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Gotowa bibliografia na temat „Strain tensor”

Autor: Grafiati

Data publikacji: 4 czerwca 2021

Data aktualizacji: 10 marca 2023

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Artykuły w czasopismach na temat "Strain tensor"

Morawiec, A. "On accounting for preferred crystallite orientations in determination of average elastic strain by diffraction." Journal of Applied Crystallography 51, no. 1 (February 1, 2018): 148–56. http://dx.doi.org/10.1107/s1600576718000079.

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Standard diffraction-based measurements of elastic strains in polycrystalline materials rely on shifts of Bragg peaks. Measurement results are usually given in the form of a single tensor assumed to represent the average stress in the material, but the question about the true relationship between the tensor and the average stress generally goes without notice. This paper describes a novel procedure for analysis of data obtained from such measurements. It is applicable in cases when spatial correlations in the material are ignored and statistical information about the polycrystalline specimen is limited to texture-related intensity pole figures and strain pole figures. A tensor closest to auxiliary strain tensors linked to the results of measurements in particular specimen directions is considered to represent the strain state. This tensor is shown to be a good approximation of the average strain tensor. A closed-form expression allowing for its direct computation from experimental pole figures is given. The performance of the procedure is illustrated using simulated data.

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Bazˇant, Zdeneˇk P. "Easy-to-Compute Tensors With Symmetric Inverse Approximating Hencky Finite Strain and Its Rate." Journal of Engineering Materials and Technology 120, no. 2 (April 1, 1998): 131–36. http://dx.doi.org/10.1115/1.2807001.

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It is shown that there exist approximations of the Hencky (logarithmic) finite strain tensor of various degrees of accuracy, having the following characteristics: (1) The tensors are close enough to the Hencky strain tensor for most practical purposes and coincide with it up to the quadratic term of the Taylor series expansion; (2) are easy to compute (the spectral representation being unnecessary); and (3) exhibit tension-compression symmetry (i.e., the strain tensor of the inverse transformation is minus the original strain tensor). Furthermore, an additive decomposition of the proposed strain tensor into volumetric and deviatoric (isochoric) parts is given. The deviatoric part depends on the volume change, but this dependence is negligible for materials that are incapable of large volume changes. A general relationship between the rate of the approximate Hencky strain tensor and the deformation rate tensor can be easily established.

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Chandra, N., and Zhiyum Xie. "Development of Generalized Plane-Strain Tensors for the Concentric Cylinder." Journal of Applied Mechanics 62, no. 3 (September 1, 1995): 590–94. http://dx.doi.org/10.1115/1.2895986.

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A pair of two new tensors called GPS tensors S and D is proposed for the concentric cylindrical inclusion problem. GPS tensor S relates the strain in the inclusion constrained by the matrix of finite radius to the uniform transformation strain (eigenstrain), whereas tensor D relates the strain in the matrix to the same eigenstrain. When the cylindrical matrix is of infinite radius, tensor S reduces to the appropriate Eshelby’s tensor. Explicit expressions to evaluate thermal residual stresses σr, σθ and σz in the matrix and the fiber using tensor D and tensor S, respectively, are developed. Since the geometry of the present problem is of finite radius, the effect of fiber volume fraction on the stress distribution can be easily studied. Results for the thermal residual stress distributions are compared with Eshelby’s infinite domain solution and finite element results for a specified fiber volume fraction.

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Boutelier, David, Christoph Schrank, and Klaus Regenauer-Lieb. "2-D finite displacements and strain from particle imaging velocimetry (PIV) analysis of tectonic analogue models with TecPIV." Solid Earth 10, no. 4 (July 15, 2019): 1123–39. http://dx.doi.org/10.5194/se-10-1123-2019.

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Abstract. Image correlation techniques have provided new ways to analyse the distribution of deformation in analogue models of tectonics in space and time. Here, we demonstrate, using a new version of our software package (TecPIV), how the correlation of successive time-lapse images of a deforming model allows not only to evaluate the components of the strain-rate tensor at any time in the model but also to calculate the finite displacements and finite strain tensor. We illustrate with synthetic images how the algorithm produces maps of the velocity gradients, small-strain tensor components, incremental or instantaneous principal strains and maximum shear. The incremental displacements can then be summed up with Eulerian or Lagrangian summation, and the components of the 2-D finite strain tensor can be calculated together with the finite principal strain and maximum finite shear. We benchmark the measures of finite displacements using specific synthetic tests for each summation mode. The deformation gradient tensor is calculated from the deformed state and decomposed into the finite rigid-body rotation and left or right finite-stretch tensors, allowing the deformation ellipsoids to be drawn. The finite strain has long been the only quantified measure of strain in analogue models. The presented software package allows producing these finite strain measures while also accessing incremental measures of strain. The more complete characterisation of the deformation of tectonic analogue models will facilitate the comparison with numerical simulations and geological data and help produce conceptual mechanical models.

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Surana, Karan S., and Stephen W. Long. "Ordered Rate Constitutive Theories for Non-Classical Thermofluids Based on Convected Time Derivatives of the Strain and Higher Order Rotation Rate Tensors Using Entropy Inequality." Entropy 22, no. 4 (April 14, 2020): 443. http://dx.doi.org/10.3390/e22040443.

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This paper considers non-classical continuum theory for thermoviscous fluids without memory incorporating internal rotation rates resulting from the antisymmetric part of the velocity gradient tensor to derive ordered rate constitutive theories for the Cauchy stress and the Cauchy moment tensor based on entropy inequality and representation theorem. Using the generalization of the conjugate pairs in the entropy inequality, the ordered rate constitutive theory for Cauchy stress tensor considers convected time derivatives of the Green’s strain tensor (or Almansi strain tensor) of up to orders n ε as its argument tensors and the ordered rate constitutive theory for the Cauchy moment tensor considers convected time derivatives of the symmetric part of the rotation gradient tensor up to orders n Θ . While the convected time derivatives of the strain tensors are well known the convected time derivatives of higher orders of the symmetric part of the rotation gradient tensor need to be derived and are presented in this paper. Complete and general constitutive theories based on integrity using conjugate pairs in the entropy inequality and the generalization of the argument tensors of the constitutive variables and the representation theorem are derived and the material coefficients are established. It is shown that for the type of non-classical thermofluids considered in this paper the dissipation mechanism is an ordered rate mechanism due to convected time derivatives of the strain tensor as well as the convected time derivatives of the symmetric part of the rotation gradient tensor. The derivations of the constitutive theories presented in the paper is basis independent but can be made basis specific depending upon the choice of the specific basis for the constitutive variables and the argument tensors. Simplified linear theories are also presented as subset of the general constitutive theories and are compared with published works.

