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Добірка наукової літератури з теми "Continuum Elasticity"

Автор: Grafiati
Опубліковано: 11 березня 2023

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Статті в журналах з теми "Continuum Elasticity"

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Charlotte, M., and L. Truskinovsky. "Towards multi-scale continuum elasticity theory." Continuum Mechanics and Thermodynamics 20, no. 3 (2008): 133–61. http://dx.doi.org/10.1007/s00161-008-0075-z.

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2

Tarasov, Vasily E. "Fractional Gradient Elasticity from Spatial Dispersion Law." ISRN Condensed Matter Physics 2014 (April 3, 2014): 1–13. http://dx.doi.org/10.1155/2014/794097.

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Анотація:
Nonlocal elasticity models in continuum mechanics can be treated with two different approaches: the gradient elasticity models (weak nonlocality) and the integral nonlocal models (strong nonlocality). This paper focuses on the fractional generalization of gradient elasticity that allows us to describe a weak nonlocality of power-law type. We suggest a lattice model with spatial dispersion of power-law type as a microscopic model of fractional gradient elastic continuum. We demonstrate how the continuum limit transforms the equations for lattice with this spatial dispersion into the continuum equations with fractional Laplacians in Riesz's form. A weak nonlocality of power-law type in the nonlocal elasticity theory is derived from the fractional weak spatial dispersion in the lattice model. The continuum equations with derivatives of noninteger orders, which are obtained from the lattice model, can be considered as a fractional generalization of the gradient elasticity. These equations of fractional elasticity are solved for some special cases: subgradient elasticity and supergradient elasticity.
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3

Haq, Omer, and Sergei Shabanov. "Bound States in the Continuum in Elasticity." Wave Motion 103 (June 2021): 102718. http://dx.doi.org/10.1016/j.wavemoti.2021.102718.

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4

OKAMOTO, Hirosuke. "Dispersion and continuum models of powder elasticity." Journal of the Society of Powder Technology, Japan 27, no. 3 (1990): 146–52. http://dx.doi.org/10.4164/sptj.27.146.

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Lerner, Edan, Eric DeGiuli, Gustavo Düring, and Matthieu Wyart. "Breakdown of continuum elasticity in amorphous solids." Soft Matter 10, no. 28 (2014): 5085. http://dx.doi.org/10.1039/c4sm00311j.

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Okamoto, Hirosuke. "Dispersion and Continuum Models of powder Elasticity [Translated]†." KONA Powder and Particle Journal 9 (1991): 28–35. http://dx.doi.org/10.14356/kona.1991008.

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Wang, Jing. "Effect of Temperature on Elasticity of Silicon Nanowires." Key Engineering Materials 483 (June 2011): 526–31. http://dx.doi.org/10.4028/www.scientific.net/kem.483.526.

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A semi-continuum approach is developed for mechanical analysis of a silicon nanowire, which captures the atomistic physics and retains the efficiency of continuum models. By using the Keating model, the strain energy of the nanowire required in the semi-continuum approach is obtained. Young’s modulus of the silicon (001) nanowire along [100] direction is obtained by the developed semi-continuum approach. Young’s modulus decreases dramatically as the size of a silicon nanowire width and thickness scaling down, especially at several nanometers, which is different from its bulk counterpart. The semi-continuum approach is extended to perform a mechanical analysis of the silicon nanowire at finite temperature. Taking into account the variations of the lattice parameter and the bond length with the temperature, the strain energy of the system is computed by using Keating anharmonic model. The dependence of young’s modulus of the nanowire on temperature is predicted, and it exhibits a negative temperature coefficient.
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Lakes, R. "Experimental Micro Mechanics Methods for Conventional and Negative Poisson’s Ratio Cellular Solids as Cosserat Continua." Journal of Engineering Materials and Technology 113, no. 1 (1991): 148–55. http://dx.doi.org/10.1115/1.2903371.

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Анотація:
Continuum representations of micromechanical phenomena in structured materials are described, with emphasis on cellular solids. These phenomena are interpreted in light of Cosserat elasticity, a generalized continuum theory which admits degrees of freedom not present in classical elasticity. These are the rotation of points in the material, and a couple per unit area or couple stress. Experimental work in this area is reviewed, and other interpretation schemes are discussed. The applicability of Cosserat elasticity to cellular solids and fibrous composite materials is considered as is the application of related generalized continuum theories. New experimental results are presented for foam materials with negative Poisson’s ratios.
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Gao, Bin, Yu Zhou Sun, and Shen Li. "Higher-Order Elasticity Constants of Carbon Nanotubes." Advanced Materials Research 815 (October 2013): 516–19. http://dx.doi.org/10.4028/www.scientific.net/amr.815.516.

