Surface Settlement of a Deep Elastic Stratum Whose Modulus Increases Linearly with Depth

1972 ◽  
Vol 9 (4) ◽  
pp. 467-476 ◽  
Author(s):  
P. T. Brown ◽  
R. E. Gibson
Keyword(s):  
Half Space ◽  
Elastic Material ◽  
Poisson’S Ratio ◽  
Surface Displacement ◽  
Vertical Surface ◽  
Surface Settlement ◽  
Poisson's Ratio ◽  
Uniform Load ◽  
Circular Area ◽  
Wide Range

An examination has been made of the behavior of a half space of elastic material of constant Poisson's ratio, whose Young's modulus increases linearly with depth, and which is subject to a strip or circle of uniform load. Poisson's ratio was considered in the range zero to one-half, and the surface modulus ranged from zero to the value corresponding to a homogeneous material.Numerical values are presented for vertical surface displacement due to a load uniformly distributed over a circular area for Poisson's ratio = 1/2, 1/3 and 0, and for a wide range of inhomogeneity.

Dispersive characteristics of the first three Rayleigh modes for a single surface layer

1966 ◽  
Vol 56 (1) ◽  
pp. 43-67 ◽  
Author(s):  
Harold M. Mooney ◽  
Bruce A. Bolt
Keyword(s):  
Surface Layer ◽  
Half Space ◽  
Poisson’S Ratio ◽  
Velocity Ratio ◽  
Surface Displacement ◽  
Shear Velocity ◽  
Poisson's Ratio ◽  
Wave Number ◽  
Model Parameters ◽  
Higher Modes

abstract The dispersive characteristics of a single elastic layer overlying an elastic half-space are examined in detail for the fundamental and the first and second higher modes of Rayleigh waves. Phase velocity, group velocity, and the ratio of horizontal to vertical surface displacement are computed as functions of dimensionless quantities proportional to period and wave number. The significant range for the independent variable, B1T/H, proves to be largely independent of the parameters of the structure. The range is 1 to 20 for the fundamental, 0.3 to cutoff for the first higher mode, and 0.2 to cutoff for the second higher mode. The most important parameter of the structure for Rayleigh wave dispersion is the shear velocity ratio. Variations in the Poisson's ratio in the surface layer and the density contrast may produce substantial effects. Poisson's ratio in the half-space is of least significance. The dependence on model parameters of the long-period cutoff for the higher modes is determined. Specific results are given for the following geophysical examples: continental crust, continental ice cap, sedimentary basin, alluvial overburden, and laboratory seismic models.

scholarly journals Modelling the elastic mechanical properties of bioactive glass-derived scaffolds

2020 ◽  
Vol 6 (1) ◽  
pp. 50-56
Author(s):  
Francesco Baino ◽  
Elisa Fiume
Keyword(s):  
Elastic Properties ◽  
Poisson’S Ratio ◽  
Mechanical Performance ◽  
Solid Material ◽  
Poisson's Ratio ◽  
Predictive Capability ◽  
Shear Moduli ◽  
Wide Range ◽  
Constitutive Parameters ◽  
The Relationship

AbstractPorosity is known to play a pivotal role in dictating the functional properties of biomedical scaffolds, with special reference to mechanical performance. While compressive strength is relatively easy to be experimentally assessed even for brittle ceramic and glass foams, elastic properties are much more difficult to be reliably estimated. Therefore, describing and, hence, predicting the relationship between porosity and elastic properties based only on the constitutive parameters of the solid material is still a challenge. In this work, we quantitatively compare the predictive capability of a set of different models in describing, over a wide range of porosity, the elastic modulus (7 models), shear modulus (3 models) and Poisson’s ratio (7 models) of bioactive silicate glass-derived scaffolds produced by foam replication. For these types of biomedical materials, the porosity dependence of elastic and shear moduli follows a second-order power-law approximation, whereas the relationship between porosity and Poisson’s ratio is well fitted by a linear equation.

