Two-dimensional isotropic system with a negative poisson ratio

1989 ◽  
Vol 137 (1-2) ◽  
pp. 60-64 ◽  
Author(s):  
K.W. Wojciechowski
Keyword(s):  
Poisson Ratio ◽  
Two Dimensional ◽  
Isotropic System

Bending of an Infinite Beam on an Elastic Foundation

1937 ◽  
Vol 4 (1) ◽  
pp. A1-A7 ◽  
Author(s):  
M. A. Biot
Keyword(s):  
Elastic Foundation ◽  
Poisson Ratio ◽  
Elementary Theory ◽  
Three Dimensional ◽  
Bending Moment ◽  
Two Dimensional ◽  
Concentrated Load ◽  
Elastic Continuum ◽  
Infinite Beam ◽  
A Value

Abstract The elementary theory of the bending of a beam on an elastic foundation is based on the assumption that the beam is resting on a continuously distributed set of springs the stiffness of which is defined by a “modulus of the foundation” k. Very seldom, however, does it happen that the foundation is actually constituted this way. Generally, the foundation is an elastic continuum characterized by two elastic constants, a modulus of elasticity E, and a Poisson ratio ν. The problem of the bending of a beam resting on such a foundation has been approached already by various authors. The author attempts to give in this paper a more exact solution of one aspect of this problem, i.e., the case of an infinite beam under a concentrated load. A notable difference exists between the results obtained from the assumptions of a two-dimensional foundation and of a three-dimensional foundation. Bending-moment and deflection curves for the two-dimensional case are shown in Figs. 4 and 5. A value of the modulus k is given for both cases by which the elementary theory can be used and leads to results which are fairly acceptable. These values depend on the stiffness of the beam and on the elasticity of the foundation.

scholarly journals Half-Auxeticity and Anisotropic Transport in Pd Decorated Two-Dimensional Boron Sheets

2020 ◽  
Author(s):  
Fengxian Ma ◽  
Yalong Jiao ◽  
Weikang Wu ◽  
Ying Liu ◽  
Shengyuan A. Yang ◽  
...  
Keyword(s):  
Electronic Properties ◽  
Poisson Ratio ◽  
Two Dimensional ◽  
Peculiar Property ◽  
Opposite Behavior ◽  
Boron Sheets ◽  
Anisotropic Transport

If one strains a material along a direction, most materials shrink normal to that direction. Similarly, if you compress the material, it will expand in the direction orthogonal to the pressure. Few materials, those of negative Poisson ratio, show the opposite behavior. Here, we show an unprecedented feature, a material that expands normal to the direction of force regardless if it is strained or compressed. Such behavior, called half-auxeticity, has been found for a borophene sheet stabilized by decorating Pd atoms. Herein, we explore Pd-decorated borophene, identify three stable phases of which one has this peculiar property of half auxeticity. After carefully analyzing stability, mechanical and electronic properties we explore the origin of this very uncommon behavior.<br>

Half-Auxeticity and Anisotropic Transport in Pd Decorated Two-Dimensional Boron Sheets

2020 ◽  
Author(s):  
Fengxian Ma ◽  
Yalong Jiao ◽  
Weikang Wu ◽  
Ying Liu ◽  
Shengyuan A. Yang ◽  
...  
Keyword(s):  
Structural Feature ◽  
Electronic Properties ◽  
Poisson Ratio ◽  
Applied Strain ◽  
Two Dimensional ◽  
Peculiar Property ◽  
Opposite Behavior ◽  
2D Nanomaterials ◽  
Boron Sheets ◽  
Anisotropic Transport

<p>If one strains a material, most materials shrink normal to the direction of applied strain. Similarly, if a material is compressed, it will expand in the direction orthogonal to the pressure. Few materials, those of negative Poisson ratio, show the opposite behavior. Here, we show an unprecedented feature, a material that expands normal to the direction of stress, regardless if it is strained or compressed. Such behavior, namely half-auxeticity, is demonstrated for a borophene sheet stabilized by decorating Pd atoms. We explore Pd-decorated borophene, identify three stable phases of which one has this peculiar property of half auxeticity. After carefully analyzing stability, mechanical and electronic properties we explore the origin of this very uncommon behavior, and identify it as a structural feature that may also be employed to design further 2D nanomaterials.</p><br>