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Анотація:
In this paper, the higher-order elasticity constants are evaluated in the theoretical scheme of higher-order continuum. A single-walled carbon nanotube is treated as a higher-order continuum cylindrical tube with a thin wall, and the representative cell is chosen as a triangle unit that contains four carbon atoms. The Brenner potential is employed to describe the C-C atomic interaction, and the higher-order constitutive relationship is derived by virtue of the higher-order Cauchy-Born rule. The higher-order elasticity constants of carbon nanotubes are evaluated based on the derived higher-order constitutive model, which can provide a foundation for the further analysis of the mechanical properties of carbon nanotubes in the theoretical scheme of higher-order continuum.
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Wang, Jing. "Size-Dependence of Elasticity of Phosphorus-Doped Silicon Nano-Plates." Advanced Materials Research 486 (March 2012): 80–83. http://dx.doi.org/10.4028/www.scientific.net/amr.486.80.

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Elasticity of phosphorus (P)-doped silicon nanoplates has been investigated by a semi-continuum approach which captures the atomistic physics and retains the efficiency of continuum models. Youngs modulus of silicon (001) nanoplates along [10 direction is obtained by the developed semi-continuum approach. The results show that P-doping has an effect on the elasticity of silicon nanoplates, especially with the variation of doping concentration. The model predicts that Youngs moduli of P-doped silicon nanoplates are size-dependence.
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Дисертації з теми "Continuum Elasticity"

1

Segall, Darren Eric 1970. "Coarse-graining electronic behavior in condensed matter systems : from electrons to continuum elasticity." Thesis, Massachusetts Institute of Technology, 2002. http://hdl.handle.net/1721.1/29307.

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Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Physics, 2002.<br>Includes bibliographical references (leaves 131-137).<br>In this thesis properties of various condensed matter systems are studied, whose dependency on electronic behavior is incorporated through coarse-grained interactions. Three specific systems are considered. In the first system of study, high momentum, plane wave states of the electronic wave function are coarse-grained, while the low momentum states are fully resolved. Moreover, the coarse-graining procedure incorporates the response of the high momentum states to environmental changes and its couplings to changes in the low momentum states. Within density functional theory this allows the representation of the electronic wave function, when using a plane wave basis, to be computationally feasible without having to make the pseudopotential approximation. This coarse-graining procedure is beneficial for the study of high pressure systems, where the response of the core region is important. With this method we study a number of solid phases of boron and reveal a number of important structural and electronic properties on its high pressure and superconducting phase. The second system of study focuses on a slightly coarser scale, where a theory for the elasticity of nanometer sized objects is developed. This theory provides a powerful way of understanding nanoscale elasticity in terms of local group contributions and acts as a bridge between the atomic and the continuum regimes. This theory properly describes elastic fluctuations on length scales on the order of the decay length of the force constant matrix; allowing for straightforward development of new relations between the bending and stretching properties of nanomechanical resonators, which prove to be much more accurate than the continuum-based relations currently employed in experimental analysis.<br>(cont.) This theory is then used to link features of the underlining electronic structure to the local elastic response in silicon nanoresonators, emphasizing the importance of electronic structure on the local and overall elastic response. Our final system of study focuses on the longest length scales, the continuum. It is shown that the inclusion of electronic structure is crucial in the study of the role of dislocations on the macroscopic property of slip. This thesis explores the discrepancy between experimental data and theoretical calculations of the lattice resistance in bcc metals. This thesis presents results for the temperature dependence of the Peierls stress and the first ab initio calculation of the zero-temperature Peierls stress which employ periodic boundary conditions. The ab initio value for the Peierls stress is over five times larger than current extrapolations of experimental lattice resistance to zero-temperature. Although it is found that the common techniques for such extrapolation indeed tend to underestimate the zero-temperature limit, in this work it is shown that other mechanisms other than the simple Peierls mechanism are important in controlling the process of low temperature slip.<br>by Darren Eric Segall.<br>Ph.D.
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CADELANO, EMILIANO. "Graphene under strain. A combined continuum-atomistic approach." Doctoral thesis, Università degli Studi di Cagliari, 2011. http://hdl.handle.net/11584/265920.

