Academic literature on the topic 'Almansi Strain'
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Journal articles on the topic "Almansi Strain"
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Kozlova, O. V., E. P. Zharikova, and A. I. Khromov. "Fields of a Finite Strain Tensor in the Neighborhood of Discontinuity of the Velocity Field of Displacements under Axisymmetric Strain." Materials Science Forum 945 (February 2019): 873–78. http://dx.doi.org/10.4028/www.scientific.net/msf.945.873.
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The problem of the distribution fields of a finite strain tensor in the neighborhood of points of discontinuities of speeds of movements under axisymmetric strain conditions is considered. The Almansi finite strain tensor is a measure of deformation, the motion of points of discontinuities is assumed to be given from the solution of the problems strain bodies taking into account change geometry of the free surface. The relations defining fields of a tensor the finite strains are obtained by integrating the system of equations, binding components of The Almansi finite strain tensor and strain rate tensor along the trajectory of the movement of the material particles. At the same time features of the displacement velocity field are considered in the form of cross points of characteristics of indicial equations which define displacement velocity field (center of the fan of characteristics for a deformation case in axisymmetric deformation of ideal rigid-plastic bodies conditions). The limiting trajectories of the motion of particles contracting to the discontinuity point are considered.
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Sciammarella, Cesar A., Luciano Lamberti, and Federico M. Sciammarella. "Verification of Continuum Mechanics Predictions with Experimental Mechanics." Materials 13, no. 1 (2019): 77. http://dx.doi.org/10.3390/ma13010077.
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The general goal of the study is to connect theoretical predictions of continuum mechanics with actual experimental observations that support these predictions. The representative volume element (RVE) bridges the theoretical concept of continuum with the actual discontinuous structure of matter. This paper presents an experimental verification of the RVE concept. Foundations of continuum kinematics as well as mathematical functions relating displacement vectorial fields to the recording of these fields by a light sensor in the form of gray-level scalar fields are reviewed. The Eulerian derivative field tensors are related to the deformation of the continuum: the Euler–Almansi tensor is extracted, and its properties are discussed. The compatibility between the Euler–Almansi tensor and the Cauchy stress tensor is analyzed. In order to verify the concept of the RVE, a multiscale analysis of an Al–SiC composite material is carried out. Furthermore, it is proven that the Euler–Almansi strain tensor and the Cauchy stress tensor are conjugate in the Hill–Mandel sense by solving an identification problem of the constitutive model of urethane rubber.
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Degener, M., D. H. Hodges, and D. Petersen. "Analytical and Experimental Study of Beam Torsional Stiffness With Large Axial Elongation." Journal of Applied Mechanics 55, no. 1 (1988): 171–78. http://dx.doi.org/10.1115/1.3173624.
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The axial force and effective torsional stiffness versus axial elongation are investigated analytically and experimentally for a beam of circular cross section and made of an incompressible material that can sustain large elastic deformation. An approach based on a strain energy function identical to that used in linear elasticity, except with its strain components replaced by those of some finite-deformation tensor, would be expected to provide only limited predictive capability for this large-strain problem. Indeed, such an approach based on Green strain components (commonly referred to as the geometrically nonlinear theory of elasticity) incorrectly predicts a change in volume and predicts the wrong trend regarding the experimentally determined axial force and effective torsional stiffness. On the other hand, use of the same strain energy function, only with the Hencky logarithmic strain components, correctly predicts constant volume and provides excellent agreement with experimental data for lateral contraction, tensile force, and torsional stiffness—even when the axial elongation is large. For strain measures other than Hencky, the strain energy function must be modified to consistently account for large strains. For comparison, theoretical curves derived from a modified Green strain energy function are added. This approach provides results identical to those of the Neo-Hookean formulation for incompressible materials yielding fair agreement with the experimental results for coupled tension and torsion. An alternative approach, proposed in the present paper and based on a modified Almansi strain energy function, provides very good agreement with experimental data and is somewhat easier to manage than the Hencky strain energy approach.
