Relevant bibliographies by topics / Tensor of elasticity

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  1. Journal articles
  2. Dissertations / Theses
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  4. Book chapters
  5. Conference papers

Academic literature on the topic 'Tensor of elasticity'

Author: Grafiati
Published: 4 June 2021
Last updated: 5 February 2022

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Journal articles on the topic "Tensor of elasticity"

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Milton, Graeme W., and Andrej V. Cherkaev. "Which Elasticity Tensors are Realizable?" Journal of Engineering Materials and Technology 117, no. 4 (October 1, 1995): 483–93. http://dx.doi.org/10.1115/1.2804743.

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It is shown that any given positive definite fourth order tensor satisfying the usual symmetries of elasticity tensors can be realized as the effective elasticity tensor of a two-phase composite comprised of a sufficiently compliant isotropic phase and a sufficiently rigid isotropic phase configured in an suitable microstructure. The building blocks for constructing this composite are what we call extremal materials. These are composites of the two phases which are extremely stiff to a set of arbitrary given stresses and, at the same time, are extremely compliant to any orthogonal stress. An appropriately chosen subset of the extremal materials are layered together to form the composite with elasticity tensor matching the given tensor.
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He, Q. C. "A Remarkable Tensor in Plane Linear Elasticity." Journal of Applied Mechanics 64, no. 3 (September 1, 1997): 704–7. http://dx.doi.org/10.1115/1.2788952.

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It is shown that any two-dimensional elastic tensor can be orthogonally and uniquely decomposed into a symmetric tensor and an antisymmetric tensor. To within a scalar multiplier, the latter turns out to be equal to the right-angle rotation on the space of two-dimensional second-order symmetric tensors. On the basis of these facts, several useful results are derived for the traction boundary value problem of plane linear elasticity.
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Sutcliffe, S. "Spectral Decomposition of the Elasticity Tensor." Journal of Applied Mechanics 59, no. 4 (December 1, 1992): 762–73. http://dx.doi.org/10.1115/1.2894040.

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The elasticity tensor in anisotropic elasticity can be regarded as a symmetric linear transformation on the nine-dimensional space of second-order tensors. This allows the elasticity tensor to be expressed in terms of its spectral decomposition. The structures of the spectral decompositions are determined by the sets of invariant subspaces that are consistent with material symmetry. Eigenvalues always depend on the values of the elastic constants, but the eigenvectors are, in part, independent of these values. The structures of the spectral decompositions are presented for the classical symmetry groups of crystallography, and numerical results are presented for representative materials in each group. Spectral forms for the equilibrium equations, the acoustic tensor, and the stored energy function are also derived.
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Kochetov, Mikhail, and Michael A. Slawinski. "Estimating effective elasticity tensors from Christoffel equations." GEOPHYSICS 74, no. 5 (September 2009): WB67—WB73. http://dx.doi.org/10.1190/1.3155163.

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We consider the problem of obtaining the orientation and elasticity parameters of an effective tensor of particular symmetry that corresponds to measurable traveltime and polarization quantities. These quantities — the wavefront-slowness and polarization vectors — are used in the Christoffel equation, a characteristic equation of the elastodynamic equation that brings seismic concepts to our formulation and relates experimental data to the elasticity tensor. To obtain an effective tensor of particular symmetry, we do not assume its orientation; thus, the regression using the residuals of the Christoffel equation results in a nonlinear optimization problem. We find the absolute extremum and, to avoid numerical instability of a global search, obtain an accurate initial guess using the tensor of given symmetry closest to the generally anisotropic tensor obtained from data by linear regression. The issue is twofold. First, finding the closest tensor of particular symmetry without assuming its orientation is challenging. Second, the closest tensor is not the effective tensor in the sense of regression because the process of finding it carries neither seismic concepts nor statistical information; rather, it relies on an abstract norm in the space of elasticity tensors. To include seismic concepts and statistical information, we distinguish between the closest tensor of particular symmetry and the effective one; the former is the initial guess to search for the latter.
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Diner, Çağrı. "The Structure of Moment Tensors in Transversely Isotropic Focal Regions." Bulletin of the Seismological Society of America 109, no. 6 (September 24, 2019): 2415–26. http://dx.doi.org/10.1785/0120180316.

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Abstract Full moment tensor inversion has become a standard method for understanding the mechanisms of earthquakes as the resolution of the inversion process increases. Thus, it is important to know the possible forms of non–double‐couple (non‐DC) moment tensors, which can be obtained because of either the different source mechanisms or the anisotropy of the focal regions. In this study, the form of the moment tensors of seismic sources occurring in transversely isotropic (TI) focal regions is obtained using the eigendecomposition of the elasticity tensor. More precisely, a moment tensor is obtained as a linear combination of the eigenspaces of TI elasticity tensor in which the coefficients of the terms are the corresponding eigenvalues multiplied with the projection of the potency tensor onto the corresponding eigenspaces. Moreover, the eigendecomposition method is also applied to obtain the three different forms of moment tensors in isotropic focal regions, in particular, for the shear source, tensile source, and for any type of potency tensor whose rank is three. This linear algebra point of view makes the structure of the moment tensors more apparent; for example, a shear source tensor is an eigenvector of isotropic elasticity tensor, and hence the resulting moment tensor is proportional to its shear source tensor. Moreover, a geometric interpretation for the scalar seismic moment, which is the norm of the moment tensor, for anisotropic focal regions is achieved through the eigendecomposition method. This method also gives a simple way to quantify the percentage of the isotropic component of the moment tensor of shear sources in TI focal regions. Hence, the complexities in the moment tensor introduced by the anisotropy of the focal region and by the source mechanism can be differentiated.
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Lazar, Markus, and Giacomo Po. "On Mindlin’s isotropic strain gradient elasticity: Green tensors, regularization, and operator-split." Journal of Micromechanics and Molecular Physics 03, no. 03n04 (September 2018): 1840008. http://dx.doi.org/10.1142/s2424913018400088.

