properties of eigenvalues and eigenvectors of random matrices. This article focuses on the universal macroscopic properties of Wigner matrices belonging to the Lévy basin of attraction, matrices representing stable free random variables, and a class of heavy-tailed matrices obtained by parametric deformations of standard ensembles. It first examines the properties of heavy-tailed symmetric matrices known as Wigner–Lévy matrices before discussing free random variables and free Lévy matrices as well as heavy-tailed deformations. In particular, it describes random matrix ensembles obtained from standard ensembles by a reweighting of the probability measure. It also analyses several matrix models belonging to heavy-tailed random matrices and presents methods for integrating them.
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Book chapters on the topic "Macroscopic deformation"

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Childs, T. H. C. "Deformation and Flow of Metals in Sliding Friction." In Fundamentals of Friction: Macroscopic and Microscopic Processes, 209–25. Dordrecht: Springer Netherlands, 1992. http://dx.doi.org/10.1007/978-94-011-2811-7_11.

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De Buhan, Patrick, Jean Salencon, and Alberto Taliercio. "Lower and Upper Bound Estimates for the Macroscopic Strength Criterion of Fiber Composite Materials." In Inelastic Deformation of Composite Materials, 563–80. New York, NY: Springer New York, 1991. http://dx.doi.org/10.1007/978-1-4613-9109-8_27.

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Sakaguchi, Hide, and Hans-Bernd Mühlhaus. "Hybrid Modelling of Coupled Pore Fluid-solid Deformation Problems." In Microscopic and Macroscopic Simulation: Towards Predictive Modelling of the Earthquake Process, 1889–904. Basel: Birkhäuser Basel, 2000. http://dx.doi.org/10.1007/978-3-0348-7695-7_5.

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Coulon, Antoine, Emmanuel De Bilbao, Rudy Michel, Marie-Laure Bouchetou, Séverine Brassamin, Camille Gazeau, Didier Zanghi, and Jacques Poirier. "Effect of Slag Impregnation on Macroscopic Deformation of Bauxite-Based Material." In Advances in Molten Slags, Fluxes, and Salts: Proceedings of the 10th International Conference on Molten Slags, Fluxes and Salts 2016, 1093–99. Cham: Springer International Publishing, 2016. http://dx.doi.org/10.1007/978-3-319-48769-4_116.

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COULON, Antoine, Emmanuel DE BILBAO, Rudy MICHEL, Marie-Laure BOUCHETOU, Séverine BRASSAMIN, Camille GAZEAU, Didier ZANGHI, and Jacques POIRIER. "Effect of Slag Impregnation on Macroscopic Deformation of Bauxite-Based Material." In Advances in Molten Slags, Fluxes, and Salts, 1093–99. Hoboken, NJ, USA: John Wiley & Sons, Inc., 2016. http://dx.doi.org/10.1002/9781119333197.ch116.

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Sagiya, Takeshi, Shin’ichi Miyazaki, and Takashi Tada. "Continuous GPS Array and Present-day Crustal Deformation of Japan." In Microscopic and Macroscopic Simulation: Towards Predictive Modelling of the Earthquake Process, 2303–22. Basel: Birkhäuser Basel, 2000. http://dx.doi.org/10.1007/978-3-0348-7695-7_26.

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Yamanoi, Yoshinori, Kenichiro Omoto, Toyotaka Nakae, and Masaki Nishio. "Thermosalient Phenomena in Molecular Crystals: A Case Study of Representative Molecules." In The Materials Research Society Series, 131–53. Singapore: Springer Nature Singapore, 2023. http://dx.doi.org/10.1007/978-981-99-0260-6_8.

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AbstractMolecular crystals have a regularly packed structure, and their physical properties often depend on intramolecular and intermolecular interactions. Here, we review the crystal jumping phenomena under a thermal stimulus (thermosalient phenomenon). Thermosalient phenomena are characterized by thermal phase transitions and anisotropic lattice expansion/contraction at a microscopic scale and jumping behavior through bending/deformation/rotation/cleavage of crystals at a macroscopic scale. The absence of strong intermolecular interaction in the crystal and the misalignment of the crystal plane associated with the phase transition are explained as factors causing the thermosalient phenomena. In this chapter, various case studies with representative molecular crystals that exhibit the thermosalient phenomenon are explained in detail.
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Ryabicheva, Lyudmila, and Dmytro Usatyuk. "Modelling of the Dynamic Processes of Structure Formation by Macroscopic Parameters of Plastic Deformation." In Materials Science Forum, 563–67. Stafa: Trans Tech Publications Ltd., 2007. http://dx.doi.org/10.4028/0-87849-443-x.563.

