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Elastic and Viscoelastic Poisson’s Ratios: The Theoretical Mechanics Perspective

Materials sciences and Applications 2017年第4期8卷 291-332页

作者： Harry H. Hilton Aerospace Engineering Department College of Engineering and Private Sector Program Division The National Center for Supercomputing Applications University of Illinois at Urbana-Champaign (UIUC) Urbana IL USA

A recent review publication presented an extensive and comprehensive assessment of the phenomenological relations of Poisson’s ratios (PRs) to the behavior and responses of contemporary materials under specific loading conditions. The present review and analysis paper is intended as a theoretical mechanics complement covering mathematical and physical modeling of a single original elastic and of six time and process (i.e. path and stress) dependent viscoelastic PR definitions as well as a seventh special path independent one. The implications and consequences of such models on material characterization are analyzed and summarized. Indeed, PRs based on experimentally obtained 2-D strains under distinct creep and/or relaxation processes exhibit radically different time responses for identical material specimen. These results confirm the PR’s implicit path dependence in addition to their separate intrinsic time reliance. such non-uniqueness of viscoelastic PRs renders them unsuitable as universal material descriptors. Analytical formulations and experimental measurements also examine the physical impossibility of instantaneously achieving time independent loads or strains or their rates thus making certain PR definitions based on constant state variables, while mathematically valid, physically unrealistic and unachievable. A newly developed theoretical/experimental protocol for the determination of the time when loading patterns reach stead-state conditions based on strain accelerations demonstrates the capability to measure this time from experimental data. Due to the process dependent PRs, i.e. stress and stress history paths, the non-existence of a unique viscoelastic PR and of a universal elastic-viscoelastic correspondence principle or analogy (EVCP) in terms of PRs is demonstrated. Additionally and independently, the required double convolution integral construction of linear viscoelastic constitutive relations with the inclusion of PRs is cumbersome analytically and computationally needlessly highly CPU inten

关键词： Elastic and Viscoelastic Poisson’s Ratios (PRs) Transient Load Build up Viscoelasticity PR Nonlinearities PR Categories Loading History PR Dependence

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High Accurate Fourth-Order Finite Difference solutions of the Three Dimensional Poisson’s Equation in Cylindrical Coordinate

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American Journal of Computational Mathematics 2014年第2期4卷 73-86页

作者： Alemayehu shiferaw Ramesh Chand Mittal Department of Mathematics Indian Institute of Technology Roorkee India

In this work, by extending the method of Hockney into three dimensions, the Poisson’s equation in cylindrical coordinates system with the Dirichlet’s boundary conditions in a portion of a cylinder for is solved directly. The poisson equation is approximated by fourth-order finite differences and the resulting large algebraic system of linear equations is treated systematically in order to get a block tri-diagonal system. The accuracy of this method is tested for some Poisson’s equations with known analytical solutions and the numerical results obtained show that the method produces accurate results.

关键词： Poisson’s Equation Tri-Diagonal Matrix Fourth-Order Finite Difference Approximation Hockney’s Method Thomas Algorithm

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Fast Finite Difference solutions of the Three Dimensional Poisson’s Equation in Cylindrical Coordinates

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American Journal of Computational Mathematics 2013年第4期3卷 356-361页

作者： Alemayehu shiferaw R. C. Mittal Department of Mathematics Indian Institute of Technology Roorkee India

In this work, the three-dimensional Poisson’s equation in cylindrical coordinates system with the Dirichlet’s boundary conditions in a portion of a cylinder for is solved directly, by extending the method of Hockney. The poisson equation is approximated by second-order finite differences and the resulting large algebraic system of linear equations is treated systematically in order to get a block tri-diagonal system. The accuracy of this method is tested for some Poisson’s equations with known analytical solutions and the numerical results obtained show that the method produces accurate results.

关键词： Poisson’s Equation Hockney’s Method Thomas Algorithm

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An Efficient Direct Method to solve the Three Dimensional Poisson’s Equation

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American Journal of Computational Mathematics 2011年第4期1卷 285-293页

作者： Alemayehu shiferaw Ramesh Chand Mittal Department of Mathematics Indian Institute of Technology

In this work, the three dimensional Poisson’s equation in Cartesian coordinates with the Dirichlet’s boundary conditions in a cube is solved directly, by extending the method of Hockney. The poisson equation is approximated by 19-points and 27-points fourth order finite difference approximation schemes and the resulting large algebraic system of linear equations is treated systematically in order to get a block tri-diagonal system. The efficiency of this method is tested for some Poisson’s equations with known analytical solutions and the numerical results obtained show that the method produces accurate results. It is shown that 19-point formula produces comparable results with 27-point formula, though computational efforts are more in 27-point formula.