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The theory of Mindlin’s isotropic strain gradient elasticity of form II is reviewed. Three-dimensional and two-dimensional Green tensors and their first and second derivatives are derived for an unbounded medium. Using an operator-split in Mindlin’s strain gradient elasticity, three-dimensional and two-dimensional regularization function tensors are computed, which are the three-dimensional and two-dimensional Green tensors of a tensorial Helmholtz equation. In addition, a length scale tensor is introduced, which is responsible for the characteristic material lengths of strain gradient elasticity. Moreover, based on the Green tensors of Mindlin’s strain gradient elasticity, point, line and double forces are studied.
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Suchocki, Cyprian. "A Finite Element Implementation of Knowles Stored-Energy Function: Theory, Coding and Applications." Archive of Mechanical Engineering 58, no. 3 (January 1, 2011): 319–46. http://dx.doi.org/10.2478/v10180-011-0021-7.

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A Finite Element Implementation of Knowles Stored-Energy Function: Theory, Coding and Applications This paper contains the full way of implementing a user-defined hyperelastic constitutive model into the finite element method (FEM) through defining an appropriate elasticity tensor. The Knowles stored-energy potential has been chosen to illustrate the implementation, as this particular potential function proved to be very effective in modeling nonlinear elasticity within moderate deformations. Thus, the Knowles stored-energy potential allows for appropriate modeling of thermoplastics, resins, polymeric composites and living tissues, such as bone for example. The decoupling of volumetric and isochoric behavior within a hyperelastic constitutive equation has been extensively discussed. An analytical elasticity tensor, corresponding to the Knowles stored-energy potential, has been derived. To the best of author's knowledge, this tensor has not been presented in the literature yet. The way of deriving analytical elasticity tensors for hyperelastic materials has been discussed in detail. The analytical elasticity tensor may be further used to develop visco-hyperelastic, nonlinear viscoelastic or viscoplastic constitutive models. A FORTRAN 77 code has been written in order to implement the Knowles hyperelastic model into a FEM system. The performance of the developed code is examined using an exemplary problem.
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Le Quang, Hung, Qi-Chang He, and Nicolas Auffray. "Classification of first strain-gradient elasticity tensors by symmetry planes." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 477, no. 2251 (July 2021): 20210165. http://dx.doi.org/10.1098/rspa.2021.0165.

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First strain-gradient elasticity is a generalized continuum theory capable of modelling size effects in materials. This extended capability comes from the inclusion in the mechanical energy density of terms related to the strain-gradient. In its linear formulation, the constitutive law is defined by three elasticity tensors whose orders range from four to six. In the present contribution, the symmetry properties of the sixth-order elasticity tensors involved in this model are investigated. If their classification with respect to the orthogonal symmetry group is known, their classification with respect to symmetry planes is still missing. This last classification is important since it is deeply connected with some identification procedures. The classification of sixth-order elasticity tensors in terms of invariance properties with respect to symmetry planes is given in the present contribution. Precisely, it is demonstrated that there exist 11 reflection symmetry classes. This classification is distinct from the one obtained with respect to the orthogonal group, according to which there exist 17 different symmetry classes. These results for the sixth-order elasticity tensor are very different from those obtained for the classical fourth-order elasticity tensor, since in the latter case the two classifications coincide. A few numerical examples are provided to illustrate how some different orthogonal classes merge into one reflection class.
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Truman, C. E. "An Introduction to Tensor Elasticity." Strain 39, no. 4 (November 2003): 161–65. http://dx.doi.org/10.1046/j.1475-1305.2003.00089.x.

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Desmorat, R., N. Auffray, B. Desmorat, B. Kolev, and M. Olive. "Generic separating sets for three-dimensional elasticity tensors." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 475, no. 2226 (June 2019): 20190056. http://dx.doi.org/10.1098/rspa.2019.0056.

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We define a generic separating set of invariant functions (a.k.a. a weak functional basis ) for tensors. We then produce two generic separating sets of polynomial invariants for three-dimensional elasticity tensors, one consisting of 19 polynomials and one consisting of 21 polynomials (but easier to compute), and a generic separating set of 18 rational invariants. As a by-product, a new integrity basis for the fourth-order harmonic tensor is provided.
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Dissertations / Theses on the topic "Tensor of elasticity"

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Deymier, P. A., and K. Runge. "Non-separable states in a bipartite elastic system." AMER INST PHYSICS, 2017. http://hdl.handle.net/10150/624037.

