scholarly journals The General Relationships Between the Elastic Constants of Isotropic Materials in n Dimensions

1958 ◽  
Vol 11 (2) ◽  
pp. 154 ◽  
Author(s):  
NW Tschoegl
Keyword(s):  
Elastic Constants ◽  
Poisson’S Ratio ◽  
Three Dimensional ◽  
Poisson's Ratio ◽  
Isotropic Materials ◽  
Monomolecular Films

The relationships between the elastic constants of homogeneous isotropic materials in n dimension are derived and are shown to depend on n. The maximal value of the generalized Poisson's ratio is 1/(n?1). The n-dimensional formulae reproduce the well-known three-dimensional relations for n=3, while n=2 produces the relations, appropriate for monomolecular films. The correct degeneration is shown for n= 1.

Micromechanical Aspects of Isotropic Granular Assemblies With Linear Contact Interactions

1988 ◽  
Vol 55 (1) ◽  
pp. 17-23 ◽  
Author(s):  
R. J. Bathurst ◽  
L. Rothenburg
Keyword(s):  
Numerical Simulations ◽  
Contact Force ◽  
Elastic Constants ◽  
Poisson’S Ratio ◽  
Three Dimensional ◽  
Poisson's Ratio ◽  
Spherical Particles ◽  
Two Dimensional ◽  
Normal Contact ◽  
Granular Assemblies

The paper presents a micromechanical analysis of plane granular assemblies of discs with a range of diameters, and interacting according to linear contact force-interparticle compliance relationships. Contacts are assumed to be fixed and indestructible. Macroscopically, the system is described in terms of a two-dimensional analogue of generalized Hooke’s law. Explicit expressions for elastic constants in terms of microstructure are derived for dense isotropic assemblies. It is shown that Poisson’s ratio for dense systems depends on the ratio of tangential to normal contact stiffnesses. The derived expression for Poisson’s ratio is verified by numerically simulating plane assemblies comprising 1000 particles. The effect of density on Poisson’s ratio is investigated using numerical simulations. The theory of dense plane systems is extended to dense three-dimensional systems comprising spheres. Finally, it is shown that Poisson’s result ν=1/4 is recovered for spherical particles with central interactions.

scholarly journals Direct Determination of Dynamic Elastic Modulus and Poisson’s Ratio of Timoshenko Rods

Vibration ◽  
2019 ◽  
Vol 2 (1) ◽  
pp. 157-173 ◽  
Author(s):  
Guadalupe Leon ◽  
Hung-Liang Chen
Keyword(s):  
Exact Solution ◽  
Finite Element ◽  
Elastic Constants ◽  
Frequency Ratio ◽  
Poisson’S Ratio ◽  
Direct Determination ◽  
Poisson's Ratio ◽  
Torsional Mode ◽  
Bending Mode ◽  
Resonance Frequencies

In this paper, the exact solution of the Timoshenko circular beam vibration frequency equation under free-free boundary conditions was determined with an accurate shear shape factor. The exact solution was compared with a 3-D finite element calculation using the ABAQUS program, and the difference between the exact solution and the 3-D finite element method (FEM) was within 0.15% for both the transverse and torsional modes. Furthermore, relationships between the resonance frequencies and Poisson’s ratio were proposed that can directly determine the elastic constants. The frequency ratio between the 1st bending mode and the 1st torsional mode, or the frequency ratio between the 1st bending mode and the 2nd bending mode for any rod with a length-to-diameter ratio, L/D ≥ 2 can be directly estimated. The proposed equations were used to verify the elastic constants of a steel rod with less than 0.36% error percentage. The transverse and torsional frequencies of concrete, aluminum, and steel rods were tested. Results show that using the equations proposed in this study, the Young’s modulus and Poisson’s ratio of a rod can be determined from the measured frequency ratio quickly and efficiently.

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.

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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