关键词： Poisson’s Equation Finite Difference Method Tri-diagonal Matrix Hockney’s Method Thomas Algorithm

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A Note on the Effect of Negative Poisson’s Ratio on the Deformation of a Poroelastic Half-space by surface Loads

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Engineering（科研） 2010年第6期2卷 432-437页

作者： sunita Rani Raman Kumar sarva Jit singh Department of Mathematics Guru Jambheshwar University of Science and Technology Honorary scientist Indian National Science Academy

The aim of this note is to study the effect of negative Poisson’s ratio on the quasi-static deformation of a poroelastic half-space with anisotropic permeability and compressible fluid and solid constituents by surface loads. Two particular cases considered are: two-dimensional normal strip loading and axisymmetric normal disc loading. It is found that a negative Poisson’s ratio makes the Mandel-Cryer effect more prominent. It also results in an increase in the magnitude of the surface settlement.

关键词： Anisotropic Permeability Auxetic Material Negative Poisson’s Ratio Poroelastic Half-space Quasi-static Deformation surface Loading

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Uniqueness and stability in an inverse problem for a poisson's equation

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science China Mathematics 2007年第7期50卷 967-976页

作者： Li-xin FENG~(1+) Yan-cheng QU~2 1 school of Mathematical sciences,Heilongjiang University,Harbin 150080,China 2 Research Center of Control and Inertial Technology,Harbin Institute of Technology,Harbin 150001,China school of Mathematical sciences Heilongjiang University Harbin China Research Center of Control and Inertial Technology Harbin Institute of Technology Harbin China

Consider the Poisson’s equation（?）″（x）=-ev-（?）+e（?）-v-N（x）with the Diriehlet boundary data,and we mainly investigate the inverse problem of determining the unknown function N（x）from a parameter function ... 详细信息

Consider the Poisson’s equation（?）″（x）=-esup>v-（?）sup>+esup>（?）-vsup>-N（x）with the Diriehlet boundary data,and we mainly investigate the inverse problem of determining the unknown function N（x）from a parameter function family.some uniqueness and stability results in the inverse problem are obtained.

关键词： Poisson’s equation well-posedness inverse problem

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Poisson’s Ratio of surface soils and shallow sediments Determined from seismic Compressional and shear Wave Velocities

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International Journal of Geosciences 2014年第12期5卷 1540-1546页

作者： U. E. Essien A. O. Akankpo M. U. Igboekwe Department of science Technology AkwaIbom State Polytechnic Ikot Osurua Nigeria Department of Physics University of Uyo Uyo Nigeria Department of Physics Michael Okpara University of Agriculture Umudike Nigeria

This paper presents the results of seismic compressional, P- and shear, s-wave measurements carried out on the unconsolidated top-soil at the different locations of the study area to determine Poisson’s ratio. In this work, seismic refraction data is used to determine Poisson’s ratio as an aid to engineering foundation. A 12-channel seismograph with signal stacking ability was used together with high frequency (100 Hz) geophones on the top-soil. The geophone intervals were set to 5 m at the all locations. In all the locations, Vp/Vs ratio ranged from 1.0289 to 1.4185 for the top layer. Vp/Vs ratio in the second layer ranged from 1.0512 to 1.5834. The Poisson’s ratio for the first layer ranged from -8.0324 to 0.2060. For the second layer, the Poisson’s ratio ranged from -0.7567 to 0.1683. The values of Vp/Vs ratio less than in the first layer and in some locations in the second layer resulted in negative Poisson’s ratio. The low and negative values of Poisson’s ratio are symptomatic of occurrence of ripable anisotropic materials in the locations where they occur, which suggests that indicated average depth should be removed and refilled with geomaterials that may be resilient to carry engineering loads.