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Анотація:
By combining continuum elasticity theory and atomistic simulations, we provide a picture of the elastic behavior of graphene, which was addressed as a two-dimensional crystal membrane. Thus, the constitutive nonlinear stress-strain relations for graphene, as well as its hydrogenated conformers, have been derived in the framework of the two-dimensional elastic theory, and all the corresponding linear and nonlinear elastic moduli have been computed by atomistic simulations. Moreover, we discuss the effects of an applied stretching on graphene lattice to its electronic band structure, in particular regards the concept of strain-induced band gap engineering. Finally, we focus on the emergence of a stretching field induced on a graphene nanoribbon by bending, providing that such an in-plane strain field can be decomposed in a first contribution due to the actual bending of the sheet and a second one due to the edge effects induced by the finite size of the nanoribbon.------------------------------------------------------ABSTRACT ITA-------Combinando la teoria dell‘elasticità del continuo con calcoli eseguiti attraverso simulazioni atomistiche, si è affrontato lo studio del comportamento elastico del grafene, ovvero di una struttura cristallina bidimensionale a base carbonio. In tal modo, nell‘ambito della teoria elastica bidimensionale, sono state derivate le equazioni costitutive non lineari per il grafene e per il suo composto con l‘idrogeno, detto grafane; conseguentemente sono stati determinati per mezzo di simulazioni atomistiche tutti i relativi moduli elastici lineari e non lineari. Inoltre, abbiamo discusso gli effetti dovuti a deformazioni omogenee applicate al reticolo di grafene sulle sue bande elettroniche, con particolare attenzione al concetto di ingegnerizzazione della gap elettronica indotta da deformazione. Infine, discutiamo l‘insorgenza di un campo di deformazione su un campione di grafene finito sottoposto a piegamento, evidenziando come tale campo possa essere decomposto in un contributo causato della flessione reale subita e in un secondo dovuto ai soli effetti di bordo. v
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3

Ayoub, Sherif Fathy. "Analysis of elastic-plastic continuum at large deformation using hybrid descriptions and finite element method /." The Ohio State University, 1986. http://rave.ohiolink.edu/etdc/view?acc_num=osu1487265555439612.

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SALVALAGLIO, MARCO. "Continuum modeling of vertical heterostructures: elastic properties and morphological evolution." Doctoral thesis, Università degli Studi di Milano-Bicocca, 2016. http://hdl.handle.net/10281/100682.

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Анотація:
The development of cutting-edge opto- and micro-electronic devices requires novel fabrication techniques, able to deliver high-quality materials, monolithically integrable into Si-based technology. Theoretical models and simulations supporting the experimental activities are highly needed to fully understand the growth physics at the nano- and micro-scale and tailor semiconductor heterostructures for technological applications. In this work, the modeling of the plasticity onset and of the morphological evolution for Ge/Si vertical heterostructures is introduced, fostered by the peculiar features of such systems with respect to the standard heteroepitaxy. Indeed, the aim of this thesis is to understand the main properties of systems with large height-to-base aspect-ratios, in order to offer new solutions for the realization of heterostructures with unprecedented material quality. Continuum models are selected to describe length scales ranging from a few nanometers to microns, and time scales of minutes (or even more). By means of the linear elasticity theory equations, solved by Finite Element Method (FEM) simulations, the competition between elastic and plastic relaxation in vertical Ge/Si systems is investigated. The critical parameters for the insertion of dislocations are determined for a single-layer structure, made of a SiGe layer on a Si pillar, and then generalized to multilayer configurations. Moreover, the possibility to achieve coherent structures at any size is demonstrated, provided that a proper grading of the Ge content during the growth is considered. A recipe for the calculation of such a grading of the Ge content is also introduced. Several comparisons with experiments show the generality of the proposed investigation for heterostructures at the nanoscale, and the versatility of the developed method. Moreover, thanks to dedicated experiments stimulated by the theoretical predictions, dislocation-free structures are proven to be feasible also at the micrometer scale. The three-dimensional evolution in time of vertical microcrystals is investigated by means of a phase-field model and FEM simulations. In particular, the annealing of Ge on Si microcrystals is modeled by considering the surface diffusion driven by the tendency toward the minimization of the surface energy. This allows the evolution induced by annealing of single structures to be described. Moreover, the coalescence mechanism for crystal arrays, resulting in the formation of a suspended film, is predicted. Such an evolution is confirmed by dedicated experiments and leads to the fabrication of a promising system for the high-quality heterogeneous integration of semiconductors. The coalescence occurring for closely spaced crystals during high-temperature growth is also assessed. The original extensions of the PF model, required by the theoretical investigations of the morphological evolution, are illustrated in the details. Particular attention is devoted to the description of anisotropic surface energies responsible for crystal faceting in thermodynamic regimes. Moreover, further extensions of the method, dealing with an accurate description of the growth processes, are reported.
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Mühlich, Uwe. "Generalised continuum approach for modelling quasi-brittle failure." Doctoral thesis, Technische Universitaet Bergakademie Freiberg Universitaetsbibliothek "Georgius Agricola", 2014. http://nbn-resolving.de/urn:nbn:de:bsz:105-qucosa-137217.