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We consider two one-dimensional harmonic chains coupled along their length via linear springs. Casting the elastic wave equation for this system in a Dirac-like form reveals a directional representation. The elastic band structure, in a spectral representation, is constituted of two branches corresponding to symmetric and antisymmetric modes. In the directional representation, the antisymmetric states of the elastic waves possess a plane wave orbital part and a 4x1 spinor part. Two of the components of the spinor part of the wave function relate to the amplitude of the forward component of waves propagating in both chains. The other two components relate to the amplitude of the backward component of waves. The 4x1 spinorial state of the two coupled chains is supported by the tensor product Hilbert space of two identical subsystems composed of a non-interacting chain with linear springs coupled to a rigid substrate. The 4x1 spinor of the coupled system is shown to be in general not separable into the tensor product of the two 2x1 spinors of the uncoupled subsystems in the directional representation. (C) 2017 Author(s). All article content, except where otherwise noted, is licensed under a Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).
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Song, Min Jae. "Direct tensor expression by Eulerian approach for constitutive relations based on strain invariants in transversely isotropic green elasticity - finite extension and torsion." [College Station, Tex. : Texas A&M University, 2006. http://hdl.handle.net/1969.1/ETD-TAMU-1667.

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Blanc, Katy. "Description de contenu vidéo : mouvements et élasticité temporelle." Thesis, Université Côte d'Azur (ComUE), 2018. http://www.theses.fr/2018AZUR4212/document.

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La reconnaissance en vidéo atteint de meilleures performances ces dernières années, notamment grâce à l'amélioration des réseaux de neurones profonds sur les images. Pourtant l'explosion des taux de reconnaissance en images ne s'est pas directement répercuté sur les taux en reconnaissance vidéo. Cela est dû à cette dimension supplémentaire qu'est le temps et dont il est encore difficile d'extraire une description robuste. Les réseaux de neurones récurrents introduisent une temporalité mais ils ont une mémoire limitée dans le temps. Les méthodes de description vidéo de l'état de l'art gèrent généralement le temps comme une dimension spatiale supplémentaire et la combinaison de plusieurs méthodes de description vidéo apportent les meilleures performances actuelles. Or la dimension temporelle possède une élasticité propre, différente des dimensions spatiales. En effet, la dimension temporelle peut être déformée localement : une dilatation partielle provoquera un ralentissement visuel de la vidéo sans en changer la compréhension, à l'inverse d'une dilatation spatiale sur une image qui modifierait les proportions des objets. On peut donc espérer améliorer encore la classification de contenu vidéo par la conception d'une description invariante aux changements de vitesse. Cette thèse porte sur la problématique d'une description robuste de vidéo en considérant l'élasticité de la dimension temporelle sous trois angles différents. Dans un premier temps, nous avons décrit localement et explicitement les informations de mouvements. Des singularités sont détectées sur le flot optique, puis traquées et agrégées dans une chaîne pour décrire des portions de vidéos. Nous avons utilisé cette description sur du contenu sportif. Puis nous avons extrait des descriptions globales implicites grâce aux décompositions tensorielles. Les tenseurs permettent de considérer une vidéo comme un tableau de données multi-dimensionnelles. Les descriptions extraites sont évaluées dans une tache de classification. Pour finir, nous avons étudié les méthodes de normalisation de la dimension temporelle. Nous avons utilisé les méthodes de déformations temporelles dynamiques des séquences. Nous avons montré que cette normalisation aide à une meilleure classification
Video recognition gain in performance during the last years, especially due to the improvement in the deep learning performances on images. However the jump in recognition rate on images does not directly impact the recognition rate on videos. This limitation is certainly due to this added dimension, the time, on which a robust description is still hard to extract. The recurrent neural networks introduce temporality but they have a limited memory. State of the art methods for video description usually handle time as a spatial dimension and the combination of video description methods reach the current best accuracies. However the temporal dimension has its own elasticity, different from the spatial dimensions. Indeed, the temporal dimension of a video can be locally deformed: a partial dilatation produces a visual slow down during the video, without changing the understanding, in contrast with a spatial dilatation on an image which will modify the proportions of the shown objects. We can thus expect to improve the video content classification by creating an invariant description to these speed changes. This thesis focus on the question of a robust video description considering the elasticity of the temporal dimension under three different angles. First, we have locally and explicitly described the motion content. Singularities are detected in the optical flow, then tracked along the time axis and organized in chain to describe video part. We have used this description on sport content. Then we have extracted global and implicit description thanks to tensor decompositions. Tensor enables to consider a video as a multi-dimensional data table. The extracted description are evaluated in a classification task. Finally, we have studied speed normalization method thanks to Dynamical Time Warping methods on series. We have showed that this normalization improve the classification rates
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Chemello, Emiliano. "Avaliação de diferentes potenciais interatômicos no cálculo do tensor de elasticidade do tungstato de zircônio." reponame:Repositório Institucional da UCS, 2009. https://repositorio.ucs.br/handle/11338/413.