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Tomita, Yoshihiro, and Makoto Uchida. "Micro- to Macroscopic Deformation Behavior of Amorphous Polymer with Slightly Heterogeneous Distribution of Molecular Chains." In Solid Mechanics and Its Applications, 33–40. Dordrecht: Springer Netherlands, 2004. http://dx.doi.org/10.1007/978-94-017-0483-0_5.

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Zuev, Lev B., and Svetlana A. Barannikova. "The Effect of Solids Microcharacteristics on the Macroscopic Parameters of Plastic Deformation Localization in Metals." In The Mechanical Behavior of Materials X, 93–96. Stafa: Trans Tech Publications Ltd., 2007. http://dx.doi.org/10.4028/0-87849-440-5.93.

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Conference papers on the topic "Macroscopic deformation"

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Murasawa, Go, Kazuhiro Kitamura, Shuichi Miyazaki, Akihiro Nishioka, Ken Miyata, and Tomonori Koda. "Local deformation behavior arising in NiTi plate and its influence on macroscopic deformation behavior." In SPIE Smart Structures and Materials + Nondestructive Evaluation and Health Monitoring, edited by Zoubeida Ounaies and Jiangyu Li. SPIE, 2009. http://dx.doi.org/10.1117/12.815666.

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Urayama, Kenji, Atsushi Fukunaga, Ichiro Kobayashi, and Toshikazu Takigawa. "Electro-optical effect coupled with macroscopic deformation of swollen nematic elastomers." In Photonic Devices + Applications, edited by Iam Choon Khoo. SPIE, 2007. http://dx.doi.org/10.1117/12.734761.

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Ahmed, Shakil, Tobias M. Müller, Jiabin Liang, Genyang Tang, and Mahyar Madadi. "Macroscopic Deformation Moduli of Porous Rocks: Insights from Digital Image Pore-Scale Simulations." In Sixth Biot Conference on Poromechanics. Reston, VA: American Society of Civil Engineers, 2017. http://dx.doi.org/10.1061/9780784480779.101.

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Kruyt, N. P., and L. Rothenburg. "Maximum Entropy Methods in the Mechanics of Quasi-Static Deformation of Granular Materials." In ASME 2002 International Mechanical Engineering Congress and Exposition. ASMEDC, 2002. http://dx.doi.org/10.1115/imece2002-32494.

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In statistical physics of dilute gases maximum entropy methods are widely used for theoretical predictions of macroscopic quantities in terms of microscopic quantities. In this study an analogous approach to the mechanics of quasi-static deformation of granular materials is proposed. The reasoning is presented that leads to the definition of an entropy that is appropriate to quasi-static deformation of granular materials. This entropy is formulated in terms of contact quantities, since contacts constitute the relevant microscopic level for granular materials that consist of semirigid particles. The proposed maximum entropy approach is then applied to two cases. The first case deals with the probability density functions of contact forces in a two-dimensional assembly with frictional contacts under prescribed hydrostatic stress. The second case deals with the elastic behaviour of two-dimensional assemblies of non-rotating particles with bonded contacts. For both cases the probability density functions of contact forces are determined from the proposed maximum entropy method, under the constraints appropriate to the case. These constraints form the macroscopic information available about the system. With the probability density functions for contact forces thus determined, theoretical predictions of macroscopic quantities can be made. These theoretical predictions are then compared with results obtained from two-dimensional Discrete Element simulations and from experiments.
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Kolosov, S. V., P. V. Iskhakova, G. V. Shlyakhova, S. A. Barannikova, and L. B. Zuev. "EFFECT OF TEMPERATURE ON MICRO- AND MACROSCOPIC PARAMETERS OF PLASTIC DEFORMATION OF POLYCRYSTALLINE ALUMINUM." In Physical Mesomechanics of Materials. Physical Principles of Multi-Layer Structure Forming and Mechanisms of Non-Linear Behavior. Novosibirsk State University, 2022. http://dx.doi.org/10.25205/978-5-4437-1353-3-86.