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Анотація:
A proper description of quasi-brittle failure within the frame of continuum Mechanics can only be achieved by models based on so-called generalised continua. This thesis focuses on a strain gradient generalised continuum and provides a specific methodology to derive corresponding models which account for the essential features of quasi-brittle failure. This methodology is discussed by means of four peer-reviewed journal articles. Furthermore, an extensive overview of the state of the art in the field of generalised continua is given at the beginning of the thesis. This overview discusses phenomenological extensions of standard Continuum Mechanics towards generalised continua together with corresponding homogenisation strategies for materials with periodic or random microstructure<br>Eine geeignete, kontinuumsmechanische Beschreibung quasi-spröden Versagens ist nur unter Verwendung verallgemeinerter Kontinuumstheorien möglich. In dieser Habilitationsschrift stehen sogenannte Gradientenkontinua im Vordergrund. Für diese wird eine Methodik vorgeschlagen, welche die Herleitung von Modellen erlaubt, die in der Lage sind, quasi-sprödes Versagen adäquat abzubilden. Diese Methodik wird anhand von vier Publikationen dargestellt und diskutiert. Ein umfangreicher Überblick über den Stand der Forschung auf dem Gebiet der veralgemeinerten Kontinuumstheorien wird am Anfang der Habilitationschrift gegeben. Dabei werden neben phänomenologischen Ansätzen zur Ableitung verallgemeinerter Kontinuumstheorien auch die entsprechenden Homogenisierungskonzepte dargestellt. Letztere werden für Materialien mit periodischer Mikrostruktur und für Materialien mit zufälliger Mikrostruktur diskutiert
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Ortigosa, Martinez Rogelio. "On a new variational and computational framework for polyconvex nonlinear continuum mechanics and convex multi-variable nonlinear electro-elasticity." Thesis, Swansea University, 2016. https://cronfa.swan.ac.uk/Record/cronfa34893.

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Анотація:
The world of smart materials has experienced a dramatic revolution in the last decades. Electro Active and Magneto Active Materials are some of the most iconic of these, among which, dielectric and magnetostrictive elastomers are becoming extremely popular due to their outstanding actuation capabilities, and in lesser degree, to their energy harvesting capabilities. A clear example illustrating these extraordinary capabilities has been reported in the experimental literature, which has shown unprecedented extreme electrically induced deformations for the most representative dielectric elastomer, namely the acrylic elastomer VHB 4910.This thesis is focused on the development of well-posed constitutive models for nonlinear electro-elasticity in scenarios characterised by extreme deformations and extreme electric fields. This fundamental objective represents the underlying ingredient for the novel variational and computational frameworks developed hereby in the context of electro-elasticity. Very remarkably, the similarity between the equations in both electro-elasticity and magneto-elasticity, enables the variational and computational frameworks developed to be extended to the latter scenario, characterised by magnetomechanical interactions. Despite the enormous interest of the experimental and computational scientific community, the definition of suitable constitutive models is still at its early stages for both electro and magneto active materials. In the more specic context of elasticity, considerable effort has been devoted to the denition of polyconvex energy functionals, which entail the most widely accepted constitutive restriction, namely the ellipticity or Legendre-Hadamard condition. This condition, strongly related to the material stability of the constitutive equations, ensures the well-posedness of the governing equations. An extension of the ellipticity condition to the context of nonlinear electro-elasticity and hence, magneto-elasticity, is proposed in this work, ensuring the well-posedness of the equations for the entire range of deformations and electric or magnetic fields. It is important to emphasise that in this work, the extension of the ellipticity condition to the field of electro-elasticity is exclusively based on material stability considerations. The energy functional encoding the constitutive response of the electro active material is defined according to a novel convex multi-variable representation in terms of an extended set of arguments which ensures material stability. The extended set of arguments, including those characterising the concept of polyconvexity in the more specic scenario of nonlinear elasticity, is further enriched with additional electromechanical entities. Unfortunately, proof of sequential weak lower semicontinuity of the proposed definition of multi-variable convexity is not provided in this work. This condition, and the additional requirement of appropriate coercivity conditions on the energy functional, would ensure the existence of minimisers. Nevertheless, although of extreme relevance and scientific interest, this topic is not in the scope of the thesis and could be the objective of further research.
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7

Dingreville, Remi. "Modeling and Characterization of the Elastic Behavior of Interfaces in Nanostructured Materials: From an Atomistic Description to a Continuum Approach." Diss., Atlanta, Ga. : Georgia Institute of Technology, 2007. http://hdl.handle.net/1853/19776.

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Thesis (Ph.D)--Mechanical Engineering, Georgia Institute of Technology, 2008.<br>Committee Chair: Jianmin Qu; Committee Member: David McDowell; Committee Member: Elisa Riedo; Committee Member: Min Zhou; Committee Member: Mo Li.
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8

Quignon-Tosoni, Justine. "Rhéologie des matériaux pâteux : vers un continuum des régimes solide et liquide. Application aux boues résiduaires." Thesis, Clermont-Ferrand 2, 2015. http://www.theses.fr/2015CLF22629/document.