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Theocaris, P. S., and D. P. Sokolis. "Linear elastic eigenstates of the compliance tensor for trigonal crystals." Zeitschrift für Kristallographie - Crystalline Materials 215, no. 1 (January 1, 2000): 1–9. http://dx.doi.org/10.1524/zkri.2000.215.1.01.

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The spectral decomposition of the compliance fourth-rank tensor, representative of a trigonal crystalline or other anisotropic medium, is offered in this paper, and its characteristic values and idempotent fourth-rank tensors are established, with respect to the Cartesian tensor components. Consequently, it is proven that the idempotent tensors serve to analyse the second-rank symmetric tensor space into orthogonal subspaces, resolving the stress and strain tensors for the trigonal medium into their eigentensors, and, finally, decomposing the total elastic strain energy density into distinct, autonomous components. Finally, bounds on the values of the compliance tensor components for the trigonal system, dictated by the classical thermodynamical argument for the elastic potential to be positive definite, are estimated by imposing the characteristic values of the compliance tensor to be strictly positive.

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Sokolova, M. Yu, and D. V. Khristich. "FINITE STRAINS OF NONLINEAR ELASTIC ANISOTROPIC MATERIALS." Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mekhanika, no. 70 (2021): 103–16. http://dx.doi.org/10.17223/19988621/70/9.

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Anisotropic materials with the symmetry of elastic properties inherent in crystals of cubic syngony are considered. Cubic materials are close to isotropic ones by their mechanical properties. For a cubic material, the elasticity tensor written in an arbitrary (laboratory) coordinate system, in the general case, has 21 non-zero components that are not independent. An experimental method is proposed for determining such a coordinate system, called canonical, in which a tensor of elastic properties includes only three nonzero independent constants. The nonlinear model of the mechanical behavior of cubic materials is developed, taking into account geometric and physical nonlinearities. The specific potential strain energy for a hyperelastic cubic material is written as a function of the tensor invariants, which are projections of the Cauchy-Green strain tensor into eigensubspaces of the cubic material. Expansions of elasticity tensors of the fourth and sixth ranks in tensor bases in eigensubspaces are determined for the cubic material. Relations between stresses and finite strains containing the second degree of deformations are obtained. The expressions for the stress tensor reflect the mutual influence of the processes occurring in various eigensubspaces of the material under consideration.

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Theocaris, Pericles S., and Dimitrios P. Sokolis. "Spectral decomposition of the linear elastic tensor for monoclinic symmetry." Acta Crystallographica Section A Foundations of Crystallography 55, no. 4 (July 1, 1999): 635–47. http://dx.doi.org/10.1107/s0108767398016766.

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The compliance fourth-rank tensor related to crystalline or other anisotropic media belonging to the monoclinic crystal system is spectrally decomposed for the first time, and its characteristic values and idempotent fourth-rank tensors are established. Further, it is proven that the idempotent tensors resolve the stress and strain second-rank tensors into eigentensors, thus giving rise to a decomposition of the total elastic strain-energy density into non-interacting strain-energy parts. Several examples of representative inorganic crystals of the monoclinic system illustrate the results of the theoretical analysis. It is also proven that the essential parameters required for a coordinate-invariant characterization of the elastic properties of a crystal exhibiting monoclinic symmetry are both the six characteristic values of the compliance tensor and seven dimensionless parameters. These material constants, referred to as the eigenangles, are shown to be accountable for the orientation of the stress and strain eigentensors, when represented in a stress coordinate system. Finally, the restrictions dictated by the classical thermodynamical argument on the elements of the compliance tensor, which are necessary and sufficient for the elastic strain-energy density to be positive definite, are investigated for the monoclinic symmetry.

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Moore, J. G., S. A. Schorn, and J. Moore. "Education Committee Best Paper of 1995 Award: Methods of Classical Mechanics Applied to Turbulence Stresses in a Tip Leakage Vortex." Journal of Turbomachinery 118, no. 4 (October 1, 1996): 622–29. http://dx.doi.org/10.1115/1.2840917.

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Moore et al. measured the six Reynolds stresses in a tip leakage vortex in a linear turbine cascade. Stress tensor analysis, as used in classical mechanics, has been applied to the measured turbulence stress tensors. Principal directions and principal normal stresses are found. A solid surface model, or three-dimensional glyph, for the Reynolds stress tensor is proposed and used to view the stresses throughout the tip leakage vortex. Modeled Reynolds stresses using the Boussinesq approximation are obtained from the measured mean velocity strain rate tensor. The comparison of the principal directions and the three-dimensional graphic representations of the strain and Reynolds stress tensors aids in the understanding of the turbulence and what is required to model it.

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Elata, D., and M. B. Rubin. "Isotropy of Strain Energy Functions Which Depend Only on a Finite Number of Directional Strain Measures." Journal of Applied Mechanics 61, no. 2 (June 1, 1994): 284–89. http://dx.doi.org/10.1115/1.2901442.

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Motivated by studies of low-density materials and fiber-dominated composites, we consider an elastic material whose strain energy function depends only on a finite number of directional strain measures, which correspond to the strains of material fibers in specific material directions. It is shown that an arbitrary set of six distinct direction vectors can be used to define six symmetric base tensors which span the space of all symmetric second-order tensors. Using these base tensors and their reciprocal tensors we develop a representation for the strain tensor in terms of six directional strain measures. The functional form of the strain energy of a general anisotropic nonlinear elastic material may then be expressed in terms of these directional strain measures. Next, we consider general nonlinear isotropic response by developing explicit functional forms for three independent strain invariants in terms of these directional strain measures. Finally, with reference to previous work, we discuss isotropy of specific functional forms of directional strain measures associated with up to 15 directions in space.

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Rozprawy doktorskie na temat "Strain tensor"

Jacot, Benjamin (Benjamin Paul Emmanuel). "A strain tensor method for three-dimensional optimal Michell structures." Thesis, Massachusetts Institute of Technology, 2016. http://hdl.handle.net/1721.1/104125.

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Thesis: M. Eng., Massachusetts Institute of Technology, Department of Civil and Environmental Engineering, 2016. This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections. Cataloged from student-submitted PDF version of thesis. Includes bibliographical references (pages 94-95). In the design of discrete structures such as trusses and frames, important quantitative goals such as minimal weight or minimal compliance often dominate. Many numerical techniques exist to address these needs. However, an analytical approach exists to meet similar goals, which was initiated by A.G.M. Michell (1904) and has been mostly used for two-dimensional structures so far. This thesis develops a method to extend the existing mainly two-dimensional approach to apply to three-dimensional structures. It will be referred as the Michell strain tensor method (MSTM). First, the proof that MSTM is consistent with the existing theory in two dimensions is provided. Second, two-dimensional known solutions will be replicated based on MSTM. Finally, MSTM will be used to solve new three- dimensional cases. by Benjamin Jacot. M. Eng.