Metamaterials with enhanced mechanical properties and tuneable Poisson’s ratio

2021 ◽  
Author(s):  
Amer Alomarah ◽  
Syed Masood ◽  
Dong Ruan
Keyword(s):  
Poisson’S Ratio ◽  
Structural Modification ◽  
Mechanical Response ◽  
Good Alternative ◽  
Poisson's Ratio ◽  
Polyamide 12 ◽  
Loading Direction ◽  
Wide Range ◽  
Potential Applications ◽  
Parametric Studies

Abstract This paper reports a structural modification of an auxetic metamaterial with a combination of representative re-entrant and chiral topologies, namely, a re-entrant chiral auxetic (RCA). The main driving force for the structural modification was to overcome the undesirable properties of the RCA metamaterial such as anisotropic mechanical response under uniaxial compression. Additively manufactured polyamide 12 specimens via Multi Jet Fusion (MJF) were quasi-statically compressed along the two in-plane directions. The experimental results confirmed that the modified structure was less sensitive to the loading direction and the deformation was more uniform. Moreover, similar energy absorptions were obtained when the modified metamaterial was crushed along the two in-plane directions. The energy absorptions were improved from 390 to 950 kJ/m³ and from 500 to 1000 kJ/m³ compared with the RCA when they were crushed along the X and Y directions, respectively. The absorbed energy per unit mass (SEA) also improved from 1.4 to 2.9 J/g and from 1.78 to 3.1 J/g compared with that of the RCA under the axial compression along the X and Y directions. Furthermore, parametric studies were performed and the effects of geometric parameters of the modified metamaterial were numerically investigated. Tuneable auxetic feature was obtained. The energy absorption and Poisson’s ratio of the modified metamaterial offer it a good alternative for a wide range of potential applications in the areas such as aerospace, automotive, and human protective equipment.

Large Deflection of Circular Auxetic Membranes Under Uniform Load

2016 ◽  
Vol 138 (4) ◽  
Author(s):  
Teik-Cheng Lim
Keyword(s):  
Empirical Model ◽  
Poisson’S Ratio ◽  
Large Deflection ◽  
Radial Distance ◽  
Poisson's Ratio ◽  
Circular Membrane ◽  
Membrane Material ◽  
Uniform Load ◽  
Direct Computation ◽  
Semi Empirical

Currently, available results for the large deflection of circular isotropic membranes are valid for Poisson's ratio of 0.2, 0.3, and 0.4 only. This paper explores the deflection of circular membranes when the membrane material is auxetic, i.e., when they possess negative Poisson's ratio and compared against conventional ones. Due to the multistage calculations involved in the exact method, a generic semi-empirical model is proposed to facilitate convenient and direct computation of the membrane deflection as a function of the radial distance; additionally, a specific semi-empirical model is given to provide a more accurate maximum deflection. Comparison of deflection distributions verifies the validity of the semi-empirical model vis-à-vis the exact model. The deflection of circular membrane increases with the diminishing effect as the Poisson's ratio of the membrane material becomes more negative.

The Effect of Contact Conditions on the Onset of Plastic Yielding in a Spherical Shell Compressed by a Rigid Flat

2010 ◽  
Author(s):  
Longqiu Li ◽  
Lin Wang ◽  
Izhak Etsion ◽  
Frank Talke
Keyword(s):  
Spherical Shell ◽  
Poisson’S Ratio ◽  
Load Ratio ◽  
Contact Condition ◽  
Poisson's Ratio ◽  
Plastic Yielding ◽  
Element Analysis ◽  
Contact Conditions ◽  
Wide Range ◽  
Shell Parameter

The effect of contact conditions on yield inception of a spherical shell compressed by a rigid flat is studied using finite element analysis. A wide range of material properties and shell thickness values, corresponding to the dimensionless shell parameter, were studied. This work provides the critical load ratio as a function of the shell parameter for different values of the Poisson’s ratio under both slip and stick contact condition. At small values of the Poisson’s ratio the behavior in stick is very different from that in slip. At high values of the Poisson’s ratio the yield inception in stick and slip is similar.