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Анотація:
Dans un contexte d’augmentation constante des volumes de boues d’épuration à traiter, l’optimisation du traitement des boues est un enjeu primordial. Les étapes de traitement, et de transport mettent en jeu des écoulements qu’il est nécessaire de comprendre et de prédire afin, par exemple, de pour pouvoir estimer les pertes de charges en conduite ou bien pour dimensionner les installations de pompage. D’un point de vue physique, les boues peuvent être considérées comme une suspension de particules dans un gel suspendant. Ainsi, le comportement rhéologique des boues d’épuration présente des similitudes importantes avec les suspensions colloïdales et les gels polymériques. Ces trois types de matériaux, i.e. les boues d’épuration, les gels colloïdaux et les suspensions polymériques, présentent un comportement rhéologique complexe dépendant du temps et de la sollicitation imposée. Ils présentent un comportement dual, solide aux contraintes faibles, et liquide pour des contraintes élevées. La transition solide-liquide est généralement modélisée par la définition d’un seuil de contrainte ou de déformation, supposé séparer les régimes solide et liquide. Cependant, cette notion de seuil suppose une transition abrupte, et s’oppose aux observations expérimentales qui mettent en évidence une transition continue et progressive. L’étude de la littérature a permis de mettre en évidence une nécessité d’améliorer la compréhension et la modélisation du phénomène de transition solide-liquide. De plus, il est nécessaire d’unifier la description des régimes solide et liquide sous un même modèle, afin de mettre en lien une continuité mathématique avec le caractère continu et progressif du phénomène physique modélisé. Une analyse des résultats disponibles dans la littérature nous a permis de construire un modèle mathématique unique pour décrire le comportement solide et le comportement liquide des matériaux étudiés. Les hypothèses posées à partir de la littérature pour construire ce modèle ont ensuite été validées expérimentalement. Le modèle proposé est basé sur la décomposition de la complaisance du matériau en la somme d’une contribution solide et d’une contribution liquide, dépendant du temps, de la sollicitation appliquée et de l’histoire du matériau. Ce modèle permet une description commune des comportements solides et liquides du matériau, en tenant compte de l’existence d’une élasticité résiduelle y compris pour des contraintes élevées, et d’une dissipation visqueuse faible pour les contraintes faibles, conformément aux résultats expérimentaux. Ces travaux de thèse ont permis de mettre en évidence le fait que le mécanisme de transition solide-liquide était piloté non pas par la contrainte ou par la déformation, mais par la complaisance du matériau. De plus, ils ont permis d’ouvrir la voie à une nouvelle manière d’appréhender la thixotropie et la transition solide-liquide des matériaux pâteux. En effet, le comportement d’un matériau pâteux est piloté par deux paramètres : un module élastique plateau correspondant à un état totalement structuré, et une viscosité infinie correspondant à un état totalement déstructuré. Ces paramètres intrinsèques au matériau sont alors pondérés par des évolutions de la microstructure, menant à une compétition entre les effets élastiques et les effets visqueux. Ainsi, la différence entre un comportement de type loi de puissance et un comportement de type loi de puissance à seuil peut être expliquée simplement par l’apparition d’effets élastiques non négligeables<br>In a context of constant increasing volumes of wastewater treatment sludge, optimizing the treatment of sludge appears to be crucial. Each step of treatment and transportation involves flows. It appears necessary to understand and predict these flows in order, for example, to estimate pressure drops in pipes or to size properly pumping facilities. In a physical point of view, sludge can be considered as a suspension of particles in a gel. Thus, its rheological behaviour presents significant similarities to that of colloidal suspensions of polymeric gels. These three types of materials, i.e. wastewater treatment sludge, colloidal suspensions and polymeric gels, present a complex rheological behaviour which depend on both time and the applied solicitation. They exhibit a dual behaviour, solid at low shear stresses, and liquid when the applied shear stress is high. The solid-liquid behaviour is generally modelled by defining a critical shear stress or a critical strain, supposed to be the limit between the solid and liquid regimes. Nevertheless, this concept implies an abrupt transition, unlike experimental observations showing a continuous and progressive transition. The study of the literature permitted to highlight the need to improve the understanding and modelling of the solid-liquid transition. Moreover, it appears necessary to unify the description of the solid and liquid regime in a unique model, in order to link a mathematical continuity with thecontinuous and progressive nature of the physical phenomenon to model. The study of the results available in the literature permited us to build a unique mathematical model to describe both the solid behaviour and the liquid behaviour of the studied materials. The assumptions made from the literature results have thus been experimentally validated. The proposed model is based on the decomposition of the compliance of the material in the sum of a solid contribution and a liquid contribution, depending on time, the applied solicitation and the story of the material. This model permits a unique description of solide and liquid regimes of the material, taking into account the existence of a residual elasticity at high shear stresses, and a viscous dissipation for low shear stresses, in accordance with experimental results. This work permitted to highlight the fact that the solid-liquid transition mecanism is controlled by the compliance of the material, and not the shear stress or the strain. Moreover, it opened the way to a new way of understanding the thixotropy and the solid-liquid transition of pasty materials. Thus, the behaviour of a pasty material is controlled by two parameters : a plateau elastic modulus corresponding to a totally structured state, and an infinite viscosity corresponding to a totally destructured state. These parameters intrinsic to the material are pondered by the evolutions of the microstructure, leading to a competition between elastic and viscous effects. Thus, the difference between the power law behaviour and the Herschel-Bulkley behaviour can be simply explained by the apparition of elastic effects that can’t be neglected
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9

Beauregard, Matthew Alan. "Nonlinear Dynamics of Elastic Filaments Conveying a Fluid and Numerical Applications to the Static Kirchhoff Equations." Diss., The University of Arizona, 2008. http://hdl.handle.net/10150/194164.