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Rönnbrant, Anders. "Implementing a visualization tool for myocardial strain tensors." Thesis, Linköping University, Department of Biomedical Engineering, 2005. http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-5173.

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The heart is a complex three-dimensional structure with mechanical properties that are inhomogeneous, non-linear, time-variant and anisotropic. These properties affect major physiological factors within the heart, such as the pumping performance of the ventricles, the oxygen demand in the tissue and the distribution of coronary blood flow.During the cardiac cycle the heart muscle tissue is deformed as a consequence of the active contraction of the muscle fibers and their relaxation respectively. A mapping of this deformation would give increased understanding of the mechanical properties of the heart. The deformation induces strain and stress in the tissue which are both mechanical properties and can be described with a mathematical tensor object.The aim of this master's thesis is to develop a visualization tool for the strain tensor objects that can aid a user to see and/or understand various differences between different hearts and spatial and temporal differences within the same heart. Preferably should the tool be general enough for use with different types of data.

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Kellermann, David Conrad Mechanical &amp Manufacturing Engineering Faculty of Engineering UNSW. "Strongly orthotropic continuum mechanics." Publisher:University of New South Wales. Mechanical & Manufacturing Engineering, 2008. http://handle.unsw.edu.au/1959.4/41454.

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The principal contribution of this dissertation is a theory of Strongly Orthotropic Continuum Mechanics that is derived entirely from an assertion of geometric strain indeterminacy. Implementable into the finite element method, it can resolve widespread kinematic misrepresentations and offer unique and purportedly exact strain-induced energies by removing the assumptions of strain tensor symmetry. This continuum theory births the proposal of a new class of physical tensors described as the Intrinsic Field Tensors capable of generalising the response of most classical mechanical metrics, a number of specialised formulations and the solutions shown to be kinematically intermediate. A series of numerical examples demonstrate Euclidean objectivity, material frame-indifference, patch test satisfaction, and agreement between the subsequent Material Principal Co-rotation and P??I??C decomposition methods that produce the intermediary stress/strain fields. The encompassing theory has wide applicability owing to its fundamental divergence from conventional mechanics, it offers non-trivial outcomes when applied to even very simple problems and its use of not the Eulerian, Lagrangian but the Intrinsic Frame generates previously unreported results in strongly orthotropic continua.

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Lundgren, Katarina. "Investigation of transmural cardiac and fiber strain in ischemic and non-ischemic tissue during diastole." Thesis, Linköping University, Department of Biomedical Engineering, 2006. http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-7955.

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The cardiac wall has complex three-dimensional fiber structures and mechanical properties that enable the heart to efficiently pump the blood through the body. By studying the myocardial strains induced during diastole, information about the pumping performance of the heart and what mechanisms that are responsible for this effective blood filling, can be achieved. Two different computation methods for myocardial strain, both based on data acquired from marker technique, were compared using a theoretical cylinder model. The non-homogeneous polynomial fitting method yielded higher accuracy than a homogeneous tetrahedron method, and was further used to investigate cardiac and fiber strains at different wall depths and myocardial regions in normal and ischemic ovine hearts. Large spatial and regional variations were found, as well as alterations, conveyed by ischemic conditions, of fiber mechanisms responsible for the circumferential expansion and wall thinning during diastole.

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Kindberg, Katarina. "Regional Kinematics of the Heart: Investigation with Marker Tracking and with Phase Contrast Magnetic Resonance Imaging." Thesis, Linköping University, Department of Biomedical Engineering, 2003. http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-1735.

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The pumping performance of the heart is affected by the mechanical properties of the muscle fibre part of the cardiac wall, the myocardium. The myocardium has a complex structure, where muscle fibres have different orientations at different locations, and during the cardiac cycle, the myocardium undergoes large elastic deformations. Hence, myocardial strain pattern is complex. In this thesis work, a computation method for myocardial strain and a detailed map of myocardial transmural strain during the cardiac cycle are found by the use of surgically implanted metallic markers and beads. The strain is characterized in a local cardiac coordinate system. Thereafter, non-invasive phase contrast magnetic resonance imaging (PC-MRI) is used to compare strain at different myocardial regions. The difference in resolution between marker data and PC-MRI data is elucidated and some of the problems associated with the low resolution of PC-MRI are given.

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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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Sigfridsson, Andreas. "Multidimensional MRI of Myocardial Dynamics : Acquisition, Reconstruction and Visualization." Doctoral thesis, Linköpings universitet, Medicinsk informatik, 2009. http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-51489.

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Methods for measuring deformation and motion of the human heart in-vivo are crucial in the assessment of cardiac function. Applications ranging from basic physiological research, through early detection of disease to follow-up studies, all rely on the quality of the measurements of heart dynamics. This thesis presents new improved magnetic resonance imaging methods for acquisition, image reconstruction and visualization of cardiac motion and deformation.As the heart moves and changes shape during the acquisition, synchronization to the heart dynamics is necessary. Here, a method to resolve not only the cardiac cycle but also the respiratory cycle is presented. Combined with volumetric imaging, this produces a five-dimensional data set with two cyclic temporal dimensions. This type of data reveals unique physiological information, such as interventricular coupling in the heart in different phases of the respiratory cycle.The acquisition can also be sensitized to motion, measuring not only the magnitude of the magnetization but also a signal proportional to local velocity or displacement. This allows for quantification of the motion which is especially suitable for functional study of the cardiac deformation. In this work, an evaluation of the influence of several factors on the signal-to-noise ratio is presented for in-vivo displacement encoded imaging. Additionally, an extension of the method to acquire multiple displacement encoded slices in a single breath hold is also presented.Magnetic resonance imaging is usually associated with long scan times, and many methods exist to shorten the acquisition time while maintaining acceptable image quality. One class of such methods involves acquiring only a sparse subset of k-space. A special reconstruction is then necessary in order to obtain an artifact-free image. One family of these reconstruction techniques tailored for dynamic imaging is the k-t BLAST approach, which incorporates data-driven prior knowledge to suppress aliasing artifacts that otherwise occur with the sparse sampling. In this work, an extension of the original k-t BLAST method to two temporal dimensions is presented and applied to data acquired with full coverage of the cardio-respiratory cycles. Using this technique, termed k-t2 BLAST, simultaneous reduction of scan time and improved spatial resolution is demonstrated. Further, the loss of temporal fidelity when using the k-t BLAST approach is investigated, and an improved reconstruction is proposed for the application of cardiac function analysis.Visualization is a crucial part of the imaging chain. Scalar data, such as regular anatomical images, are straightforward to display. Myocardial strain and strain-rate, however, are tensor quantities which do not lend themselves to direct visualization. The problem of visualizing the tensor field is approached in this work by combining a local visualization that displays all degrees of freedom for a single tensor with an overview visualization using a scalar field representation of the complete tensor field. The scalar field is obtained by iterated adaptive filtering of a noise field, creating a continuous geometrical representation of the myocardial strain-rate tensor field.The results of the work presented in this thesis provide opportunities for improved imaging of myocardial function, in all areas of the imaging chain; acquisition, reconstruction and visualization.