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O Tungstato de Zircônio (ZrW2O8) é um material que exibe Expansão Térmica Negativa (ETN), isotrópica em um amplo intervalo de temperatura (0,3 a 1050 K). Apesar de amplamente estudado, existem controvérsias acerca dos mecanismos microscópicos responsáveis por este comportamento. A fase cúbica deste composto, denominada a-ZrW2O8, já foi motivo de estudo através de simulações computacionais utilizando Potenciais Interatômicos (PI) e Dinâmica de Rede na Aproximação Quasi-Harmônica (DRQH). Nos dois PI distintos propostos na literatura conseguiu-se reproduzir a ETN da a-ZrW2O8, mas não a dependência com a temperatura do tensor de elasticidade. É partindo desta observação que este trabalho pretende avaliar o desempenho de PI existentes e de novos PI em simulações computacionais visando a descrição da dependência com a temperatura do tensor de elasticidade da a-ZrW2O8 entre 0 e 300 K. Utilizaram-se dados experimentais, tais como posições atômicas, parâmetros de rede e o tensor de elasticidade da a-ZrW2O8 em temperaturas entre 0 e 300 K e, em outra série de cálculos, a hipersuperfície de energia ab initio no limite atérmico para obter os parâmetros dos PI. Diferentes estratégias foram empregadas na busca pelos parâmetros dos PI incluindo minimização em linha, Newton-Raphson/BFGS e Algoritmo Genético (AG). Concluiu-se que não é possível descrever as propriedades estruturais e elásticas da a-ZrW2O8 em função da temperatura com PI simples e que esta incapacidade não está relacionada a qualquer limitação da DRQH ou dos parâmetros dos PI, mas à forma analítica dos PI empregados. Isto sugere que se deve ter cautela na interpretação de resultados obtidos com estes potencias já disponíveis na literatura. Como alternativas para a solução deste problema, pode-se considerar o uso de redes neurais para a representação da hipersuperfície de energia ab initio, o uso de PI mais sofisticados que levam em consideração a vizinhança atômica (bond order potentials) e, também, cálculo ab initio a T > 0, este último a um custo computacional muito mais elevado.
Submitted by Marcelo Teixeira (mvteixeira@ucs.br) on 2014-05-28T17:16:32Z No. of bitstreams: 1 Dissertacao Emiliano Chemello.pdf: 1343523 bytes, checksum: 46461698a2b6139def916307ab93478f (MD5)
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Zirconium tungstate (ZrW2O8) is a material that exhibits negative thermal expansion (NTE), over a wide temperature range (0.3 at 1050 K). Although thoroughly studied, controversies still remain concerning the microscopic mechanisms responsible for this behavior. The cubic phase of this compound, denominated a-ZrW2O8, was already the subject of study through computer simulations using interatomic potentials (IP) and lattice dynamics in quasiharmonic approximation (LDQH). In two different IPs proposed in the literature succeeded in reproducing the a-ZrW2O8 NTE, but not the dependence with temperature of the elasticity tensor. Starting from this observation, this work intends to evaluate of existent IPs and same proposed new IPs in computer simulations aiming the calculation of the tensor of elasticity for a-ZrW2O8 between 0 and 300 K. Experimental data (such as atomic positions, lattice parameters and the tensor of elasticity of a-ZrW2O8 at 0 and 300 K) and, in another series of calculations, the ab initio energy hypersurface in the athermic limit, were used to obtain the parameters of the IPs. Different strategies were used in the search for the parameters of IP, including line minimization, Newton-Raphson/BFGS and genetic algorithm (GA). At the end of an exhaustive search we were led to conclude that it is not possible to describe the structure and elastic properties of a-ZrW2O8 as a function of temperature with simple IPs and that this incapacity is not related the any limitation of LDQH or of the parameters of the IPs, but instead to the analytical form of the tested IPs. This suggests that same results obtained with IPs already available in the literature may be unreliable. As alternatives for the solution of this problem, it can be considered the use of a neural network for the representation of the ab initio energy hypersurface, the use of more sophisticated IPs than take into account the atomic neighborhood (bond order potentials) and even (with a computational cost much higher) ab initio calculations at T > 0.
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Gao, Liang. "Ultrasound Elasticity Imaging of Human Posterior Tibial Tendon." Diss., The University of Arizona, 2014. http://hdl.handle.net/10150/338897.

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Posterior tibial tendon dysfunction (PTTD) is a common degenerative condition leading to a severe impairment of gait. There is currently no effective method to determine whether a patient with advanced PTTD would benefit from several months of bracing and physical therapy or ultimately require surgery. Tendon degeneration is closely associated with irreversible degradation of its collagen structure, leading to changes to its mechanical properties. If these properties could be monitored in vivo, it could be used to quantify the severity of tendonosis and help determine the appropriate treatment. Ultrasound elasticity imaging (UEI) is a real-time, noninvasive technique to objectively measure mechanical properties in soft tissue. It consists of acquiring a sequence of ultrasound frames and applying speckle tracking to estimate displacement and strain at each pixel. The goals of my dissertation were to 1) use acoustic simulations to investigate the performance of UEI during tendon deformation with different geometries; 2) develop and validate UEI as a potentially noninvasive technique for quantifying tendon mechanical properties in human cadaver experiments; 3) design a platform for UEI to measure mechanical properties of the PTT in vivo and determine whether there are detectable and quantifiable differences between healthy and diseased tendons. First, ultrasound simulations of tendon deformation were performed using an acoustic modeling program. The effects of different tendon geometries (cylinder and curved cylinder) on the performance of UEI were investigated. Modeling results indicated that UEI accurately estimated the strain in the cylinder geometry, but underestimated in the curved cylinder. The simulation also predicted that the out-of-the-plane motion of the PTT would cause a non-uniform strain pattern within incompressible homogeneous isotropic material. However, to average within a small region of interest determined by principal component analysis (PCA) would improve the estimation. Next, UEI was performed on five human cadaver feet mounted in a materials testing system (MTS) while the PTT was attached to a force actuator. A portable ultrasound scanner collected 2D data during loading cycles. Young's modulus was calculated from the strain, loading force and cross sectional area of the PTT. Average Young's modulus for the five tendons was (0.45±0.16GPa) using UEI. This was consistent with simultaneous measurements made by the MTS across the whole tendon (0.52±0.18GPa). We also calculated the scaling factor (0.12±0.01) between the load on the PTT and the inversion force at the forefoot, a measurable quantity in vivo. This study suggests that UEI could be a reliable in vivo technique for estimating the mechanical properties of the human PTT. Finally, we built a custom ankle inversion platform for in vivo imaging of human subjects (eight healthy volunteers and nine advanced PTTD patients). We found non-linear elastic properties of the PTTD, which could be quantified by the slope between the elastic modulus (E) and the inversion force (F). This slope (ΔE/ΔF), or Non-linear Elasticity Parameter (NEP), was significantly different for the two groups: 0.16±0.20 MPa/N for healthy tendons and 0.45±0.43 MPa/N for PTTD tendons. A receiver operating characteristic (ROC) curve revealed an area under the curve (AUC) of 0.83±0.07, which indicated that the classifier system is valid. In summary, the acoustic modeling, cadaveric studies, and in vivo experiments together demonstrated that UEI accurately quantifies tendon mechanical properties. As a valuable clinical tool, UEI also has the potential to help guide treatment decisions for advanced PTTD and other tendinopathies.
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Lichtwark, Glen Anthony. "The role of muscle tendon unit elasticity in real life activities." Thesis, University College London (University of London), 2005. http://discovery.ucl.ac.uk/1444942/.