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Kim, Jae-Yong, Dong-Bock Kim, Hee-Jeong Cho, Soon-Bum Kwon, and Young-Doo Kwon. "A Critical Heat Generation for Safe Nuclear Fuels after a LOCA." Science and Technology of Nuclear Installations 2014 (2014): 1–8. http://dx.doi.org/10.1155/2014/150985.
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This study applies a thermo-elasto-plastic-creep finite element procedure to the analysis of an accidental behavior of nuclear fuel as well as normal behavior. The result will be used as basic data for the robust design of nuclear power plant and fuels. We extended the range of mechanical strain from small or medium to large adopting the Hencky logarithmic strain measure in addition to the Green-Lagrange strain and Almansi strain measures, for the possible large strain situation in accidental environments. We found that there is a critical heat generation after LOCA without ECCS (event category 5), under which the cladding of fuel sustains the internal pressure and temperature for the time being for the rescue of the power plant. With the heat generation above the critical value caused by malfunctioning of the control rods, the stiffness of cladding becomes zero due to the softening by high temperature. The weak position of cladding along the length continuously bulges radially to burst and to discharge radioactive substances. This kind of cases should be avoid by any means.
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Markin, Alexey, Marina Sokolova, Dmitrii Khristich, and Yuri Astapov. "The Physically Nonlinear Model of an Elastic Material and Its Identification." International Journal of Applied Mechanics 11, no. 07 (2019): 1950064. http://dx.doi.org/10.1142/s1758825119500649.
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This work is devoted to the new variant of relations between the energetically conjugated Hencky strain tensor and corotational Kirchhoff stress tensor. The elastic energy is represented as a third-order polynomial of the Hencky tensor containing five material constants. Unlike the Almansi tensor in the Murnaghan model, the Hencky tensor allows assigning a clear physical meaning to material constants. Linear part of the constitutive relation represents the Hencky model and contains the bulk modulus and the shear modulus. The two extra constants express nonlinear effects at a purely volumetric strain and a purely isochoric strain, whereas the third constant takes into account the possible deviation from the similarity of the deviators of the Hencky stress and strain tensors. The resulting relations are naturally generalized for incompressible materials. In this case, the overall number of constants decreases from five to two. The designed test unit was used for a compression test of prismatic specimens made of incompressible material. The proposed version of the relations is in good agreement with the experimental data on the compression of rubber samples.
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Moreau, C., S. Thuillier, G. Rio, and V. Grolleau. "The Mechanical Behavior of a Slightly Compressible Rubber-Like Material: Correlation of Simulations and Experiments." Rubber Chemistry and Technology 72, no. 2 (1999): 269–82. http://dx.doi.org/10.5254/1.3538800.
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Abstract The purpose of this paper is to present a different approach for modeling the mechanical behavior of a compressible rubber-like material. In this approach, the motion of the body is described in the current configuration in convected material frames and the Cauchy stress tensor and Almansi strain tensor are used. The hyperelastic constitutive law, corresponding to this approach, is also presented. Non-homogeneous experiments on compact chloroprene specimens were carried out, in order to show the possibilities of the model. The material parameters are identified using an inverse problem approach, based on the minimization of the gap between the experimental load-displacement curve and the simulated one and on a numerical calculation of the cost function gradient. Results show that over a set of three different non-homogeneous and multiaxial tests, there is a good correlation between experiments and simulation.
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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 (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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Tian, Lian, Zhijie Wang, Roderic S. Lakes, and Naomi C. Chesler. "Comparison of Approaches to Quantify Arterial Damping Capacity From Pressurization Tests on Mouse Conduit Arteries." Journal of Biomechanical Engineering 135, no. 5 (2013). http://dx.doi.org/10.1115/1.4024135.