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Eissa, Leila. "Utilisation de méthodes de l'astrogéodésie et de la géodésie spatiale pour des études de déformations de l’écorce terrestre : représentations de déformations et de leur degré de signification par des tenseurs régulièrement répartis." Thesis, Paris Est, 2011. http://www.theses.fr/2011PEST1018/document.

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Les outils de la géodésie spatiale sont aujourd'hui très fortement impliqués dans les études géophysiques. Le champ de déformations horizontales d'un site d'étude est fourni par les vecteurs déplacement ou par un champ tensoriel. Ce dernier possède l'avantage d'être indépendant de tout référentiel, contrairement à ce qui est nécessaire pour exprimer les vecteurs vitesse. Néanmoins, les méthodes de calcul de tenseurs dépendent souvent d'une décomposition arbitraire en figures élémentaires à partir des points de mesures géodésiques. De plus, la représentation de ces tenseurs selon leurs axes principaux est d'une lecture et d'une interprétation assez difficiles et nécessitent un certain entraînement. Cette thèse traite, dans un premier temps, le problème de fournir un champ continu de déformations sous la forme des tenseurs régulièrement répartis, de façon peu dépendante des points de mesure, et dans un deuxième temps, de fournir une représentation cartographique intuitive de ces tenseurs avec, pour la première fois, une représentation simultanée de leur degré de significativité. L'estimation des incertitudes de la déformation obtenue est analysée selon deux points de vue : d'une part, une méthode de Monte Carlo est appliquée pour la détermination des barres d'erreurs liées aux mesures, son résultat permet le calcul de degré de significativité des tenseurs par comparaison des valeurs de tenseurs par rapport à leurs incertitudes, et d'autre part, une estimation des contraintes imposées par la géométrie de distribution des points de mesures qui est ensuite combinée avec la première source d'erreur. La nouvelle approche de représentation a été analysée via une enquête auprès d'un groupe de géophysiciens, en leur fournissant plusieurs possibilités de représentations. En se basant sur les résultats de cette enquête, nous avons pu valider la nouvelle représentation qui permet de mettre en évidence certains aspects mal mis en évidence par la représentation classique, et donc le choix des éléments graphiques de la carte permettant de fournir la représentation la plus intuitive possible Space geodesy tools are now strongly involved in geophysical studies. The horizontal deformation field for a region of interest is provided by two main methods : a velocity field and a strain tensor field. A strain tensors field solution has the advantage of being independent of the reference frame in which the velocities are expressed. Nevertheless, the current methods of calculation of a strain tensors field depend on the positioning of geodetic points. Furthermore, the current mapping method of tensors by their mains axis is not easy to read and to interpret, needing some training. This thesis is devoted to the problem of calculating a continuous field of regularly spaced strain tensors, and providing an intuitive mapping method of these tensors with a simultaneous representation of their significance level on the same map. The estimation of uncertainties related to the deformation field is made in two steps : firstly, a Monte Carlo method is applied for the calculation of uncertainties related to the measurements, its results allow to define the significance level of tensors by normalizing tensor's values with respect to their related uncertainties, then, the constraints coming from the distribution of the network of measurement points are calculated and combined with the first source of error. The new approach of mapping tensors was analyzed through an opinion survey by providing several possibilities of representation. The results of this opinion survey allowed us to validate this new mapping method by geophysicists for representing a deformation field, because it allows highlighting some aspects not well illustrated by the classical mapping method of tensors, and therefore choosing the graphical elements of the map which provide the best intuitive method of mapping a strain tensors field

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ALBISETTI, A. FIGINI. "Structural and Thermodiffractometric Studies of Coordination Polymers Containing Ditopic Exobidentate Nitrogen Ligand." Doctoral thesis, Università degli Studi di Milano, 2008. http://hdl.handle.net/2434/57743.

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Zahradník, Martin. "Dynamic control of magnetization for spintronic applications studied by magneto-optical methods." Thesis, Université Paris-Saclay (ComUE), 2019. http://www.theses.fr/2019SACLS155/document.