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The interaction of a muscle and associated tendon during dynamic activities such as locomotion is critical for both force production and economical movement. It is generally assumed that, under sub-maximal conditions, muscle activation patterns are optimised to achieve maximum efficiency of work. Here, I explore the interaction between the contractile component (CC) and the elastic tendinous tissue to understand the relationship between a muscle's power output and efficiency. In this thesis, I examine the interaction of the CE and the elastic tendinous tissue and its effect on power output and efficiency of muscle using both experimental and modelling techniques. In the first chapter, a model of muscle energetics is developed and validated against dynamic muscle contractions of different muscle types. I then used this model to explore how optimal muscle power and efficiency varies with different activation conditions, clastic properties and length change trajectories. The third and forth chapter presents experiments which explore ultrasound measurement techniques for determining the length changes and mechanical properties of the human gastrocnemius medial is (GM) muscle fibres and Achilles tendon (AT) respectively. I then used similar techniques to explore musclc-tcndon unit (MTU) interaction during gait under different gait conditions. Specifically, I explore how GM power output and efficiency vary with different speeds and inclination and explore how variation in tendinous compliance might influence muscle efficiency. The results suggest that muscles remain highly efficient due to compliant tendons allowing muscle fibres to act at highly powerful and efficient velocities. However variation in power output and particularly muscle function affects the efficiency of muscle. Finally, I determined that the optimal value of tendon stiffness for maximum GM efficiency during walking and running is close to that determined experimentally.
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VALLEJOS, CASTRO GABRIELA. "A Tension Please." Thesis, Högskolan i Borås, Institutionen Textilhögskolan, 2014. http://urn.kb.se/resolve?urn=urn:nbn:se:hb:diva-18107.

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This degree work is about the exploration of the stretch in textile materials by using cartridge pleats as a method to create weight and thereby create tension. Through research in materials and stretch fabrics versus heavier woven textiles the work strives for expressions in movement as well as new ways of combining lightness and weight.
Program: Modedesignutbildningen
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Günnel, Andreas, and Roland Herzog. "Optimal Control Problems in Finite-Strain Elasticity by Inner Pressure and Fiber Tension." Universitätsbibliothek Chemnitz, 2016. http://nbn-resolving.de/urn:nbn:de:bsz:ch1-qucosa-209295.

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Optimal control problems for finite-strain elasticity are considered. An inner pressure or an inner fiber tension is acting as a driving force. Such internal forces are typical, for instance, for the motion of heliotropic plants, and for muscle tissue. Non-standard objective functions relevant for elasticity problems are introduced. Optimality conditions are derived on a formal basis, and a limited-memory quasi-Newton algorithm for their solution is formulated in function space. Numerical experiments confirm the expected mesh-independent performance.
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Romani, Marcelo. "A influência do controle da tensão do elastano durante o processo produtivo nas propriedades elásticas dos tecidos com elastano para fitness." Universidade de São Paulo, 2016. http://www.teses.usp.br/teses/disponiveis/100/100133/tde-27092016-104157/.