关键词： seismic Refraction Eket Vp/Vs Ratio Poisson’s Ratio

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Experimental characterization of the 3D linear viscoelastic behavior of cold recycled bitumen emulsion mixtures

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Journal of Traffic and Transportation Engineering(English Edition) 2019年第4期6卷 324-336页

作者： Andrea Graziani Carlotta Godenzoni Francesco Canestrari Dipartimento di Ingegneria Civile Edile e Architettura Università Politecnica delle Marche

Cold mixtures with bitumen emulsion are produced at ambient temperature, leading to substantial reductions of energy consumption and atmospheric emissions. In cold recycling applications, cement is normally used to improve the mixture performance. Thus, the rheological behavior of cold recycled mixtures is different from that of conventional hot mixtures because it is due to the interaction of fresh bitumen, aged bitumen and cementitious bonds. In this study, we investigated the three-dimensional(3 D) linear viscoelastic(LVE) behavior of a cement-bitumen treated material(CBTM) mixture fabricated using bitumen emulsion and cement. For comparison, we also investigated the 3 D LVE behavior of hot-mix asphalt containing 25% of reclaimed asphalt and fabricated using polymermodified binder. sinusoidal axial tests on cylindrical specimens, were carried out at various temperatures(from 0℃ to 50℃) and frequencies(from 0.1 to 12 Hz). The complex Young’s modulus E~*and the complex Poisson’s ratio v~*were determined through the measurement of axial and transverse strain. We show that when considering E*, CBTM mixtures may be considered thermo-rheologically simple and the Huet-sayegh model can be used to simulate the frequencyetemperature dependence. On the other hand, when considering v*the behavior of CBTM mixtures is very different from that of hot mix asphalt. In particular, its absolute value is almost constant and very close to 0.15.

关键词： Bitumen emulsion Cold recycling Complex modulus Complex Poisson’s ratio Huet-sayegh model

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A methodology to determine the elastic properties of anisotropic rocks from a single uniaxial compression test

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Journal of Rock Mechanics and Geotechnical Engineering 2019年第6期11卷 1166-1183页

作者： Morteza Nejati Marie Luise Texas Dambly Martin Osaar Department of Earth sciences ETH ZurichZurichSwitzerland Geothermal Energy and Geofluids Department of Earth SciencesETH ZurichZurichSwitzerland

This paper introduces a new methodology to measure the elastic constants of transversely isotropic rocks from a single uniaxial compression test.We first give the mathematical proof that a uniaxial compression test provides only four independent strain equations.As a result,the exact determination of all five independent elastic constants from only one test is not possible.An approximate determination of the Young’s moduli and the Poisson’s ratios is however practical and efficient when adding the saint-Venant relation as the fifth equation.Explicit formulae are then developed to calculate both secant and tangent definitions of the five elastic constants from a minimum of four strain measurements.The results of this new methodology applied on three granitic samples demonstrate a significant stress-induced nonlinear behavior,where the tangent moduli increase by a factor of three to four when the rock is loaded up to 20 MPa.The static elastic constants obtained from the uniaxial compression test are also found to be significantly smaller than the dynamic ones obtained from the ultrasonic measurements.

关键词： Transversely isotropic rock Elastic constants Young’s modulus Poisson’s ratio seismic anisotropy Uniaxial compression Granite

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Determination　of　Elastic-plastic　poisson's　Ratio　in　Elastic-Plastic　FEM

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Journal of Harbin Institute of Technology(New series) 1998年第1期5卷 93-96页

作者： XU Weili XING Zhongwen LI Chunfeng

ＤｅｔｅｒｍｉｎａｔｉｏｎｏｆＥｌａｓｔｉｃ－ｐｌａｓｔｉｃＰｏｉｓｓｏｎ＇ｓＲａｔｉｏｉｎＥｌａｓｔｉｃ－ＰｌａｓｔｉｃＦＥＭＸＵＷｅｉｌｉ，ＸＩＮＧＺｈｏｎｇｗｅｎ，ＬＩＣｈｕｎｆｅｎｇ，ＹＡＮＧＹｕｙｉｎｇ（徐... 详细信息

ＤｅｔｅｒｍｉｎａｔｉｏｎｏｆＥｌａｓｔｉｃ－ｐｌａｓｔｉｃＰｏｉｓｓｏｎ＇ｓＲａｔｉｏｉｎＥｌａｓｔｉｃ－ＰｌａｓｔｉｃＦＥＭＸＵＷｅｉｌｉ，ＸＩＮＧＺｈｏｎｇｗｅｎ，ＬＩＣｈｕｎｆｅｎｇ，ＹＡＮＧＹｕｙｉｎｇ（徐伟力）（邢忠文）（李春峰）（杨玉英...

关键词： FEM 李春 Determination Elastic-Plastic Elastic-plastic Poisson’s Ratio

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