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Deux mécanismes importants reliant la préparation des couches ultraminces d’oxydes magnétiques à leurs propriétés physiques ont été étudiés dans ce travail. En premier lieu, l’influence de la contrainte épitaxiale sur les propriétés magnéto-optiques de la manganite La₂/₃Sr₁/₃MnO₃ (LSMO) a été étudiée. Les couches ultraminces ont été déposées par ablation laser pulsé sur quatre substrats différents, ce qui a fourni différentes valeurs statiques de la contrainte épitaxiale. Les propriétés magnétiques ont été révélées comme se détériorant avec l’augmentation de la contrainte, ce qui était prévisible à cause de la distorsion grandissante de la maille unitaire ainsi qu’à cause de l’effet de la couche magnétiquement inerte. La combinaison de l’ellipsométrie spectroscopique et de la spectroscopie Kerr magnéto-optique a été utilisée afin de déterminer les spectres des éléments diagonaux et non diagonaux du tenseur de permittivité. L’étude des éléments non-diagonaux a confirmé la présence déjà rapportée de deux transitions électroniques dans les spectres de toutes les couches. De plus, elle a révélé une autre transition électronique autour de l’énergie de 4.3 eV, mais seulement dans les spectres des couches déposées avec une contrainte compressive. Nous avons proposé la classification de cette transition comme une transition paramagnétique du champ cristallin Mn t2g → eg. Cette classification a été confortée par des calculs ab initio. Nous avons ainsi montré le rôle clé de la contrainte dans le contrôle des propriétés magnéto-optiques des couches pérovskites ultraminces. En revanche, l’application dynamique de la contrainte par l’utilisation d’une sous-couche piézoélectrique est restée peu concluante. Le transfert de la contrainte entre la sous-couche piézoélectrique et la couche LSMO nécessite des améliorations ultérieures. En second lieu, l’influence de la désorientation du substrat a été étudiée par rapport à la dynamique de l’aimantation dans l’oxyde SrRuO₃ (SRO). Comme attendu, nous avons trouvé qu’un grand angle de désorientation mène à la suppression de la croissance de plusieurs variants cristallographiques du SRO. Au moyen de la microscopie à force magnétique, nous avons montré que la présence de plusieurs variants de SRO mène à l’augmentation de la densité de défauts agissant comme points d’ancrage ou de nucléation pour les domaines magnétiques. Nous avons donc montré que l’emploi d’un substrat vicinal est important pour la fabrication des couches ultraminces de SRO de haute qualité, avec une faible densité de défauts cristallographiques et d’excellentes propriétés magnétiques Two important mechanisms in preparation of ultrathin films of magnetic oxides were systematically investigated in this work. First, inﬂuence of epitaxial strain on resulting magneto-optical properties of La₂/₃Sr₁/₃MnO₃ (LSMO) ultrathin films was studied. The investigated films were grown by pulsed laser deposition on four different substrates, providing a broad range of induced epitaxial strains. Magnetic properties were found to deteriorate with increasing value of the epitaxial strain, as expected due to the unit cell distortion increasingly deviating from the bulk and effect of the magnetically inert layer. A combination of spectroscopic ellipsometry and magneto-optical Kerr effect spectroscopy was used to determine spectra of the diagonal and off-diagonal elements of permittivity tensor. The off-diagonal elements confirmed presence of two previously reported electronic transitions in spectra of all films. Moreover, they revealed another electronic transition around 4.3 eV only in spectra of films grown under compressive strain. We proposed classification of this transition as crystal field paramagnetic Mn t2g → eg transition, which was further supported by ab initio calculations. A key role of strain in controlling electronic structure of ultrathin perovskite films was demonstrated. Dynamic application of strain via use of piezoelectric underlayer remained inconclusive, requiring further improvement of the strain transfer from the piezoelectric layer into the LSMO. Second, inﬂuence of substrate miscut on magnetization dynamics in SrRuO₃ (SRO) was studied. As expected we found that high miscut angle leads to suppression of multi-variant growth. By means of magnetic force microscopy we showed that presence of multiple SRO variants leads to higher density of defects acting as pinning or nucleation sites for the magnetic domains, which consequently results in deterioration of magnetic properties. We demonstrated that use of vicinal substrate with high miscut angle is important for fabrication of high quality SRO ultrathin films with low density of crystallographic defects and excellent magnetic properties

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Książki na temat "Strain tensor"

Erlebacher, Gordon. Statistical analysis of the rate of strain tensor in compressible homogeneous turbulence. Hampton, Va: Institute for Computer Applications in Science and Engineering, 1992.

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Canada Centre For Mineral and Energy Technology. Mineral Research Program. Stress Tensor Determinations with the South African Biaxial Strain Cell (Doorstopper). S.l: s.n, 1985.

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S, Sarkar, and Langley Research Center, eds. Statistical analysis of the rate of strain tensor in compressible homogeneous turbulence. Hampton, Va: National Aeronautics and Space Administration, Langley Research Center, 1992.

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Freed, Alan David. Natural strain. [Washington, D.C: National Aeronautics and Space Administration, 1995.

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Oertel, G. F. Stress and deformation: A handbook on tensors in geology. New York: Oxford University Press, 1996.

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B, Gatski T., Speziale C. G. 1948-, and Institute for Computer Applications in Science and Engineering., eds. On the prediction of free turbulent jets with swirl using a quadratic pressure-strain model. Hampton, Va: National Aeronautics and Space Administration, Langley Research Center, Institute for Computer Applications in Science and Engineering, 1994.

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Innis, Pauline B. Bridge across the seas. Washington, DC: Devon Pub. Co., 1995.

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Części książek na temat "Strain tensor"

Zhilin, Pavel A., Holm Altenbach, Elena A. Ivanova, and Anton Krivtsov. "Material Strain Tensor." In Advanced Structured Materials, 321–31. Berlin, Heidelberg: Springer Berlin Heidelberg, 2013. http://dx.doi.org/10.1007/978-3-642-36394-8_19.

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Lorentzen, T., and T. Leffers. "Strain Tensor Measurements by Neutron Diffraction." In Measurement of Residual and Applied Stress Using Neutron Diffraction, 253–61. Dordrecht: Springer Netherlands, 1992. http://dx.doi.org/10.1007/978-94-011-2797-4_16.

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Malgrange, Cécile, Christian Ricolleau, and Michel Schlenker. "Deformation of a solid. The strain tensor." In Symmetry and Physical Properties of Crystals, 241–57. Dordrecht: Springer Netherlands, 2014. http://dx.doi.org/10.1007/978-94-017-8993-6_12.

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Horio, Hideyuki, Yoshihiro Kuroda, Tomohiro Kuroda, Osamu Oshiro, Shigeo Wada, Ryo Haraguchi, and Kazuo Nakazawa. "Analysis of Cardiac Torsion with Strain Tensor." In IFMBE Proceedings, 304–7. Berlin, Heidelberg: Springer Berlin Heidelberg, 2009. http://dx.doi.org/10.1007/978-3-642-03882-2_80.

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Sosa-Cabrera, Darío, Karl Krissian, Javier González-Fernández, Luis Gómez-Déniz, Eduardo Rovaris, Carlos Castaño-Moraga, and Juan Ruiz-Alzola. "Strain Tensor Elastography: 2D and 3D Visualizations." In Tensors in Image Processing and Computer Vision, 381–403. London: Springer London, 2009. http://dx.doi.org/10.1007/978-1-84882-299-3_18.

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Zhang, W. C., and K. E. Evans. "A Strain Tensor Polynomial Failure Criterion for Anisotropic Materials." In Transient/Dynamic Analysis and Constitutive Laws for Engineering Materials, 651–58. Dordrecht: Springer Netherlands, 1987. http://dx.doi.org/10.1007/978-94-009-3655-3_71.

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Pyrz, Ryszard. "Atomistic/Continuum Transition – the Concept of Atomic Strain Tensor." In Fracture of Materials: Moving Forwards, 193–98. Stafa: Trans Tech Publications Ltd., 2006. http://dx.doi.org/10.4028/0-87849-994-6.193.

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Abd-Elmoniem, Khaled Z., Matthias Stuber, and Jerry L. Prince. "Multi-slice Three-Dimensional Myocardial Strain Tensor Quantification Using zHARP." In Lecture Notes in Computer Science, 62–73. Berlin, Heidelberg: Springer Berlin Heidelberg, 2007. http://dx.doi.org/10.1007/978-3-540-73273-0_6.