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O objetivo deste estudo é verificar qual é a efetiva contribuição prática que o monitoramento da tensão do elastano durante o processo produtivo de tecidos destinados à moda esportiva, terá sobre as características de gramatura e elasticidade, esta última traduzida como força de recuperação do tecido, na tentativa de tornar o processo mais eficiente no atendimento dos anseios dos clientes em ter o \"handle\" ou \"mão\" do tecido apresentando elevado \"power\" ou resistência ao alongamento, avaliação subjetiva muito utilizada nas confecções de artigos para fitness e moda esportiva em geral e que deve ser cientificamente parametrizada em termos de processo de forma a garantir que tais necessidades sejam atendidas. Para a manutenção de um único padrão de regulagem a ser estudado, e o estudo livre de outras variáveis, o L.F.A. e a tensão do fio de poliamida são mantidos constantes. Foi aplicado um monitoramento da tensão do elastano para mantê-lo na condição mais alta afim de evitar suas variações a menor, causada pelas variações da matéria prima, o que teoricamente leva ao empobrecimento desta força ou mão. Através deste monitoramento foi possível constatar por análise estatística, uma melhora no índice de capacidade do processo com maior número de peças dentro das faixas desejadas para o produto com suas médias mostrando o ganho de força sem alterações significativas da gramatura dos produtos conforme premissa inicial
The aim of this study is to determine what is the effective practical contribution to the monitoring of elastane tension during the production of knitted fabrics for the sports fashion, mainly on the characteristics of fabric weight and elasticity, the latter translated as tissue recovery strength, attempt to make the process more efficient in customer desires of service to have the \"handle\" or \"hand\" of the fabric featuring high \"power\" or resistance to stretching, subjective evaluation widely used in clothing articles for fitness and sports fashion in general and must be scientifically parameterized in terms of the process to ensure that these needs are met. In order to maintain a single standard regulation to be studied, and the free study other variables, L.F.A. and the tension of polyamide yarn is kept constant. The monitoring of the elastane tension was applied to keep it in the highest condition in order to prevent their smaller the variations caused by variations of the raw material, which theoretically leads to the impoverishment of this force or hand. Through this monitoring, it was verified by statistical analysis, an improvement in the capacity index of the process with the largest number of parts within the desired ranges for the product with their average showing strength gains without significant changes in the fabric weight of the product as initial premise
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Du, Wenwen. "Material Tensors and Pseudotensors of Weakly-Textured Polycrystals with Orientation Measure Defined on the Orthogonal Group." UKnowledge, 2014. http://uknowledge.uky.edu/math_etds/22.

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Material properties of polycrystalline aggregates should manifest the influence of crystallographic texture as defined by the orientation distribution function (ODF). A representation theorem on material tensors of weakly-textured polycrystals was established by Man and Huang (2012), by which a given material tensor can be expressed as a linear combination of an orthonormal set of irreducible basis tensors, with the components given explicitly in terms of texture coefficients and a number of undetermined material parameters. Man and Huang's theorem is based on the classical assumption in texture analysis that ODFs are defined on the rotation group SO(3), which strictly speaking makes it applicable only to polycrystals with (single) crystal symmetry defined by a proper point group. In the present study we consider ODFs defined on the orthogonal group O(3) and extend the representation theorem of Man and Huang to cover pseudotensors and polycrystals with crystal symmetry defined by any improper point group. This extension is important because many materials, including common metals such as aluminum, copper, iron, have their group of crystal symmetry being an improper point group. We present the restrictions on texture coefficients imposed by crystal symmetry for all the 21 improper point groups and we illustrate the extended representation theorem by its application to elasticity.
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Books on the topic "Tensor of elasticity"

1

J, Pagano Nicholas, ed. Elasticity: Tensor, dyadic, and engineering approaches. New York: Dover Publications, 1992.

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Renton, J. D. Applied elasticity: Matrix and tensor analysis of elastic continua. Chichester: E. Horwood, 1987.

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Matrix and tensor calculus: With applications to mechanics, elasticity, and aeronautics. Mineola, N.Y: Dover Publications, 2008.

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Die Entstehung des Tensorkalküls: Von den Anfängen in der Elastizitätstheorie bis zur Verwendung in der Baustatik. Stuttgart: F. Steiner, 1991.

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Applied Elasticity: Matrix and Tensor Analysis of Elastic Continua (Horwood Engineering Science). 2nd ed. Horwood Publishing Limited, 2003.

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Escudier, Marcel. Fluids and fluid properties. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198719878.003.0002.

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In this chapter it is shown that the differences between solids, liquids, and gases have to be explained at the level of the molecular structure. The continuum hypothesis makes it possible to characterise any fluid and ultimately analyse its response to pressure difference Δ‎p and shear stress τ‎ through macroscopic physical properties, dependent only upon absolute temperature T and pressure p, which can be defined at any point in a fluid. The most important of these physical properties are density ρ‎ and viscosity μ‎, while some problems are also influenced by compressibility, vapour pressure pV, and surface tension σ‎. It is also shown that the bulk modulus of elasticity Ks is a measure of fluid compressibility which determines the speed at which sound propagates through a fluid. The perfect-gas law is introduced and an equation derived for the soundspeed c.
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Newnham, Robert E. Properties of Materials. Oxford University Press, 2004. http://dx.doi.org/10.1093/oso/9780198520757.001.0001.

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Crystals are sometimes called 'Flowers of the Mineral Kingdom'. In addition to their great beauty, crystals and other textured materials are enormously useful in electronics, optics, acoustics and many other engineering applications. This richly illustrated text describes the underlying principles of crystal physics and chemistry, covering a wide range of topics and illustrating numerous applications in many fields of engineering using the most important materials today. Tensors, matrices, symmetry and structure-property relationships form the main subjects of the book. While tensors and matrices provide the mathematical framework for understanding anisotropy, on which the physical and chemical properties of crystals and textured materials often depend, atomistic arguments are also needed to quantify the property coefficients in various directions. The atomistic arguments are partly based on symmetry and partly on the basic physics and chemistry of materials. After introducing the point groups appropriate for single crystals, textured materials and ordered magnetic structures, the directional properties of many different materials are described: linear and nonlinear elasticity, piezoelectricity and electrostriction, magnetic phenomena, diffusion and other transport properties, and both primary and secondary ferroic behavior. With crystal optics (its roots in classical mineralogy) having become an important component of the information age, nonlinear optics is described along with the piexo-optics, magneto-optics, and analogous linear and nonlinear acoustic wave phenomena. Enantiomorphism, optical activity, and chemical anisotropy are discussed in the final chapters of the book.
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Book chapters on the topic "Tensor of elasticity"

1

Miu, Denny K. "Elasticity Tensor." In Mechatronics, 211–13. New York, NY: Springer New York, 1993. http://dx.doi.org/10.1007/978-1-4612-4358-8_13.

