Effect of Poisson’s Ratio on Three-Dimensional Stress Distribution

2008 ◽  
Vol 76 (1) ◽  
Author(s):  
Z. Abdulaliyev ◽  
S. Ataoglu
Keyword(s):  
Stress Distribution ◽  
Linear Elasticity ◽  
Poisson’S Ratio ◽  
Three Dimensional ◽  
Strain Analysis ◽  
Experimental Methods ◽  
The Body ◽  
Poisson's Ratio ◽  
Stress Components ◽  
Simply Connected

An examination of the effect of Poisson’s ratio on stress distribution is important to interpret the results of a stress-strain analysis by using experimental methods because the material of the model frequently has a different Poisson’s ratio from that of the prototype. In linear elasticity, the effect of Poisson’s ratio on three-dimensional stress distribution is theoretically explained for simply connected bodies by using static methods in this study. It is proven that the stress components are independent from Poisson’s ratio in sections of the body where the stress components arising are in equilibrium only with surface tractions. This result is useful in interpreting three-dimensional photoelasticity and other experiments and even in guiding the design.

scholarly journals The Multidirectional Auxeticity and Negative Linear Compressibility of a 3D Mechanical Metamaterial

Materials ◽  
2020 ◽  
Vol 13 (9) ◽  
pp. 2193 ◽  
Author(s):  
Krzysztof K. Dudek ◽  
Daphne Attard ◽  
Ruben Gatt ◽  
James N. Grima-Cornish ◽  
Joseph N. Grima
Keyword(s):  
Theoretical Model ◽  
Poisson’S Ratio ◽  
Three Dimensional ◽  
Poisson's Ratio ◽  
Negative Poisson’S Ratio ◽  
Structural Units ◽  
Loading Direction ◽  
Arbitrary Loading ◽  
Negative Poisson's Ratio ◽  
Linear Compressibility

In this work, through the use of a theoretical model, we analyse the potential of a specific three-dimensional mechanical metamaterial composed of arrowhead-like structural units to exhibit a negative Poisson’s ratio for an arbitrary loading direction. Said analysis allows us to assess its suitability for use in applications where materials must be able to respond in a desired manner to a stimulus applied in multiple directions. As a result of our studies, we show that the analysed system is capable of exhibiting auxetic behaviour for a broad range of loading directions, with isotropic behaviour being shown in some planes. In addition to that, we show that there are also certain loading directions in which the system manifests negative linear compressibility. This enhances its versatility and suitability for a number of applications where materials exhibiting auxetic behaviour or negative linear compressibility are normally implemented.

Three-dimensional porous borocarbonitride BC2N with negative Poisson's ratio

2020 ◽  
Vol 8 (44) ◽  
pp. 15771-15777
Author(s):  
Kashif Hussain ◽  
Umer Younis ◽  
Imran Muhammad ◽  
Yu Qie ◽  
Yaguang Guo ◽  
...  
Keyword(s):  
Poisson’S Ratio ◽  
Three Dimensional ◽  
Poisson's Ratio ◽  
Negative Poisson’S Ratio ◽  
Negative Poisson's Ratio ◽  
Recent Synthesis

Motivated by the recent synthesis of three-dimensional (3D) porous borocarbonitride (Angew. Chem., Int. Ed., 2019, 58, 6033–6037), we propose a porous 3D-BC2N structure composed of BC2N nanoribbons.

Auxetic deformation of the weft-knitted Miura-ori fold

2019 ◽  
Vol 90 (5-6) ◽  
pp. 617-630
Author(s):  
Kun Luan ◽  
Andre West ◽  
Emiel DenHartog ◽  
Marian McCord
Keyword(s):  
Deformation Mechanism ◽  
Poisson’S Ratio ◽  
Three Dimensional ◽  
Poisson's Ratio ◽  
Dimensional Structure ◽  
Damping Capacity ◽  
Analysis Model ◽  
Element Analysis ◽  
Specific Direction ◽  
Application Fields