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Large conduit arteries are not purely elastic, but viscoelastic, which affects not only the mechanical behavior but also the ventricular afterload. Different hysteresis loops such as pressure-diameter, pressure-luminal cross-sectional area (LCSA), and stress–strain have been used to estimate damping capacity, which is associated with the ratio of the dissipated energy to the stored energy. Typically, linearized methods are used to calculate the damping capacity of arteries despite the fact that arteries are nonlinearly viscoelastic. The differences in the calculated damping capacity between these hysteresis loops and the most common linear and correct nonlinear methods have not been fully examined. The purpose of this study was thus to examine these differences and to determine a preferred approach for arterial damping capacity estimation. Pressurization tests were performed on mouse extralobar pulmonary and carotid arteries in their physiological pressure ranges with pressure (P) and outer diameter (OD) measured. The P-inner diameter (ID), P-stretch, P-Almansi strain, P-Green strain, P-LCSA, and stress–strain loops (including the Cauchy and Piola-Kirchhoff stresses and Almansi and Green strains) were calculated using the P-OD data and arterial geometry. Then, the damping capacity was calculated from these loops with both linear and nonlinear methods. Our results demonstrate that the linear approach provides a reasonable approximation of damping capacity for all of the loops except the Cauchy stress-Almansi strain, for which the estimate of damping capacity was significantly smaller (22 ± 8% with the nonlinear method and 31 ± 10% with the linear method). Between healthy and diseased extralobar pulmonary arteries, both methods detected significant differences. However, the estimate of damping capacity provided by the linear method was significantly smaller (27 ± 11%) than that of the nonlinear method. We conclude that all loops except the Cauchy stress-Almansi strain loop can be used to estimate artery wall damping capacity in the physiological pressure range and the nonlinear method is recommended over the linear method.
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Horstemeyer, M. F., and M. I. Baskes. "Strain Tensors at the Atomic Scale." MRS Proceedings 578 (1999). http://dx.doi.org/10.1557/proc-578-15.
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AbstractAlmansi and Green strain tensors are developed for use in large deformation molecular dynamics/statics simulations that employ Embedded Atom Method (EAM) potentials for metals. The strain tensors are formulated with respect to the deformation gradient. A scalar potential function is used with a weighting function that is dependent upon a cutoff radius for the deformation gradient. For a homogeneous or inhomogeneous deformation, a cutoff distance of one lattice parameter can be used to approximate local strain level. Inhomogeneous deformation reveals different results for Almansi and Green strain tensors indicating that the small strain assumption cannot be used to determine large atomic strains.
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Sugiyama, Hiroyuki, Hirohisa Koyama, and Hiroki Yamashita. "Gradient Deficient Curved Beam Element Using the Absolute Nodal Coordinate Formulation." Journal of Computational and Nonlinear Dynamics 5, no. 2 (2010). http://dx.doi.org/10.1115/1.4000793.
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In this investigation, a gradient deficient beam element of the absolute nodal coordinate formulation is generalized to a curved beam for the analysis of multibody systems, and the performance of the proposed element is discussed by comparing with the fully parametrized curved beam element and the classical large displacement beam element with incremental solution procedures. Strain components are defined with respect to the initially curved configuration and described by the arc-length coordinate. The Green strain is used for the longitudinal stretch, while the material measure of curvature is used for bending. It is shown that strains of the curved beam can be expressed with respect to those defined in the element coordinate system using the gradient transformation, and the effect of strains at the initially curved configuration is eliminated using one-dimensional Almansi strain. This property can be effectively used with a nonincremental solution procedure employed for the absolute nodal coordinate formulation. Several numerical examples are presented in order to demonstrate the performance of the gradient deficient curved beam element developed in this investigation. It is shown that the use of the proposed element leads to better element convergence as compared with the fully parametrized element and the classical large displacement beam element with incremental solution procedures.
Dissertations / Theses on the topic "Almansi Strain"
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Jakel, Roland. "Analysis of Hyperelastic Materials with Mechanica - Theory and Application Examples." Universitätsbibliothek Chemnitz, 2010. http://nbn-resolving.de/urn:nbn:de:bsz:ch1-201000705.