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Talpaert, Yves R. "Linear Elasticity." In Tensor Analysis and Continuum Mechanics, 455–540. Dordrecht: Springer Netherlands, 2002. http://dx.doi.org/10.1007/978-94-015-9988-7_6.

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Boehler, J. P. "Anisotropic Linear Elasticity." In Applications of Tensor Functions in Solid Mechanics, 55–65. Vienna: Springer Vienna, 1987. http://dx.doi.org/10.1007/978-3-7091-2810-7_4.

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Coman, Ciprian D. "Compatibility of the Infinitesimal Deformation Tensor." In Continuum Mechanics and Linear Elasticity, 281–318. Dordrecht: Springer Netherlands, 2019. http://dx.doi.org/10.1007/978-94-024-1771-5_6.

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Jikov, V. V., S. M. Kozlov, and O. A. Oleinik. "Estimates for the Homogenized Elasticity Tensor." In Homogenization of Differential Operators and Integral Functionals, 391–414. Berlin, Heidelberg: Springer Berlin Heidelberg, 1994. http://dx.doi.org/10.1007/978-3-642-84659-5_13.

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Herberthson, Magnus, Evren Özarslan, and Carl-Fredrik Westin. "Variance Measures for Symmetric Positive (Semi-) Definite Tensors in Two Dimensions." In Mathematics and Visualization, 3–22. Cham: Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-56215-1_1.

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AbstractCalculating the variance of a family of tensors, each represented by a symmetric positive semi-definite second order tensor/matrix, involves the formation of a fourth order tensor $$R_{abcd}$$ R abcd . To form this tensor, the tensor product of each second order tensor with itself is formed, and these products are then summed, giving the tensor $$R_{abcd}$$ R abcd the same symmetry properties as the elasticity tensor in continuum mechanics. This tensor has been studied with respect to many properties: representations, invariants, decomposition, the equivalence problem et cetera. In this paper we focus on the two-dimensional case where we give a set of invariants which ensures equivalence of two such fourth order tensors $$R_{abcd}$$ R abcd and $$\widetilde{R}_{abcd}$$ R ~ abcd . In terms of components, such an equivalence means that components $$R_{ijkl}$$ R ijkl of the first tensor will transform into the components $$\widetilde{R}_{ijkl}$$ R ~ ijkl of the second tensor for some change of the coordinate system.
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Malyarenko, Anatoliy, and Martin Ostoja-Starzewski. "Spectral Expansion of Three-Dimensional Elasticity Tensor Random Fields." In Engineering Mathematics I, 281–300. Cham: Springer International Publishing, 2016. http://dx.doi.org/10.1007/978-3-319-42082-0_16.

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He, Q. C., and A. Curnier. "Characterising a 2D Elasticity Tensor by Two Orientation Distribution Functions." In Solid Mechanics and Its Applications, 25–30. Dordrecht: Springer Netherlands, 1995. http://dx.doi.org/10.1007/978-94-015-8494-4_3.

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Hoppe, Ronald H. W., Svetozara I. Petrova, and Yuri V. Vassilevski. "Adaptive Grid Refinement for Computation of the Homogenized Elasticity Tensor." In Large-Scale Scientific Computing, 371–78. Berlin, Heidelberg: Springer Berlin Heidelberg, 2004. http://dx.doi.org/10.1007/978-3-540-24588-9_42.

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Neff, Patrizio, Robert J. Martin, and Bernhard Eidel. "New Thoughts in Nonlinear Elasticity Theory via Hencky’s Logarithmic Strain Tensor." In Advanced Structured Materials, 165–80. Singapore: Springer Singapore, 2017. http://dx.doi.org/10.1007/978-981-10-3764-1_11.

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Conference papers on the topic "Tensor of elasticity"

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Bóna, A., D. Nadri, and M. Brajanovski. "Elasticity Tensor Inversion from Spherical Sample Measurements." In 71st EAGE Conference and Exhibition incorporating SPE EUROPEC 2009. European Association of Geoscientists & Engineers, 2009. http://dx.doi.org/10.3997/2214-4609.201400117.

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Vaz, E. G. L. R. "Mathematical Properties of the Elasticity Difference Tensor." In A CENTURY OF RELATIVITY PHYSICS: ERE 2005; XXVIII Spanish Relativity Meeting. AIP, 2006. http://dx.doi.org/10.1063/1.2218255.

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Ran, Jie, Rui Lin, Hayden K. H. So, Graziano Chesi, and Ngai Wong. "Exploiting Elasticity in Tensor Ranks for Compressing Neural Networks." In 2020 25th International Conference on Pattern Recognition (ICPR). IEEE, 2021. http://dx.doi.org/10.1109/icpr48806.2021.9412765.