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Анотація:
Two problems in the study of elastic filaments are considered.First, a reliable numerical algorithm is developed that candetermine the shape of a static elastic rod under a variety ofconditions. In this algorithm the governing equations are writtenentirely in terms of local coordinates and are discretized usingfinite differences. The algorithm has two significant advantages:firstly, it can be implemented for a wide variety of the boundaryconditions and, secondly, it enables the user to work with generalconstitutive relationships with only minor changes to thealgorithm. In the second problem a model is presented describingthe dynamics of an elastic tube conveying a fluid. First weanalyze instabilities that are present in a straight rod or tubeunder tension subject to increasing twist in the absence of afluid. As the twist is increased beyond a critical value, thefilament undergoes a twist-to-writhe bifurcation. A multiplescales expansion is used to derive nonlinear amplitude equationsto examine the dynamics of the elastic rod beyond the bifurcationthreshold. This problem is then reinvestigated for an elastic tubeconveying a fluid to study the effect of fluid flow on thetwist-to-writhe instability. A linear stability analysisdemonstrates that for an infinite rod the twist-to-writhethreshold is lowered by the presence of a fluid flow. Amplitudeequations are then derived from which the delay of bifurcation dueto finite tube length is determined. It is shown that the delayedbifurcation threshold depends delicately on the length of the tubeand that it can be either raised or lowered relative to thefluid-free case. The amplitude equations derived for the case of aconstant average fluid flux are compared to the case where theflux depends on the curvature. In this latter case it is shownthat inclusion of curvature results in small changes in some ofthe coefficients in the amplitude equations and has only a smalleffect on the post-bifurcation dynamics.
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Lloyd, Jeffrey T. "Microstructure-sensitive simulation of shock loading in metals." Diss., Georgia Institute of Technology, 2014. http://hdl.handle.net/1853/51853.

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A constitutive model has been developed to model the shock response of single crystal aluminum from peak pressures ranging from 2-110 GPa. This model couples a description of higher-order thermoelasticity with a dislocation-based viscoplastic formulation, both of which are formulated for single crystals. The constitutive model has been implemented using two numerical methods: a plane wave method that tracks the propagating wave front; and an extended one-dimensional, finite-difference method that can be used to model spatio-temporal evolution of wave propagation in anisotropic materials. The constitutive model, as well as these numerical methods, are used to simulate shock wave propagation in single crystals, polycrystals, and pre-textured polycrystals. Model predictions are compared with extensive existing experimental data and are then used to quantify the influence of the initial material state on the subsequent shock response. A coarse-grained model is then proposed to capture orientation-dependent deformation heterogeneity, and is shown to replicate salient features predicted by direct finite-difference simulation of polycrystals in the weak shock regime. The work in this thesis establishes a general framework that can be used to quantify the influence of initial material state on subsequent shock behavior not only for aluminum single crystals, but for other face-centered cubic and lower symmetry crystalline metals as well.
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Книги з теми "Continuum Elasticity"

1

Alexander, Belyaev, ed. Theory of elasticity. Springer, 2005.

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2

Coman, Ciprian D. Continuum Mechanics and Linear Elasticity. Springer Netherlands, 2020. http://dx.doi.org/10.1007/978-94-024-1771-5.

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3

Continuum mechanics: Elasticity, plasticity, viscoelasticity. CRC/Taylor & Francis, 2007.

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4

Chandrasekharaiah, D. S. Continuum mechanics. Academic P., 1994.

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5

Constantinescu, Andrei. Elasticity with mathematica: An introduction to continuum mechanics and linear elasticity. Cambridge University Press, 2007.

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6

Jit, Singh Sarva, ed. Deformation of elastic solids. Prentice Hall, 1991.

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7

Gould, Phillip L. Introduction to Linear Elasticity. 3rd ed. Springer New York, 2013.

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8

Lattice dynamical foundations of continuum theories: Elasticity, piezoelectricity, viscoelasticity, plasticity. World Scientific, 1986.

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9

Prestressed bodies. Longman Scientific, 1989.

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10

M, Carroll Michael, and Hayes M. A, eds. Nonlinear effects in fluids and solids. Plenum Press, 1996.