Saint-Venant End Effects for Materials With Negative Poisson’s Ratios

1992 ◽  
Vol 59 (4) ◽  
pp. 744-746 ◽  
Author(s):  
R. S. Lakes
Keyword(s):  
Circular Cylinder ◽  
Elastic Material ◽  
Poisson’S Ratio ◽  
Sandwich Panel ◽  
Sandwich Panels ◽  
Poisson's Ratio ◽  
Negative Poisson’S Ratio ◽  
End Effects ◽  
Slow Decay ◽  
Negative Poisson's Ratio

In this paper we analyze Saint-Venant end effects for materials with negative Poisson ’s ratios. We present an example of slow decay of stress arising from selfequilibrated stress at the end of a circular cylinder of elastic material with a negative Poisson’s ratio. By contrast, a sandwich panel containing rigid face sheets and a compliant core exhibits no anomalous effects for negative Poisson’s ratio, but exhibits slow stress decay for core Poisson’s ratio approaching 0.5. In sandwich panels with stiff but not perfectly rigid face sheets, slow decay of stress is known to occur; a negative Poisson’s ratio results in end stress decay, which is faster than it would be otherwise.

scholarly journals Analytical relationships for re-entrant honeycombs

2020 ◽  
Author(s):  
Reza Hedayati ◽  
Naeim Ghavidelnia
Keyword(s):  
Yield Stress ◽  
Analytical Solutions ◽  
Poisson’S Ratio ◽  
Poisson's Ratio ◽  
Negative Poisson’S Ratio ◽  
Fe Method ◽  
Wide Range ◽  
Unit Cells ◽  
Negative Poisson's Ratio ◽  
Internal Angle

Mechanical metamaterials have emerged in the last few years as a new type of artificial material which show properties not usually found in nature. Such unprecedented properties include negative stiffness, negative Poisson’s ratio, negative compressibility and fluid-like behaviors. Unlike normal materials, materials with negative Poisson’s ratio (NPR), also known as auxetics, shrink laterally when a compressive load is applied to them. The 2D re-entrant honeycombs are the most prevalent auxetic structures and many studies have been dedicated to study their stiffness, large deformation behavior, and shear properties. Analytical solutions provide inexpensive and quick means to predict the behavior of 2D re-entrant structures. There have been several studies in the literature dedicated to deriving analytical relationships for hexagonal honeycomb structures where the internal angle θ is positive (i.e. when the structure has positive Poisson’s ratio). It is usually assumed that such solutions also work for corresponding re-entrant unit cells. The goal of this study was to find out whether or not the analytical relationships obtained in the literature for θ>0 are also applicable to 2D-reentrant structures (i.e. when θ<0). Therefore, this study focused on unit cells with a wide range of internal angles from very negative to very positive values. For this aim, new analytical relationships were obtained for hexagonal honeycombs with possible negativity in the internal angle θ in mind. Numerical analyses based on finite element (FE) method were also implemented to validate and evaluate the analytical solutions. The results showed that, as compared to analytical formulas presented in the literature, the analytical solutions derived in this work give the most accurate results for elastic modulus, Poisson’s ratio, and yield stress. Moreover, some of the formulas for yield stress available in the literature fail to be valid for negative ranges of internal angle (i.e. for auxetics). However, the yield stress results of the current study demonstrated good overlapping with numerical results in both the negative and positive domains of θ.

The azimuthal and polar radiation patterns obtained from a horizontal stress applied at the surface of an elastic half space

1962 ◽  
Vol 52 (1) ◽  
pp. 27-36
Author(s):  
J. T. Cherry
Keyword(s):  
Surface Wave ◽  
Half Space ◽  
Rayleigh Waves ◽  
Poisson’S Ratio ◽  
Horizontal Stress ◽  
Elastic Half Space ◽  
The Body ◽  
Body Waves ◽  
Poisson's Ratio ◽  
A Value

Abstract The body waves and surface waves radiating from a horizontal stress applied at the free surface of an elastic half space are obtained. The SV wave suffers a phase shift of π at 45 degrees from the vertical. Also, a surface wave that is SH in character but travels with the Rayleigh velocity is shown to exist. This surface wave attenuates as r−3/2. For a value of Poisson's ratio of 0.25 or 0.33, the amplitude of the Rayleigh waves from a horizontal source should be smaller than the amplitude of the Rayleigh waves from a vertical source. The ratio of vertical to horizontal amplitude for the Rayleigh waves from the horizontal source is the same as the corresponding ratio for the vertical source for all values of Poisson's ratio.