Negative Poisson ratio in a two-dimensional ‘‘isotropic’’ solid

1989 ◽  
Vol 40 (12) ◽  
pp. 7222-7225 ◽  
Author(s):  
K. W. Wojciechowski ◽  
A. C. Brańka
Keyword(s):  
Poisson Ratio ◽  
Two Dimensional ◽  
Isotropic Solid

scholarly journals Half-Auxeticity and Anisotropic Transport in Pd Decorated Two-Dimensional Boron Sheets

2021 ◽  
Author(s):  
Fengxian Ma ◽  
Yalong Jiao ◽  
Weikang Wu ◽  
Ying Liu ◽  
Shengyuan A. Yang ◽  
...  
Keyword(s):  
Structural Feature ◽  
Electronic Properties ◽  
Poisson Ratio ◽  
Applied Strain ◽  
Two Dimensional ◽  
Peculiar Property ◽  
Opposite Behavior ◽  
2D Nanomaterials ◽  
Boron Sheets ◽  
Anisotropic Transport

<p></p><p>If one strains a material, most materials shrink normal to the direction of applied strain. Similarly, if a material is compressed, it will expand in the direction orthogonal to the pressure. Few materials, those of negative Poisson ratio, show the opposite behavior. Here, we show an unprecedented feature, a material that expands normal to the direction of stress, regardless if it is strained or compressed. Such behavior, namely, half-auxeticity, is demonstrated for a borophene sheet stabilized by decorating Pd atoms. We explore Pd-decorated borophene, identify three stable phases of which one has this peculiar property of half auxeticity. After carefully analyzing stability, mechanical and electronic properties we explore the origin of this very uncommon behavior and identify it as a structural feature that may also be employed to design further 2D nanomaterials.</p><br><p></p>

scholarly journals Half-Auxeticity and Anisotropic Transport in Pd Decorated Two-Dimensional Boron Sheets

2020 ◽  
Author(s):  
Fengxian Ma ◽  
Yalong Jiao ◽  
Weikang Wu ◽  
Ying Liu ◽  
Shengyuan A. Yang ◽  
...  
Keyword(s):  
Structural Feature ◽  
Electronic Properties ◽  
Poisson Ratio ◽  
Applied Strain ◽  
Two Dimensional ◽  
Peculiar Property ◽  
Opposite Behavior ◽  
2D Nanomaterials ◽  
Boron Sheets ◽  
Anisotropic Transport

<p>If one strains a material, most materials shrink normal to the direction of applied strain. Similarly, if a material is compressed, it will expand in the direction orthogonal to the pressure. Few materials, those of negative Poisson ratio, show the opposite behavior. Here, we show an unprecedented feature, a material that expands normal to the direction of stress, regardless if it is strained or compressed. Such behavior, namely half-auxeticity, is demonstrated for a borophene sheet stabilized by decorating Pd atoms. We explore Pd-decorated borophene, identify three stable phases of which one has this peculiar property of half auxeticity. After carefully analyzing stability, mechanical and electronic properties we explore the origin of this very uncommon behavior, and identify it as a structural feature that may also be employed to design further 2D nanomaterials.</p><br>

Cross Relations Between the Planar Elastic Moduli of Perforated Structures

2004 ◽  
Vol 73 (1) ◽  
pp. 163-166 ◽  
Author(s):  
Shmuel Vigdergauz
Keyword(s):  
Complex Variable ◽  
Elastic Moduli ◽  
Poisson Ratio ◽  
Two Dimensional ◽  
Effective Moduli ◽  
Complex Variable Methods ◽  
Effective Compliance ◽  
Practical Accuracy

The effective compliance moduli of a plate with a doubly periodic set of traction-free holes are considered. Attention is drawn to the perturbation form in which they are expressed by applying the complex variable methods in two-dimensional elasticity. This permits one to derive specific dimensionless combinations of the effective moduli, which are independent of the solid Poisson ratio. Using them saves computations of the structure moduli by FEM-like methods and helps one to evaluate their practical accuracy. Thus far, the only result of this kind has been observed numerically by Day, Snyder, Garboczi, and Thorpe (J. Mech. Phys. Solids. 40, pp. 1031–1051, 1992) and later proved by Cherkaev, Lurie, and Milton (Proc. R. Soc. London, Ser. A 458, pp. 519–529, 1992).

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