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Частини книг з теми "Continuum Elasticity"

1

Romano, Antonio, and Addolorata Marasco. "Nonlinear Elasticity." In Continuum Mechanics. Birkhäuser Boston, 2010. http://dx.doi.org/10.1007/978-0-8176-4870-1_1.

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2

Romano, Antonio, and Addolorata Marasco. "Micropolar Elasticity." In Continuum Mechanics. Birkhäuser Boston, 2010. http://dx.doi.org/10.1007/978-0-8176-4870-1_2.

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3

Nayak, Prasun Kumar, and Mijanur Rahaman Seikh. "Linear Elasticity." In Continuum Mechanics. CRC Press, 2022. http://dx.doi.org/10.1201/9781003299776-5.

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4

Athanasiou, Kyriacos A., and Roman M. Natoli. "Elasticity." In Introduction to Continuum Biomechanics. Springer International Publishing, 2008. http://dx.doi.org/10.1007/978-3-031-01626-4_4.

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5

Steinmann, Paul. "Elasticity." In Geometrical Foundations of Continuum Mechanics. Springer Berlin Heidelberg, 2015. http://dx.doi.org/10.1007/978-3-662-46460-1_7.

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6

Talpaert, Yves R. "Linear Elasticity." In Tensor Analysis and Continuum Mechanics. Springer Netherlands, 2002. http://dx.doi.org/10.1007/978-94-015-9988-7_6.

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7

Romano, Antonio, and Addolorata Marasco. "Linear Elasticity." In Continuum Mechanics using Mathematica®. Springer New York, 2014. http://dx.doi.org/10.1007/978-1-4939-1604-7_10.

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8

Toupin, R. A. "Elasticity and Electro-Magnetism." In Non-linear Continuum Theories. Springer Berlin Heidelberg, 2011. http://dx.doi.org/10.1007/978-3-642-11033-7_6.

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9

Antman, Stuart S. "Three-Dimensional Continuum Mechanics." In Nonlinear Problems of Elasticity. Springer New York, 1995. http://dx.doi.org/10.1007/978-1-4757-4147-6_12.

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10

Müller, Wolfgang H. "Problems of Linear Elasticity." In An Expedition to Continuum Theory. Springer Netherlands, 2014. http://dx.doi.org/10.1007/978-94-007-7799-6_9.

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Тези доповідей конференцій з теми "Continuum Elasticity"

1

Alavinasab, Ali, Goodarz Ahmadi, and Ratneshwar Jha. "Nonlocal Continuum Theory Based Modeling of Carbon Nanotube Composites." In ASME 2008 Conference on Smart Materials, Adaptive Structures and Intelligent Systems. ASMEDC, 2008. http://dx.doi.org/10.1115/smasis2008-595.

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Analytical modeling of Carbon Nanotube (CNT) composite based on the nonlocal continuum theory is investigated. This approach accounts for nonlocal stress-strain relationships, that is, stress at any point in a structure is a function of strain in the entire structure. Finite element analysis of a representative volume element (RVE) of CNT composite is used to evaluate unknown constant in the nonlocal theory based solution. Stress distributions are obtained from finite element method (FEM), nonlocal theory, and standard (local) elasticity. Nonlocal theory and FEM stress distributions yield the same total force and first moment, whereas standard elasticity gives less accurate results.
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2

Amar, El Hadji Bouya, Didier Clamond, Nathalie Fraysse, Jean Rajchenbach, Masami Nakagawa, and Stefan Luding. "Mechanichal Behavior of a Noncohesive Packing at Small Deformations: Deviation From Continuum Elasticity." In POWDERS AND GRAINS 2009: PROCEEDINGS OF THE 6TH INTERNATIONAL CONFERENCE ON MICROMECHANICS OF GRANULAR MEDIA. AIP, 2009. http://dx.doi.org/10.1063/1.3179903.

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3

Gao, A., N. Liu, and Guang-Zhong Yang. "Toward Endobronchial Intervention: A Pre-Curved Continuum Robot with Large Deflection and Linear Elasticity." In The Hamlyn Symposium. The Hamlyn Centre, Faculty of Engineering, Imperial College London, 2018. http://dx.doi.org/10.31256/hsmr2018.7.

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4

Regueiro, Richard A. "Coupling Particle to Continuum Regions of Particulate Materials." In ASME 2007 International Mechanical Engineering Congress and Exposition. ASMEDC, 2007. http://dx.doi.org/10.1115/imece2007-42717.

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Following atomistic-continuum coupling methods for lattice-structured materials [1, 2], a method for coupling particle to continuum regions of particulate materials is presented. The particle region is modeled using particle mechanics and the discrete element method, whereas the continuum region is modeled using linear micropolar elasticity and the finite element method. The formulation for coupling particle and continuum degrees of freedom as well as partitioning kinetic and potential energies in the overlapping domain is presented. Details of the numerical implementation and numerical examples will follow in a forthcoming paper. The method is developed to model particulate materials at their physical length scale (particle size) in regions of large relative particle motion in a computationally tractable manner.
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5

Barber, J. R., and P. Hild. "Non-Uniqueness, Eigenvalue Solutions and Wedged Configurations Involving Coulomb Friction." In ASME/STLE 2004 International Joint Tribology Conference. ASMEDC, 2004. http://dx.doi.org/10.1115/trib2004-64368.