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Shurina, Ella P., and Anastasiia Y. Kutishcheva. "Numerical Determination of the Effective Elasticity Tensor of an Heterogeneous Solid." In 2018 XIV International Scientific-Technical Conference on Actual Problems of Electronics Instrument Engineering (APEIE). IEEE, 2018. http://dx.doi.org/10.1109/apeie.2018.8545721.

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Arts, Rob J., and Patrick N. J. Rasolofosaon. "Complete elasticity tensor in dry and saturated rocks: Experiments versus theory." In SEG Technical Program Expanded Abstracts 1992. Society of Exploration Geophysicists, 1992. http://dx.doi.org/10.1190/1.1822176.

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Boutaous, M’hamed, Matthieu Zinet, Rabie El Otmani, and Patrick Bourgin. "Simulation of Polymer Crystallization: Role of the Visco-Elasticity." In ASME 2010 3rd Joint US-European Fluids Engineering Summer Meeting collocated with 8th International Conference on Nanochannels, Microchannels, and Minichannels. ASMEDC, 2010. http://dx.doi.org/10.1115/fedsm-icnmm2010-30209.

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In polymer processing, it is established that the flow causes the polymer chains to stretch and store the energy, by changing their quiescent state free energy. Koscher et al. [1] presented in 2002 an experimental work concerning the flow induced crystallization. They made the assumption that the polymer melt elasticity, quantified by the first normal stress difference, is the driving force of flow-induced extra nucleation. In their work, a constant shear stress is considered, and the first normal stress difference agrees with the use of the trace of the stress tensor. The stored energy due to the flow “Δ Ge” is commonly called elastic free energy and associated to the change in conformational tensor due to flow. By extending the Marrucci theory [2], several studies link this Δ Ge to the trace of the deviatoric stress tensor (first invariant). In this paper, a numerical model able to simulate polymer crystallization is developed. It is based on the assumption that flow induced extra nucleation is linked to the trace of the deviatoric stress tensor. Thus a viscoelastic constitutive equation, the multimode Upper Convected Maxwell (UCM) model, is used to express the viscoelastic extra-stress tensor τVE, and a damping function is introduced in order to take into account the nonlinear viscoelasticity of the material. In Koscher’s work [1], the integral formulation of the Upper Convected Maxwell (UCM) model is used too, but without any damping function, i.e. they assume that the polymer behaves as linear viscoelastic. As an application, a 2D isothermal flow configuration between two plates is simulated. A comparison between the proposed model and the Koscher’s one is then performed, and interesting resultes are pesented: without introducing a damping function, the two models give similar results in the same configurations, but the introduction of a damping function leads to important discrepancies between the two models, seeming that the assumption of a linear viscoelastic behavior is not realistic when the fluid strain and/or stresses are greater than a given values.
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Nadri, Dariush, Andrej Bóna, and Miroslav Brajanovsky. "Estimation of elasticity tensor from the inversion of traveltimes in spherical shale samples." In Beijing 2009 International Geophysical Conference and Exposition. Society of Exploration Geophysicists, 2009. http://dx.doi.org/10.1190/1.3603774.

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Shariff, M. H. B. M. "A general spectral nonlinear 4th-order material elasticity tensor formula for finite element implementations." In INTERNATIONAL CONFERENCE OF NUMERICAL ANALYSIS AND APPLIED MATHEMATICS ICNAAM 2019. AIP Publishing, 2020. http://dx.doi.org/10.1063/5.0026834.

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Pisano, Aurora, Alba Sofi, and Paolo Fuschi. "A Finite Element Approach for Nonhomogeneous Nonlocal Elastic Problems." In ASME 2008 International Mechanical Engineering Congress and Exposition. ASMEDC, 2008. http://dx.doi.org/10.1115/imece2008-68240.

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The paper deals with the implementation of a method, known in the relevant literature as Nonlocal Finite Element Method, for solving 2D boundary value problems in the context of nonhomogeneous nonlocal elasticity. The method, founded on a consistent thermodynamic formulation, is here improved making use of a phenomenological strain-difference-based nonhomogeneous nonlocal elasticity model. The latter assumes a two components local/nonlocal constitutive relation in which the stress is conceived as the sum of two contributions governed by the standard elastic moduli tensor and by a nonlocal stiffness tensor, respectively. Two numerical examples are presented and the obtained results are discussed both to verify the reliability of the method and to show its potential and limits for the analysis of nonhomogeneous nonlocal elastic problems.
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Keskinen, Erno, Michel Cotsaftis, and Matti Martikainen. "Half-Critical Response of Cylindrical Rotor to Distributed Elasticity Excitation." In ASME 2005 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2005. http://dx.doi.org/10.1115/detc2005-85365.

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Due to the limitations of manufacturing accuracy, long cylindrical rotors used in heavy power transmission lines and paper machinery are dynamically excited by internal elastic forces. The origin of these forces is the out-of-roundness profile of the inner and outer radii of the rotor, which contributes to the bending stiffness distribution along the rotor span. Distributed anisotropy of the rotor under gravitational load is reason of the existence of half-critical speeds, on which the rotor experiences non-classical resonance state. This problem has been formulated in terms of nominal and deviated motion according to the splitting of the bending stiffness tensor in a similar way. This leads to a static rotor equation, whose amplification effect on to the dynamic part of the motion has been analyzed in details. This includes formal solution of the resulting dynamic Hill equation in terms of the modal coordinates of the corresponding free whirling Rayleigh beam.
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