scholarly journals A single Rayleigh mode may exist with multiple values of phase-velocity at one frequency

2020 ◽  
Vol 222 (1) ◽  
pp. 582-594
Author(s):  
Thomas Forbriger ◽  
Lingli Gao ◽  
Peter Malischewsky ◽  
Matthias Ohrnberger ◽  
Yudi Pan
Keyword(s):  
Phase Velocity ◽  
Rayleigh Wave ◽  
Half Space ◽  
Wave Velocity ◽  
Poisson’S Ratio ◽  
P Wave ◽  
Poisson's Ratio ◽  
Wave Number ◽  
Homogeneous Layer ◽  
Rayleigh Mode

SUMMARY Other than commonly assumed in seismology, the phase velocity of Rayleigh waves is not necessarily a single-valued function of frequency. In fact, a single Rayleigh mode can exist with three different values of phase velocity at one frequency. We demonstrate this for the first higher mode on a realistic shallow seismic structure of a homogeneous layer of unconsolidated sediments on top of a half-space of solid rock (LOH). In the case of LOH a significant contrast to the half-space is required to produce the phenomenon. In a simpler structure of a homogeneous layer with fixed (rigid) bottom (LFB) the phenomenon exists for values of Poisson’s ratio between 0.19 and 0.5 and is most pronounced for P-wave velocity being three times S-wave velocity (Poisson’s ratio of 0.4375). A pavement-like structure (PAV) of two layers on top of a half-space produces the multivaluedness for the fundamental mode. Programs for the computation of synthetic dispersion curves are prone to trouble in such cases. Many of them use mode-follower algorithms which loose track of the dispersion curve and miss the multivalued section. We show results for well established programs. Their inability to properly handle these cases might be one reason why the phenomenon of multivaluedness went unnoticed in seismological Rayleigh wave research for so long. For the very same reason methods of dispersion analysis must fail if they imply wave number kl(ω) for the lth Rayleigh mode to be a single-valued function of frequency ω. This applies in particular to deconvolution methods like phase-matched filters. We demonstrate that a slant-stack analysis fails in the multivalued section, while a Fourier–Bessel transformation captures the complete Rayleigh-wave signal. Waves of finite bandwidth in the multivalued section propagate with positive group-velocity and negative phase-velocity. Their eigenfunctions appear conventional and contain no conspicuous feature.

Development of uni-stretch woven fabrics with zero and negative Poisson’s ratio

2017 ◽  
Vol 88 (18) ◽  
pp. 2076-2092 ◽  
Author(s):  
Adeel Zulifqar ◽  
Tao Hua ◽  
Hong Hu
Keyword(s):  
Poisson’S Ratio ◽  
Tensile Tests ◽  
Research Area ◽  
Woven Fabrics ◽  
Poisson's Ratio ◽  
Negative Poisson’S Ratio ◽  
Wide Range ◽  
Differential Shrinkage ◽  
Weaving Technology ◽  
Negative Poisson's Ratio

Fabrics with zero or negative Poisson’s ratio are referred as auxetic fabrics, which have the unusual property of lateral expansion or zero expansion upon stretch. The use of conventional materials and machinery to produce auxetic fabrics has gained the interest of researchers in recent years. However, this approach is limited to knitted fabrics only. The development of auxetic fabric using conventional yarns and weaving technology is a research area that is still unaddressed. This paper reports a study on the development of a novel class of stretchable auxetic woven fabrics by using conventional yarns and weaving machinery. The phenomenon of differential shrinkage was successfully employed to realize auxetic geometries capable of inducing auxetic behavior in woven fabrics, and a series of auxetic woven fabrics were fabricated with elastic and non-elastic yarns and a dobby machine. The uni-axial tensile tests showed that auxetic woven fabrics developed exhibited zero or negative Poisson’s ratio over a wide range of longitudinal strain.

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