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Morawiec, A. "Determinability of Complete Residual Strain Tensor from Multiple CBED Patterns." In Materials Science Forum, 115–20. Stafa: Trans Tech Publications Ltd., 2006. http://dx.doi.org/10.4028/0-87849-414-6.115.

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Oberlack, Martin. "Closure of the Dissipation Tensor and the Pressure—Strain Tensor Based on the Two-Point Correlation Equation." In Turbulent Shear Flows 9, 33–52. Berlin, Heidelberg: Springer Berlin Heidelberg, 1995. http://dx.doi.org/10.1007/978-3-642-78823-9_4.

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Streszczenia konferencji na temat "Strain tensor"

Pyrz, Ryszard. "The Concept of Strain Tensor at Atomic Level." In ASME 2006 Multifunctional Nanocomposites International Conference. ASMEDC, 2006. http://dx.doi.org/10.1115/mn2006-17026.

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An atomic strain concept is formulated that allows calculation of continuum quantities directly within a discrete atomic (molecular) system. The concept is based on the Voronoi tessellation of the molecular system and calculation of atomic site strains, which connects continuum variables and atomic quantities when the later are averaged over a sufficiently large volume treated as a point of the continuum body. The atomic strain tensor is applied to investigate deformation of regular and disordered molecular systems. It is shown that disordered systems exhibit significant non-affine deformations which can be captured by a proper correction of the strain tensor.

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Naghdabadi, Reza, Mohsen Asghari, and Kamyar Ghavam. "Compact Basis Free Relations for Stress Tensors Conjugate to Hill’s Strain Measures." In ASME 8th Biennial Conference on Engineering Systems Design and Analysis. ASMEDC, 2006. http://dx.doi.org/10.1115/esda2006-95367.

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If the double contraction of a stress tensor such as T and rate of a Lagrangean strain tensor such as E, i.e. T : E˙, produces the stress power then these stress and strain tensors are called a conjugate pair. The applications of the conjugate stress and strain measures are in the development of the basic relations in nonlinear continuum mechanics analysis such as modeling of constitutive equations of elastic-plastic materials. In this paper relations for stress tensors conjugate to an arbitrary Lagrangean strain measure of Hill’s class are obtained. The results of this paper are more compact and simpler in compare with those available in the literature. The results are valid for the three dimensional Euclidean inner product space and the case of distinct eigenvalues of the right stretch tensor U.

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Behfar, K., A. Sheshmani, and R. Naghdabadi. "General Derivations for Conjugate Strains of Eshelby-Like Stress Tensors." In ASME 7th Biennial Conference on Engineering Systems Design and Analysis. ASMEDC, 2004. http://dx.doi.org/10.1115/esda2004-58388.

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In this paper, a general type of Eshelby-like stress tensor is defined which is based on the right stretch tensor and is equal to the product of a general class of strain and the corresponding conjugate stress tensor. The Eshelby-like stress tensor depending on the fact that from which side the stress tensor is multiplied by, is categorized into the right-weighted and left-weighted ones. General relations for conjugate strains of Eshelby-like stress tensors are investigated using the method, based on the definition of energy conjugacy and Hill’s principal axis method.

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Chetouane, Brahim, Claude Bohatier, Fre´de´ric Dubois, and Marc Vinches. "Stress and Strain Tensors in Granular Medium Application to Masonry Structures." In ASME 2003 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2003. http://dx.doi.org/10.1115/detc2003/vib-48430.

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The general framework of the present paper is the modeling of stone work, subject to dynamic loads. In this study, a masonry structure is considered as a collection of rigid blocks, linked together by Coulomb’s type friction laws. We define on such a granular medium, a stress tensor and a macroscopic strain tensor, on an elementary cell. The definition of these tensors allows us to get, locally, an average information on this granular medium.

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Hewer, Alexander, Joachim Weickert, Henning Seibert, Tobias Scheffer, and Stefan Diebels. "Lagrangian Strain Tensor Computation with Higher Order Variational Models." In British Machine Vision Conference 2013. British Machine Vision Association, 2013. http://dx.doi.org/10.5244/c.27.129.

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Lienert, U. "Nondestructive Strain Tensor Scanning within Samples of Cylindrical Symmetry." In SYNCHROTRON RADIATION INSTRUMENTATION: Eighth International Conference on Synchrotron Radiation Instrumentation. AIP, 2004. http://dx.doi.org/10.1063/1.1757984.

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Bates, Kelsey M., Matthew W. Day, Christopher L. Smallwood, Ronald Ulbricht, Travis M. Autry, Rachel C. Owen, Geoffrey Diederich, et al. "Measuring the Diamond strain Tensor with Silicon-Vacancy Centers." In CLEO: QELS_Fundamental Science. Washington, D.C.: OSA, 2020. http://dx.doi.org/10.1364/cleo_qels.2020.ftu3d.4.

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Asghari, Mohsen, and Reza Naghdabadi. "Unified Basis-Free Relation Between Two Stress Tensors Conjugate to Arbitrary Hill’s Strain Measures." In ASME 2006 Pressure Vessels and Piping/ICPVT-11 Conference. ASMEDC, 2006. http://dx.doi.org/10.1115/pvp2006-icpvt-11-93687.

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The concept of energy conjugacy for stress and strain measures states that a stress tensor T is conjugate to a strain measure E if T: E˙ provides the rate of change of the internal energy per unit reference volume of the body in an adiabatic process. The applications of the conjugate stress and strain measures are in the development of the basic relations in nonlinear analysis of solids. In this paper using eigenprojection method, unified explicit basis-free relation between two arbitrary stress tensors T(f) and T(g), respectively conjugate to two measures of Hill’s strains is determined. The result is valid for arbitrary dimension of the Euclidean inner product space and for all cases of distinct and repeated eigenvalues of the right stretch tensor U.

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Fukunaga, Masataka, and Nobuyuki Shimizu. "Three-Dimensional Fractional Derivative Models for Finite Deformation." In ASME 2011 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2011. http://dx.doi.org/10.1115/detc2011-47552.

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Fractional derivative stress-strain relations are derived for compressible viscoelastic materials based on the continuum mechanics. Several types of stress tensor and strain tensors are specified to describe the dynamics of continuous media. Consequently there are many equivalent expressions of stress-strain relations. If memory effect is not taken into account, these relations are equivalently transformed from one to another by suitable tensor operations. However, if memory effect is included in the mechanics of the materials, different types of stress-strain relations can be derived depending on the choice of the type of stress tensor, or equivalently the choice of the strain energy function. In this paper, several types of fractional derivative stress-strain relations are proposed.

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Coiret, A. L., M. L. V. Gallenne, and P. Y. M. Texier. "Tire/Pavement Strain Tensor Measurement With an Infrastructure-Based Approach." In World Tribology Congress III. ASMEDC, 2005. http://dx.doi.org/10.1115/wtc2005-64300.

