An analytical model for producing negative Poisson’s ratios and its application in explaining off-axis elastic properties of the NAT-type zeolites

The article studies the elastic properties of anisotropy and interatomic anharmonicity in a two-component Cu3Au alloy with positional order-disorder within the high temperature interval of 300 К and 725 К. It provides calculations on velocities of purely transverse and longitudinal elastic waves, elastic moduli (Young’s, shear, adiabatic bulk moduli) and Poisson’s ratios based on the stiffness constants сij(T) of the crystal. Sound velocity values were employed for determining the temperature changes of Grüneisen parameter along the crystallographic directions [100], [110] and [111].

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Acoustic and Elastic Properties of Cu3Au Alloy between 4.2...300 К

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.682.519 ◽

2014 ◽

Vol 682 ◽

pp. 519-524 ◽

Cited By ~ 4

Author(s):

Elena P. Tesleva ◽

Tatiana Belkova

Keyword(s):

Sound Velocity ◽

Elastic Properties ◽

Temperature Interval ◽

Elastic Waves ◽

Elastic Moduli ◽

Temperature Changes ◽

Two Component ◽

Poisson's Ratios ◽

Poisson’S Ratios

The article studies the elastic properties of anisotropy and interatomic anharmonicity in a two-component Cu3Au alloy with positional order-disorder within the temperature interval of 4.2 К and 300 К. It provides calculations on velocities of purely transverse and longitudinal elastic waves, elastic moduli (Young’s, shear, adiabatic bulk moduli) and Poisson’s ratios based on the stiffness constants сij(T) of the crystal. Sound velocity values were employed for determining the temperature changes of Grüneisen parameter along the crystallographic directions [100], [110] and [111].

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Elastic Properties of Solid Solutions with Intermediate Valence Sm1-xYxS

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.770.137 ◽

2015 ◽

Vol 770 ◽

pp. 137-143

Author(s):

E.G. Soboleva ◽

A.L. Igisheva ◽

T.B. Krit

Keyword(s):

Elasticity Theory ◽

Elastic Properties ◽

Solid Solutions ◽

Elastic Moduli ◽

Intermediate Valence ◽

Elastic Parameters ◽

Valence Transition ◽

The Given ◽

Poisson's Ratios ◽

Poisson’S Ratios

The given article considers acoustic analogues of elasticity theory ratios determining Poisson’s ratios of Sm1-xYxS alloy by their elastic parameters. The article discusses behavior of sound velocities, elastic moduli, Poisson’s ratios, Grüneisen parameter and brittleness-plasticity criterion ratios depending on the concentration of alloy components including valence transition from semiconductors into the metal phase.

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Anisotropic Dynamic and Static Mechanical Properties of Organic-rich Shale: The Influence of Stress

Geophysics ◽

10.1190/geo2020-0010.1 ◽

2020 ◽

pp. 1-62

Author(s):

Yang Wang ◽

Luanxiao Zhao ◽

de-hua Han ◽

Abhijit Mitra ◽

Hui Li ◽

...

Keyword(s):