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Bastawros, Ashraf, and Antonia Antoniou. "Deformation Characteristics of Solder Joints." In ASME 2003 International Electronic Packaging Technical Conference and Exhibition. ASMEDC, 2003. http://dx.doi.org/10.1115/ipack2003-35078.

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A novel experimental configuration is devised to measure the evolution of the deformation field and the corresponding toughness in solder joints for microelectronic packaging. The material system utilized comprised ductile layer of Tin based solder, encapsulated within relatively hard copper shoulders. The experimental configuration provides pure shear state within the constrained solder layer. Different Pb/Sn compositions are tested with grain size approaching the film thickness. The in-plan strain distribution within the joint thickness is measured by a microscopic digital image correlation system. The toughness evolution within such highly gradient deformation field is monitored qualitatively through a 2D surface scan with a nano-indentor. The measurements showed a highly inhomogeneous deformation field within the film with discreet shear bands of concentrated strain. The localized shear bands showed long-range correlations of the order of 2–3 grain diameter. A size-dependent macroscopic response on the layer thickness is observed. However, the corresponding film thickness is approximately 100–1000 times larger than those predicted by non-local continuum theories and discreet dislocation.
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Yuan, Zhihao, and Jaehyung Ju. "Tunable Triangular Cellular Structures by Pneumatic Control of Dual Channel Actuators." In ASME 2017 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2017. http://dx.doi.org/10.1115/imece2017-70858.

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Programmable matter, a material whose properties can be programmed to achieve desired density with volume change, shapes or structural properties (stiffness, strength, Poisson’s ratio, etc.) upon command, is an important technology for intelligent materials. Recently emerging soft robotics-based pneumatic control can be potentially used for the design of programmable matter due to its several advantages — quick response for actuation, stiffening effect with internal air pressure, easy to manufacture, inexpensive materials, etc. The objective of this work is to construct programmable two-dimensional (2D) cellular structures with pneumatic actuators, investigating the effect of local deformation of the pneumatic actuators on the macroscopic pattern generation and mechanical properties of cellular structures. We synthesize 2D soft triangular structures with pneumatic actuators embedding dual air channels wrapped with fiber reinforcement. The local deformation modes provide different macroscopic deformations of cellular structures. We build an analytical model integrating the deformation of a single actuating member with nonlinear deformation of cellular structures. Finite element based simulations and experimental validation are followed. This study integrates soft robotics with cellular structures for intelligent materials design, expanding the design space of materials with programming. The fast response of the tunable soft cellular structures may be an ideal for the application of acoustic metamaterials with tunable band gaps.
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Romero, Pedro A., and Alberto M. Cuitin˜o. "Modeling of Dynamically Loaded Open-Cell Metallic Foams." In ASME 2007 International Mechanical Engineering Congress and Exposition. ASMEDC, 2007. http://dx.doi.org/10.1115/imece2007-41906.

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Heterogeneous cellular materials such as metallic and polymeric open-celled foams are preferable in many engineering applications requiring mitigation of energy during sudden impact loading. This brief communication presents an approach for modeling dynamically loaded open-cell metallic foams. It is implicitly assumed that there exists a length scale separation where the microstructural dimensions are much smaller than the macroscopic dimensions. In this context, a macroscopic point translates into a microscopic array of identical unit cells sharing the same macroscopic fields. Dictated by a model for the metallic cell wall constitutive behavior, the effective unit cell response is then obtained from a structural micromechanical model which enforces the principle of minimum action on a representative 3D unit cell. The effective macroscopic response at every node in the FEM mesh (equilibrium, stresses, stress tangents) is then provided by the unit cell microscopic model. The present theory allows one to define a constitutive formulation for lightweight, open-celled foams based on clear and quantifiable parameters such as microstructural topology and ligament properties while capturing the effects of dynamic loading via viscous dissipation at ligament level and microinertia at unit cell level. History of deformation is considered at ligament level while axial and bending deformation are considered at unit cell level. As observed experimentally, the resulting macroscopic FEM simulations clearly demonstrate how the material undergoes heterogeneous deformation during cellular structure collapse.
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Smirnov, A. S., Yu V. Khalevitsky, and M. V. Myasnikova. "Simulating the deformation process of AlMg6/10%SiCp composite representative volume under macroscopic uniaxial strain." In MECHANICS, RESOURCE AND DIAGNOSTICS OF MATERIALS AND STRUCTURES (MRDMS-2018): Proceedings of the 12th International Conference on Mechanics, Resource and Diagnostics of Materials and Structures. Author(s), 2018. http://dx.doi.org/10.1063/1.5084426.