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Studies are conducted at the LCPC for investigating the role of infrastructures in road safety. In this context, tire/pavement contact characterization is a key point for both vehicle and road surface optimization. For this purpose, car industry usually instruments dedicated cars with wheel dynamometers but this procedure doesn’t offer the possibility to observe a large set of vehicles in practice. Regarding road management, it has been chosen to use the infrastructure itself as an instrument for acquiring the complete 6-components stress tensor. In this paper, a new test apparatus allowing this is shown, using a mechanically isolated part of the pavement. Validations are presented on a variety of situations such as emergency braking and constant speed driving. Correlations with inboard vehicle sensors measurements and numerical models have been worked out.

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Raporty organizacyjne na temat "Strain tensor"

Mott, Peter, Ali S. Morgan, and Ulrich W. Sutter. The Atomic Strain Tensor. Fort Belvoir, VA: Defense Technical Information Center, May 1991. http://dx.doi.org/10.21236/ada237287.

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Murdoch, Lawrence C., Scott DeWolf, Leonid N. Germanovich, Alexander Hanna, Robert Moak, and Stephen Moysey. Characterizing and Interpreting the In Situ Strain Tensor During CO₂ Injection. Office of Scientific and Technical Information (OSTI), June 2019. http://dx.doi.org/10.2172/1529100.

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Hubbard, Camden R. Neutron Diffraction Residual Strain Tensor Measurements Within The Phase IA Weld Mock-up Plate P-5. Office of Scientific and Technical Information (OSTI), September 2011. http://dx.doi.org/10.2172/1025403.

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Bahder, Thomas B. Transformation Properties of the Lagrangian and Eulerian Strain Tensors. Fort Belvoir, VA: Defense Technical Information Center, April 2002. http://dx.doi.org/10.21236/ada400671.

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Scheidler, Michael J. Time Rates of Generalized Strain Tensors. Part 1. Component Formulas. Fort Belvoir, VA: Defense Technical Information Center, January 1991. http://dx.doi.org/10.21236/ada232497.

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Scheidler, Michael J. Time Rates of Generalized Strain Tensors. Part 2. Approximate Basis-Free Formulas. Fort Belvoir, VA: Defense Technical Information Center, October 1991. http://dx.doi.org/10.21236/ada242095.

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Garrison, Ben, Maxim Gussev, and Kory Linton. Progress Report on Plane Strain Tension Testing of ATF FeCrAl Cladding. Office of Scientific and Technical Information (OSTI), August 2020. http://dx.doi.org/10.2172/1648931.

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Karlstrom, Karl, Laura Crossey, Allyson Matthis, and Carl Bowman. Telling time at Grand Canyon National Park: 2020 update. National Park Service, April 2021. http://dx.doi.org/10.36967/nrr-2285173.

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Grand Canyon National Park is all about time and timescales. Time is the currency of our daily life, of history, and of biological evolution. Grand Canyon’s beauty has inspired explorers, artists, and poets. Behind it all, Grand Canyon’s geology and sense of timelessness are among its most prominent and important resources. Grand Canyon has an exceptionally complete and well-exposed rock record of Earth’s history. It is an ideal place to gain a sense of geologic (or deep) time. A visit to the South or North rims, a hike into the canyon of any length, or a trip through the 277-mile (446-km) length of Grand Canyon are awe-inspiring experiences for many reasons, and they often motivate us to look deeper to understand how our human timescales of hundreds and thousands of years overlap with Earth’s many timescales reaching back millions and billions of years. This report summarizes how geologists tell time at Grand Canyon, and the resultant “best” numeric ages for the canyon’s strata based on recent scientific research. By best, we mean the most accurate and precise ages available, given the dating techniques used, geologic constraints, the availability of datable material, and the fossil record of Grand Canyon rock units. This paper updates a previously-published compilation of best numeric ages (Mathis and Bowman 2005a; 2005b; 2007) to incorporate recent revisions in the canyon’s stratigraphic nomenclature and additional numeric age determinations published in the scientific literature. From bottom to top, Grand Canyon’s rocks can be ordered into three “sets” (or primary packages), each with an overarching story. The Vishnu Basement Rocks were once tens of miles deep as North America’s crust formed via collisions of volcanic island chains with the pre-existing continent between 1,840 and 1,375 million years ago. The Grand Canyon Supergroup contains evidence for early single-celled life and represents basins that record the assembly and breakup of an early supercontinent between 729 and 1,255 million years ago. The Layered Paleozoic Rocks encode stories, layer by layer, of dramatic geologic changes and the evolution of animal life during the Paleozoic Era (period of ancient life) between 270 and 530 million years ago. In addition to characterizing the ages and geology of the three sets of rocks, we provide numeric ages for all the groups and formations within each set. Nine tables list the best ages along with information on each unit’s tectonic or depositional environment, and specific information explaining why revisions were made to previously published numeric ages. Photographs, line drawings, and diagrams of the different rock formations are included, as well as an extensive glossary of geologic terms to help define important scientific concepts. The three sets of rocks are separated by rock contacts called unconformities formed during long periods of erosion. This report unravels the Great Unconformity, named by John Wesley Powell 150 years ago, and shows that it is made up of several distinct erosion surfaces. The Great Nonconformity is between the Vishnu Basement Rocks and the Grand Canyon Supergroup. The Great Angular Unconformity is between the Grand Canyon Supergroup and the Layered Paleozoic Rocks. Powell’s term, the Great Unconformity, is used for contacts where the Vishnu Basement Rocks are directly overlain by the Layered Paleozoic Rocks. The time missing at these and other unconformities within the sets is also summarized in this paper—a topic that can be as interesting as the time recorded. Our goal is to provide a single up-to-date reference that summarizes the main facets of when the rocks exposed in the canyon’s walls were formed and their geologic history. This authoritative and readable summary of the age of Grand Canyon rocks will hopefully be helpful to National Park Service staff including resource managers and park interpreters at many levels of geologic understandings...

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Monetary Policy Report - October 2022. Banco de la República Colombia, October 2022. http://dx.doi.org/10.32468/inf-pol-mont-eng.tr4-2022.