Negative Poisson’s ratio (NPR) material with unique geometry is rare in nature and has an auxetic response under strain in a specific direction. With this unique property, this type of material is significantly promising in many specific application fields. The curling structure commonly exists in knitted products due to the unbalanced force inside a knit loop. Thus, knitted fabric is an ideal candidate to mimic natural NPR materials, since it possesses such an inherent curly configuration and the flexibility to design and process. In this work, a weft-knitted Miura-ori fold (WMF) fabric was produced that creates a self-folding three-dimensional structure with NPR performance. Also, a finite element analysis model was developed to simulate the structural auxetic response to understand the deformation mechanism of hierarchical thread-based auxetic fabrics. The simulated strain–force curves of four WMF fabrics quantitatively agree with our experimental results. The auxetic morphologies, Poisson’s ratio and damping capacity were discussed, revealing the deformation mechanism of the WMF fabrics. This study thus provides a fundamental framework for mechanical-stimulating textiles. The developed NPR knitted fabrics have a high potential to be employed in areas of tissue engineering, such as artificial blood vessels and artificial folding mucosa.

Settlement of a strip footing on a confined clay layer

1983 ◽  
Vol 20 (3) ◽  
pp. 535-542
Author(s):  
Brian B. Taylor ◽  
Elmer L. Matyas
Keyword(s):  
Stress Distribution ◽  
Plane Strain ◽  
Poisson’S Ratio ◽  
Ground Surface ◽  
Finite Depth ◽  
Strip Footing ◽  
Poisson's Ratio ◽  
Clay Layer ◽  
Line Load ◽  
Settlement Analysis

A procedure is described that permits an estimation of either consolidation or immediate settlements of a uniformly loaded, flexible strip footing founded below the ground surface. The soil above the base of the footing is sand, and the soil below the base consists of clay, which extends to a finite depth. The procedure is based on a solution of Kelvin's equations for a line load acting within an infinite solid. Charts are presented which permit an estimate of settlement for various compression moduli, Poisson's ratio, and clay thickness.The proposed method predicts consolidation settlements that are generally slightly greater than those predicted from Boussinesq theory. Consolidation settlements increase as Poisson's ratio increases. Immediate settlements are slightly greater than those reported previously. Keywords: consolidation, elasticity, footings, plane strain, settlement analysis, stress distribution.

Effective properties of composite materials containing voids

1993 ◽  
Vol 440 (1909) ◽  
pp. 461-473 ◽  
Keyword(s):  
Young’S Modulus ◽  
Poisson’S Ratio ◽  
Effective Properties ◽  
Young's Modulus ◽  
Matrix Material ◽  
Practical Importance ◽  
Three Dimensional ◽  
Poisson's Ratio ◽  
Two Dimensional ◽  
Isotropic Composite

Recent results of theoretical and practical importance prove that the two-dimensional (in-plane) effective (average) Young’s modulus for an isotropic elastic material containing voids is independent of the Poisson’s ratio of the matrix material. This result is true regardless of the shape and morphology of the voids so long as isotropy is maintained. The present work uses this proof to obtain explicit analytical forms for the effective Young’s modulus property, forms which simplify greatly because of this characteristic. In some cases, the optimal morphology for the voids can be identified, giving the shapes of the voids, at fixed volume, that maximize the effective Young’s modulus in the two-dimensional situation. Recognizing that two-dimensional isotropy is a subset of three-dimensional transversely isotropic media, it is shown in this more general case that three of the five properties are independent of Poisson’s ratio, leaving only two that depend upon it. For three-dimensionally isotropic composite media containing voids, it is shown that a somewhat comparable situation exists whereby the three-dimensional Young’s modulus is insensitive to variations in Poisson’s ratio, v m , over the range 0 ≤ v m ≤ ½, although the same is not true for negative values of v m . This further extends the practical usefulness of the two-dimensional result to three-dimensional conditions for realistic values of v m .

Chiral three-dimensional lattices with tunable Poisson’s ratio

2016 ◽  
Vol 25 (5) ◽  
pp. 054005 ◽  
Author(s):  
Chan Soo Ha ◽  
Michael E Plesha ◽  
Roderic S Lakes
Keyword(s):  
Poisson’S Ratio ◽  
Three Dimensional ◽  
Poisson's Ratio
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