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Smolin, Igor Yu, Pavel V. Makarov, and Rustam A. Bakeev. "Role of the mesoscopic rotation modes of deformation in formation of macroscopic stress–strain curves." In PROCEEDINGS OF THE INTERNATIONAL CONFERENCE ON ADVANCED MATERIALS WITH HIERARCHICAL STRUCTURE FOR NEW TECHNOLOGIES AND RELIABLE STRUCTURES 2019. AIP Publishing, 2019. http://dx.doi.org/10.1063/1.5132211.

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Reports on the topic "Macroscopic deformation"

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Oliynyk, Kateryna, and Matteo Ciantia. Application of a finite deformation multiplicative plasticity model with non-local hardening to the simulation of CPTu tests in a structured soil. University of Dundee, December 2021. http://dx.doi.org/10.20933/100001230.

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In this paper an isotropic hardening elastoplastic constitutive model for structured soils is applied to the simulation of a standard CPTu test in a saturated soft structured clay. To allow for the extreme deformations experienced by the soil during the penetration process, the model is formulated in a fully geometric non-linear setting, based on: i) the multiplicative decomposition of the deformation gradient into an elastic and a plastic part; and, ii) on the existence of a free energy function to define the elastic behaviour of the soil. The model is equipped with two bonding-related internal variables which provide a macroscopic description of the effects of clay structure. Suitable hardening laws are employed to describe the structure degradation associated to plastic deformations. The strain-softening associated to bond degradation usually leads to strain localization and consequent formation of shear bands, whose thickness is dependent on the characteristics of the microstructure (e.g, the average grain size). Standard local constitutive models are incapable of correctly capturing this phenomenon due to the lack of an internal length scale. To overcome this limitation, the model is framed using a non-local approach by adopting volume averaged values for the internal state variables. The size of the neighbourhood over which the averaging is performed (characteristic length) is a material constant related to the microstructure which controls the shear band thickness. This extension of the model has proven effective in regularizing the pathological mesh dependence of classical finite element solutions in the post-localization regime. The results of numerical simulations, conducted for different soil permeabilities and bond strengths, show that the model captures the development of plastic deformations induced by the advancement of the cone tip; the destructuration of the clay associated with such plastic deformations; the space and time evolution of pore water pressure as the cone tip advances. The possibility of modelling the CPTu tests in a rational and computationally efficient way opens a promising new perspective for their interpretation in geotechnical site investigations.
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Sparks, Paul, Jesse Sherburn, William Heard, and Brett Williams. Penetration modeling of ultra‐high performance concrete using multiscale meshfree methods. Engineer Research and Development Center (U.S.), September 2021. http://dx.doi.org/10.21079/11681/41963.

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Terminal ballistics of concrete is of extreme importance to the military and civil communities. Over the past few decades, ultra‐high performance concrete (UHPC) has been developed for various applications in the design of protective structures because UHPC has an enhanced ballistic resistance over conventional strength concrete. Developing predictive numerical models of UHPC subjected to penetration is critical in understanding the material's enhanced performance. This study employs the advanced fundamental concrete (AFC) model, and it runs inside the reproducing kernel particle method (RKPM)‐based code known as the nonlinear meshfree analysis program (NMAP). NMAP is advantageous for modeling impact and penetration problems that exhibit extreme deformation and material fragmentation. A comprehensive experimental study was conducted to characterize the UHPC. The investigation consisted of fracture toughness testing, the utilization of nondestructive microcomputed tomography analysis, and projectile penetration shots on the UHPC targets. To improve the accuracy of the model, a new scaled damage evolution law (SDEL) is employed within the microcrack informed damage model. During the homogenized macroscopic calculation, the corresponding microscopic cell needs to be dimensionally equivalent to the mesh dimension when the partial differential equation becomes ill posed and strain softening ensues. Results of numerical investigations will be compared with results of penetration experiments.
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