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1.1 Macroeconomic summary In September, headline inflation (11.4% annually) and the average of core inflation indicators (8.6% annually) continued on a rising trend, and higher increases than expected were recorded. Forecasts increased again, and inflation expectations remained above 3%. Inflationary surprises in the third quarter were significant and widespread, and they are the result of several shocks. On the one hand, international cost and price shocks, which have mainly affected goods and foods, continue to exert upwards pressure on national inflation. In addition to these external supply shocks, domestic supply shocks have also affected foods. On the other hand, the strong recovery of aggregate demand, especially for private consumption and for machinery and equipment, as well as a higher accumulated depreciation of the Colombian peso and its pass-through to domestic prices also explain the rise in inflation. Indexation also contributes, both through the Consumer Price Index (CPI) and through the Producer Price Index (PPI), which continues to have a significant impact on electricity prices and, to a lesser degree, on other public utilities and rent. In comparison with July’s report, the new forecast trajectory for headline and core inflation (excluding food and regulated items) is higher in the forecast horizon, mainly due to exchange rate pressures, higher excess demand, and indexation at higher inflation rates, but it maintains a trend of convergence towards the target. In the case of food, a good domestic supply of perishable foods and some moderation in international processed food prices are still expected. However, the technical staff estimates higher pressures on this group’s prices from labor costs, raw material prices, and exchange rates. In terms of the CPI for regulated items, the new forecast supposes reductions in electricity prices at the end of the year, but the effects of indexation at higher inflation rates and the expected rises in fuel prices would continue to push this CPI group. Therefore, the new projection suggests that, in December, inflation would reach 11.3% and would decrease throughout 2023 and 2024, closing the year at 7.1% and 3.5%, respectively. These forecasts have a high level of uncertainty, due especially to the future behavior of international financial conditions, external price and cost shocks, the persistence of depreciation of the Colombian peso, the pace of adjustment of domestic demand, the indexation degree of nominal contracts, and the decisions that would be made regarding domestic fuel and electricity prices. Economic activity continues to surprise on the upside, and the projection of growth for 2022 rose from 6.9% to 7.9% but lowered for 2023 from 1.1% to 0.5%. Thus, excess demand is higher than estimated in the previous report, and it would diminish in 2023. Economic growth in the second quarterwas higher than estimated in July due to stronger domestic demand, mainly because of private consumption. Economic activity indicators for the third quarter suggest that the GDP would stay at a high level, above its potential, with an annual change of 6.4%, and 0.6% higher than observed in the second quarter. Nevertheless, these numbers reflect deceleration in its quarterly and annual growth. Domestic demand would show similar behavior, with a high value, higher than that of output. This can be explained partly by the strong behavior of private consumption and investment in machinery and equipment. In the third quarter, investment in construction would have continued with mediocre performance, which would still place it at levels lower than those observed before the pandemic. The trade deficit would have widened due to high imports with a stronger trend than that for exports. It is expected that, in the forecast horizon, consumption would decrease from its current high levels, partly as a consequence of tighter domestic financial conditions, lower repressed demand, higher exchange rate pressures on imported goods prices, and the deterioration of actual income due to the rise in inflation. Investment would continue to lag behind, without reaching the levels observed before the pandemic, in a context of high financing costs and high uncertainty. A lower projected behavior in domestic demand and the high levels of prices for oil and other basic goods that the country exports would be reflected in a reduction in the trade deficit. Due to all of this, economic growth for all of 2022, 2023, and 2024 would be 7.9%, 0.5%, and 1.3%, respectively. Expected excess demand (measured via the output gap) is estimated to be higher than contemplated in the previous report; it would diminish in 2023 and could turn negative in 2024. These estimates remain subject to a high degree of uncertainty related to global political tension, a rise in international interest rates, and the effects of this rise on demand and financial conditions abroad. In the domestic context, the evolution of fiscal policy as well as future measures regarding economic policy and their possible effects on macroeconomic imbalances in the country, among others, are factors that generate uncertainty and affect risk premia, the exchange rate, investment, and the country’s economic activity. Interest rates at several of the world’s main central banks continue to rise, some at a pace higher than expected by the market. This is in response to the high levels of inflation and their inflation expectations, which continue to exceed the targets. Thus, global growth projections are still being moderated, risk premia have risen, and the dollar continues to gain strength against other main currencies. International pressures on global inflation have heightened. In the United States, core inflation has not receded, pressured by the behavior of the CPI for services and a tight labor market. Consequently, the U.S. Federal Reserve continued to increase the policy interest rate at a strong pace. This rate is expected to now reach higher levels than projected in the previous quarter. Other developed and emerging economies have also increased their policy interest rates. Thus, international financial conditions have tightened significantly, which reflects in a widespread strengthening of the dollar, increases in worldwide risk premia, and the devaluation of risky assets. Recently, these effects have been stronger in Colombia than in the majority of its peers in the region. Considering all of the aforementioned, the technical staff of the bank increased its assumption regarding the U.S. Federal Reserve’s interest rate, reduced the country’s external demand growth forecast, and raised the projected trajectory for the risk premium. The latter remains elevated at higher levels than its historical average, within a context of high local uncertainty and of extensive financing needs from the foreign sector and the public sector. All of this results in higher inflationary pressures associated to the depreciation of the Colombian peso. The uncertainty regarding external forecasts and its impact on the country remain elevated, given the unforeseeable evolution of the conflict between Russia and Ukraine, of geopolitical tensions, and of the tightening of external financial conditions, among others. A macroeconomic context of high inflation, inflation expectations and forecasts above 3%, and a positive output gap suggests the need for contractionary monetary policy, compatible with the macroeconomic adjustment necessary to eliminate excess demand, mitigate the risk of unanchoring in inflation expectations, and guarantee convergence of inflation at the target. In comparison with the July report forecasts, domestic demand has been more dynamic, with a higher observed output level that surpasses the economy’s productive capacity. Headline and core inflation have registered surprising rises, associated with the effects of domestic and external price shocks that were more persistent than anticipated, with excess demand and indexation processes in some CPI groups. The country’s risk premium and the observed and expected international interest rates increased. As a consequence of this, inflationary pressures from the exchange rate rose, and in this report, the probability of the neutral real interest rate being higher than estimated increased. In general, inflation expectations for all terms and the bank’s technical staff inflation forecast for 2023 increased again and continue to stray from 3%. All of the aforementioned elevated the risk of unanchoring inflation expectations and could heighten widespread indexation processes that push inflation away from the target for a longer time. In this context, it is necessary to consolidate a contractionary monetary policy that tends towards convergence of inflation at the target in the forecast horizon and towards the reduction of excess demand in order to guarantee a sustainable output level trajectory. 1.2 Monetary policy decision In its September and October of 2022 meetings, Banco de la República’s Board of Directors (BDBR) decided to continue adjusting its monetary policy. In September, the BDBR decided by a majority vote to raise the monetary policy interest rate by 100 basis points (bps), and in its October meeting, unanimously, by 100bps. Therefore, the rate is at 11.0%. Boxes 1 Food inflation: a comparison with other countries

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