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Part 1: Theoretic background information - Review of Hooke’s law for linear elastic materials - The strain energy density of linear elastic materials - Hyperelastic material - Material laws for hyperelastic materials - About selecting the material model and performing tests - Implementation of hyperelastic material laws in Mechanica - Defining hyperelastic material parameters in Mechanica - Test set-ups and specimen shapes of the supported material tests - The uniaxial compression test - Stress and strain definitions in the Mechanica LDA analysis Part 2: Application examples - A test specimen subjected to uniaxial loading - A volumetric compression test - A planar test - Influence of the material law Appendix - PTC Simulation Services Introduction - Dictionary Technical English-German<br>Teil 1: Theoretische Hintergrundinformation - Das Hookesche Gesetz für linear-elastische Werkstoffe - Die Dehnungsenergiedichte für linear-elastische Materialien - Hyperelastisches Material - Materialgesetze für Hyperelastizität - Auswählen des Materialgesetzes und Testdurchführung - Implementierung der hyperelastischen Materialgesetze in Mechanica - Definieren der hyperelastischen Materialparameter in Mechanica - Testaufbauten und Prüfkörper der unterstützten Materialtests - Der einachsige Druckversuch - Spannungs- und Dehnungsdefinition in der Mechanica-Analyse mit großen Verformungen Teil 2: Anwendungsbeispiele - Ein einachsig beanspruchter Prüfkörper - Ein volumetrischer Drucktest - Ein planarer Test - Einfluss des Materialgesetzes Anhang: - Kurzvorstellung der PTC Simulationsdienstleistungen - Wörterbuch technisches Englisch-Deutsch
Books on the topic "Almansi Strain"
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Jack, Captn. 2007 Captn. Jack's Almanac : Tice & Current Puget Sound Including the Strait of Juan De Fuca , Hood Canal, and San Juan Islands. Captain Jack's, 2006.
Find full textBook chapters on the topic "Almansi Strain"
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Havner, K. S. "A statical interpretation of the stress work-conjugate to Lagrangian-based Almansi strain." In Mechanics of Materials and Structures. Elsevier, 1994. http://dx.doi.org/10.1016/b978-0-444-89918-7.50019-8.
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Norton, Bryan G. "Aldo Leopold and the Search for an Integrated Theory of Environmental Management." In Toward Unity among Environmentalists. Oxford University Press, 1995. http://dx.doi.org/10.1093/oso/9780195093971.003.0008.
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Aldo Leopold led two lives. He was, in the best tradition of Gifford Pinchot, a forester and a coldly analytic scientific resource manager, devoted to maximizing resource productivity. But Leopold was also a romantic, who joined the Forest Service because of his love for the outdoors, a love he never lost or fully subjugated to the economic “ciphers” that so constrain public conservation work. During the last decade of his life, Leopold the romantic fashioned a little book of essays. He chose from the best of his stacks of field journals and his voluminous publications a few short essays, supplemented these with new pieces, polished them, and strung and restrung them like pearls. The manuscript, representing the essence of his long career, was given final acceptance by Oxford University Press only seven days before Leopold’s death, and the essays were published as A Sand County Almanac. The final essay in that book is “The Land Ethic,” which, Leopold said, “sets forth, in more logical terms, some ideas whereby we dissenters rationalize our dissent.” Although he was not primarily an abstract thinker, Leopold, I will assert, has been the most important figure in the history of both environmental management and environmental ethics. This evaluation is based on one reason: Having faced the environmentalists’ dilemma and, having to formulate goals and actions, he articulated a workable, practical philosophy that transcends the dilemma. The story of how he did so is a sketch of his life. Leopold was a forester in the Southwest for fifteen years. He saw the range deteriorate. He saw the main street of Carson City erode into a deep chasm, and he knew, by the early 1920s, that his agency and its Pinchotist philosophy was significantly responsible. But he was as befuddled as anyone else, and grasped at philosophical straws, or any other straws, to articulate in general terms what was going wrong. Leopold had entered the Forest Service at the height of the Hetch Hetchy controversy. He recognized, of course, that there were critics of the service, and he surely had some respect for Muir’s viewpoint.
Conference papers on the topic "Almansi Strain"
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Han, S. L., and O. A. Bauchau. "On the Almansi-Michell Problem for Flexible Multibody Dynamics." In ASME 2015 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2015. http://dx.doi.org/10.1115/detc2015-47154.