Mechanical Properties ◽

Elastic Properties ◽

Triaxial Tests ◽

Static Properties ◽

Static Mechanical ◽

Intrinsic Anisotropy ◽

The Relationship ◽

Poisson's Ratios ◽

Poisson’S Ratios ◽

Static Mechanical Properties

Understanding the relationship between dynamic and static mechanical properties of organic-rich shales is crucial for successful in-situ stress profile prediction and hydraulic fracturing stimulation in unconventional reservoirs. However, the relationship between dynamic and static properties remains ambiguous, considering the complex rock microstructure and sub-surface stress environment. We report pseudo-triaxial tests on a pair of outcrop Eagle Ford shale plugs, with the axial load applied perpendicular and parallel to bedding planes, to investigate the effects of intrinsic anisotropy and anisotropic stress on dynamic-static relationships. The bedding-parallel Young's modulus is larger than the bedding-normal one dynamically and statically, whereas there exist complex relations among three static Poisson's ratios, which are attributed to the intrinsic anisotropy induced by the lenticular texture and finely laminated alignment of kerogen. Along with a stress increment, static tests respond to superpositions of the elastic, viscoelastic, and non-elastic properties, whereas dynamic tests, with more than two orders of magnitude smaller strain amplitude, only reflect the elastic properties of rocks. As a result, the static properties characteristically exhibit more stress dependence than the dynamic properties. Moreover, the evolutions of static properties, especially two static Poisson's ratios in the horizontal plug, are significantly influenced by the applied stress orientation with respect to the bedding plane. Lastly, we calculate four independent stiffnesses using the five static mechanical parameters with the assumption of transverse isotropy to compare with those calculated from ultrasonic velocities at different stress levels. Finally, when the deviatoric stress is approximately 20 MPa, static parameters derived from stress loading, unloading, and reloading almost intersect together. At this stress level, dynamic and static stiffnesses demonstrate a reasonable correlation with the fitting coefficient of approximately 1.4.

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A Novel Mechanical Metamaterial Exhibiting Auxetic Behavior and Negative Compressibility

Materials ◽

10.3390/ma13010079 ◽

2019 ◽

Vol 13 (1) ◽

pp. 79 ◽

Cited By ~ 7

Author(s):

James N. Grima-Cornish ◽

Joseph N. Grima ◽

Daphne Attard

Keyword(s):

Mechanical Properties ◽

Hydrostatic Pressure ◽

Analytical Model ◽

Anomalous Behavior ◽

Poisson's Ratio ◽

Negative Poisson’S Ratio ◽

Negative Poisson's Ratio ◽

Poisson's Ratios ◽

Poisson’S Ratios ◽

Linear Compressibility

Auxetics (negative Poisson’s ratio) and materials with negative linear compressibility (NLC) exhibit the anomalous mechanical properties of getting wider rather than thinner when stretched and expanding in at least one direction under hydrostatic pressure, respectively. A novel mechanism—termed the ‘triangular elongation mechanism’—leading to such anomalous behavior is presented and discussed through an analytical model. Amongst other things, it is shown that this novel mechanism, when combined with the well-known ‘rotating squares’ model, can generate giant negative Poisson’s ratios when the system is stretched.

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Cellular Materials With Extremely High Negative and Positive Poisson’s Ratios: A Mechanism Based Material Design

Volume 9: Mechanics of Solids, Structures and Fluids ◽

10.1115/imece2013-63598 ◽

2013 ◽

Author(s):

Kwangwon Kim ◽

Jaehyung Ju ◽

Doo-Man Kim

Keyword(s):

Porous Materials ◽

Analytical Model ◽

Compliant Mechanisms ◽

Constitutive Relations ◽

Functional Materials ◽

Material Design ◽

The Other ◽

Yield Strain ◽

Poisson's Ratios ◽

Poisson’S Ratios

In an effort to tailor functional materials with customized anisotropic properties — stiffness and yield strain, we propose porous materials consisting of flexible mesostructures designed from the deformation of a re-entrant auxetic honeycomb and compliant mechanisms. Using an analogy between compliant mechanisms and a cellular material’s deformation, we can tailor in-plane properties of mesostructures; low stiffness and high strain in one direction and high stiffness and low strain in the other direction. Two mesostructures based on hexagonal honeycombs with positive and negative cell angles are generated. An analytical model is developed to obtain effective moduli and yield strains of the porous materials by combining the kinematics of a rigid link mechanism and deformation of flexure hinges. A numerical technique is implemented to the analytical model for nonlinear constitutive relations of the mesostructures and their strain dependent Poisson’s ratios. A Finite Element Analysis (FEA) is used to validate the analytical and numerical model. The moduli and yield strain of a porous aluminum alloy are about 6.3GPa and 0.26% in one direction and about 2.8MPa and 12% in the other direction. The mesostructures have extremely high positive and negative Poisson’s ratios, νxy* (∼ ±40) due to the large rotation of the link member in the transverse direction caused by the input displacement in the longitudinal direction. The mesostructures also show higher moduli for compressive loading due to the contact of slit edges at the center region. This paper demonstrates that compliant mesostructures can be used for a next generation material design in terms of tailoring mechanical properties; moduli, strength, strain, and Poisson’s ratios. The proposed mesostructures can also be easily manufactured using a conventional cutting method.