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It is well known that the conventional Coulomb friction condition can lead to non-uniqueness of solution in elastostatic solutions if the friction coefficient is sufficiently high. Interest in this field has centered on discrete formulations, particularly with reference to the finite element method. More recently Hild has demonstrated the existence of a multiplicity of non-unique solutions to a simple problem in two-dimensional continuum elasticity and showed how to determine the conditions for such states to exist by formulating an eigenvalue problem. Both the discrete and continuum examples of non-uniqueness seem to be related to the well known physical phenomenon whereby a frictional system can become locked or ‘wedged’ in a state of stress even when no external loads are applied (the homogeneous problem), but the equivalence is not complete because of the influence of unilateral inequalities in the physical problem. We shall discuss the relations between these concepts in the context of simple continuum and discrete problems in two-dimensional linear elasticity.
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6

Marquardt, Oliver, Stefan Schulz, Eoin P. O'Reilly, et al. "A flexible, plane-wave-based formulation of continuum elasticity and multiband k·p models." In 2011 11th International Conference on Numerical Simulation of Optoelectronic Devices (NUSOD). IEEE, 2011. http://dx.doi.org/10.1109/nusod.2011.6041165.

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7

Papusha, Alexander N. "Mathematica Implementation in the Training Courses on Continuum Mechanics: Elasticity Theory, Hydromechanics, Theory of Filtration." In Proceedings of the Fifth International Mathematica Symposium. PUBLISHED BY IMPERIAL COLLEGE PRESS AND DISTRIBUTED BY WORLD SCIENTIFIC PUBLISHING CO., 2003. http://dx.doi.org/10.1142/9781848161313_0013.

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8

Shodja, Hossein M., and Hamed Haftbaradaran. "An Embedded Elliptic Nano-Fiber in Anti-Plane Strain Couple Stress Elasticity." In ASME 2008 International Mechanical Engineering Congress and Exposition. ASMEDC, 2008. http://dx.doi.org/10.1115/imece2008-68537.

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The application of higher order continuum theories, with size effect considerations, have recently been spread in the micro and nano-scale studies. One famous version of these theories is the couple stress theory. This paper utilizes this theory to study the anti-plane problem of an elliptic nano-fiber, embedded in an infinite medium, both made of centrosymmetric isotropic material. In this framework, a characteristic length appears in the formulation, by which examination of the size effect is possible. This work presents an analytical solution for the proposed problem.
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9

Cheng, Shao-Huan, and C. T. Sun. "Applicability of Continuum Fracture Mechanics in Atomistic Systems." In ASME 2011 International Mechanical Engineering Congress and Exposition. ASMEDC, 2011. http://dx.doi.org/10.1115/imece2011-63478.

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Stress intensity factor is one of the most significant fracture parameters in linear elastic fracture mechanics (LEFM). Due to its simplicity, many researchers directly employed this concept to explain their results from molecular simulation. However, stress intensity factor defines the amplitude of the singular stress, which is the product of continuum elasticity. Under atomistic systems without the stress singularity, the concept of stress intensity factor must be examined. In addition, the difficulty of studying the stress intensity factor in atomistic systems may be traced back to the ambiguous definition of the local atomistic stress. In this study, the definition of the local virial stress is adopted. Subsequently, through the consideration of K-dominance, the approximated stress intensity factor based on the atomistic stress can be projected within a reasonable region. Moreover, the influence of cutting interatomic bonds to create traction free crack surfaces and the critical stress intensity factor is also discussed.
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10

Shojaei, Arman, Mirco Zaccariotto, and Ugo Galvanetto. "On the Coupling of Peridynamics With a Meshless Method Based on Classical Elasticity." In ASME 2016 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2016. http://dx.doi.org/10.1115/imece2016-65340.

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In this paper we introduce a simple and efficient approach to couple a discretized Peridynamic model with a meshless method based on classical continuum mechanics. The coupling is done through a complete meshless style without producing any ghost forces in the transition region. We shall show with such type of coupling it is possible to reproduce the solution of a pure Peridynamic model by a hybrid meshless method with lower computational cost.
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Звіти організацій з теми "Continuum Elasticity"

1

Fried, Eliot, and Morton E. Gurtin. Continuum mechanical and computational aspects of phase field elasticity as applied to phase transitions and fracture. Final report: DE-FG02-97ER25318, June 1, 1997 - May 31, 2000. Office of Scientific and Technical Information (OSTI), 2001. http://dx.doi.org/10.2172/808066.

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