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In flexible multibody systems, it is convenient to approximate many structural components as beams. In classical beam theories, such as Timoshenko beam theory, the beams cross-section is assumed to remain plane. While such assuption is capable of capturing the kinetic energy of the system accurately, it cannot represent the strain energy adequately. In the authorss recent paper, an systematic approach was proposed for the modeling of three-dimensional beam problems. The proposed approach is based on the Hamiltonian formalism and leads to an expansion of the solution in terms of extremity and central solutions. This paper extends the previous approach to the “Almansi-Michell problem,” i.e., three dimensional beams subjected to distributed loads. Such problems can be represented by non-homogenous Hamiltonian systems, in contrast with Saint-Venants problem, which is represented by homogenous Hamiltonian systems. The solutions of Almansi-Michells problem are not only determined by the Hamiltonian coefficient matrix but also by the applied loading distribution patterns. hence, the contributions of the loading pattern need to be taken into account. A dimensional reduction procedure is proposed and the three-dimensional governing equations of Almansi-Michells problem can be reduced to a set of one-dimensional beams equations. Furthermore, the three-dimensional displacements and stress components can be recovered from the one-dimensional beams solution.
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Sugiyama, Hiroyuki, Hirohisa Koyama, and Hiroki Yamashita. "Performance of Curved Beam Elements Using the Absolute Nodal Coordinate Formulation." In ASME 2009 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2009. http://dx.doi.org/10.1115/detc2009-86312.
Full textAbstract:
In this investigation, a gradient deficient beam element of the absolute nodal coordinate formulation is generalized to a curved beam for the analysis of multibody systems and the performance of the proposed element is discussed by comparing with the fully parameterized curved beam element and the classical large displacement beam element with incremental solution procedures. Strain components are defined with respect to the initially curved configuration and described by the arc-length coordinate. The Green strain is used for the longitudinal stretch, while the material measure of curvature is used for bending. It is shown that strains of the curved beam can be expressed with respect to those defined in the element coordinate system using the gradient transformation and the effect of strains at the initially curved configuration is eliminated using one-dimensional Almansi strain. This property can be effectively used with non-incremental solution procedure employed for the absolute nodal coordinate formulation. Several numerical examples are presented in order to demonstrate the performance of the gradient deficient curved beam element developed in this investigation. It is shown that the use of the proposed element leads to better element convergence as compared to that of the fully parameterized element and the classical large displacement beam element with incremental solution procedures.
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Bauchau, Olivier A., and Shilei Han. "Integrating 3D Stress Analysis With Flexible Multibody Dynamics Simulation." In ASME 2017 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2017. http://dx.doi.org/10.1115/detc2017-67537.
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This paper presents an approach toward the integration of 3D stress computation with the tools used for the simulation of flexible multibody dynamics. Due to the low accuracy of the floating frame of reference approach, the the multibody dynamics community has turned its attention to comprehensive analysis tools based on beam theory. These tools evaluate sectional stress resultants, not 3D stress fields. The proposed approach decomposes the 3D problem into two simpler problems: a linear 2D analysis of the cross-section of the beam and a nonlinear, 1D of the beam. This procedure is described in details. For static problems, the proposed approach provides exact solutions of three-dimensional elasticity for uniform beams of arbitrary geometric configuration and made of anisotropic composite materials. While this strategy has been applied to dynamic problems, little attention has been devoted to inertial effects. This paper assesses the range of validity of the proposed beam theory when applied to dynamics problems. When beams are subjected to large axial forces, the induced axial stress components become inclined, generating a net torque that opposes further rotation of the section and leading to an increased effective torsional stiffness. This behavior, referred to as the Wagner or trapeze effect, cannot be captured by beam formulations that assume strain components to remain small, although arbitrarily large motions are taken into account properly. A formulation of beam theory that includes higher-order strain effects in an approximate manner is developed and numerical examples are presented. The “Saint-Venant problem” refers to a three-dimensional beam loaded at its end sections only. The “Almansi-Michell problem” refers to a three-dimensional beam loaded by distributed body forces, lateral surface tractions, and forces and moments at its end sections. Numerical examples of beams subjected to distributed loads will be presented and compared with 3D finite element solutions.