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An analytical model for star-shaped re-entrant lattice structures with the orthotropic symmetry and negative Poisson's ratios

International Journal of Mechanical Sciences ◽

10.1016/j.ijmecsci.2018.06.027 ◽

2018 ◽

Vol 145 ◽

pp. 158-170 ◽

Cited By ~ 15

Author(s):

L. Ai ◽

X.-L. Gao

Keyword(s):

Analytical Model ◽

Lattice Structures ◽

Poisson's Ratios ◽

Poisson’S Ratios

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Giant negative Poisson’s ratio in two-dimensional V-shaped materials

Nanoscale Advances ◽

10.1039/d1na00212k ◽

2021 ◽

Author(s):

Xikui Ma ◽

Jian Liu ◽

Yingcai Fan ◽

Weifeng Li ◽

Jifan Hu ◽

...

Keyword(s):

Poisson’S Ratio ◽

Poisson's Ratio ◽

Negative Poisson’S Ratio ◽

Two Dimensional ◽

Auxetic Materials ◽

Negative Poisson's Ratio ◽

Poisson's Ratios ◽

Poisson’S Ratios

Two-dimensional (2D) auxetic materials with exceptional negative Poisson’s ratios (NPR) are drawing increasing interest due to the potentials in medicine, fasteners, tougher composites and many other applications. Improving the auxetic...

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Continuum Description of the Time- and Strain-Dependent Poisson’s Ratio of Ligament Under Finite Deformation

Volume 1B: Extremity; Fluid Mechanics; Gait; Growth, Remodeling, and Repair; Heart Valves; Injury Biomechanics; Mechanotransduction and Sub-Cellular Biophysics; MultiScale Biotransport; Muscle, Tendon and Ligament; Musculoskeletal Devices; Multiscale Mechanics; Thermal Medicine; Ocular Biomechanics; Pediatric Hemodynamics; Pericellular Phenomena; Tissue Mechanics; Biotransport Design and Devices; Spine; Stent Device Hemodynamics; Vascular Solid Mechanics; Student Paper and Design Competitions ◽

10.1115/sbc2013-14323 ◽

2013 ◽

Author(s):

Aaron M. Swedberg ◽

Shawn P. Reese ◽

Steve A. Maas ◽

Benjamin J. Ellis ◽

Jeffrey A. Weiss

Keyword(s):

Large Scale ◽

Mechanical Response ◽

Tensile Deformation ◽

Large Strain ◽

Fiber Direction ◽

Strain Behavior ◽

Nonlinear Stress ◽

Poisson's Ratios ◽

Poisson’S Ratios ◽

Strain Dependent

Ligament volumetric behavior controls fluid and thus nutrient movement as well as the mechanical response of the tissue to applied loads. The reported Poisson’s ratios for tendon and ligament subjected to tensile deformation loading along the fiber direction are large, ranging from 0.8 ± 0.3 in rat tail tendon fascicles [1] to 2.98 ± 2.59 in bovine flexor tendon [2]. These Poisson’s ratios are indicative of volume loss and thus fluid exudation [3,4]. We have developed micromechanical finite element models that can reproduce both the characteristic nonlinear stress-strain behavior and large, strain-dependent Poisson’s ratios seen in tendons and ligaments [5], but these models are computationally expensive and unfeasible for large scale, whole joint models. The objectives of this research were to develop an anisotropic, continuum based constitutive model for ligaments and tendons that can describe strain-dependent Poisson’s ratios much larger than the isotropic limit of 0.5. Further, we sought to demonstrate the ability of the model to describe experimental data, and to show that the model can be combined with biphasic theory to describe the rate- and time-dependent behavior of ligament and tendon.

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