scholarly journals An Anisotropic Auxetic 2D Metamaterial Based on Sliding Microstructural Mechanism

Materials ◽  
2019 ◽  
Vol 12 (3) ◽  
pp. 429 ◽  
Author(s):  
Teik-Cheng Lim
Keyword(s):  
Poisson’S Ratio ◽  
Nearest Neighbor ◽  
Rapid Change ◽  
Poisson's Ratio ◽  
Rectangular Array ◽  
A Value ◽  
Angular Change ◽  
Unit Cells ◽  
Square Array ◽  
Axes Of Symmetry

A new 2D microstructure is proposed herein in the form of rigid unit cells, each taking the form of a cross with two opposing crossbars forming slots and the other two opposing crossbars forming sliders. The unit cells in the microstructure are arranged in a rectangular array in which the nearest four neighboring cells are rotated by 90° such that a slider in each unit cell is connected to a slot from its nearest neighbor. Using a kinematics approach, the Poisson’s ratio along the axes of symmetry can be obtained, while the off-axis Poisson’s ratio is obtained using Mohr’s circle. In the special case of a square array, the results show that the Poisson’s ratio varies between 0 (for loading parallel to the axes) and −1 (for loading at 45° from the axes). For a rectangular array, the Poisson’s ratio varies from 0 (for loading along the axes) to a value more negative than −1. The obtained results suggest the proposed microstructure is useful for designing materials that permit rapid change in Poisson’s ratio for angular change.

3D-Printed Bio-inspired Zero Poisson’s Ratio Graded Metamaterials with High Energy Absorption Performance

2022 ◽  
Author(s):  
Ramin Hamzehei ◽  
Ali Zolfagharian ◽  
Soheil Dariushi ◽  
Mahdi Bodaghi
Keyword(s):  
Cell Wall ◽  
Energy Absorption ◽  
Poisson’S Ratio ◽  
High Energy ◽  
Absorption Capacity ◽  
Poisson's Ratio ◽  
Base Pairs ◽  
Energy Absorption Capacity ◽  
Static Compression ◽  
Unit Cells

Abstract This study aims at introducing a number of two-dimensional (2D) re-entrant based zero Poisson’s ratio (ZPR) graded metamaterials for energy absorption applications. The metamaterials’ designs are inspired by the 2D image of a DNA molecule. This inspiration indicates how a re-entrant unit cell must be patterned along with the two orthogonal directions to obtain a ZPR behavior. Also, how much metamaterials’ energy absorption capacity can be enhanced by taking slots and horizontal beams into account with the inspiration of the DNA molecule’s base pairs. The ZPR metamaterials comprise multi-stiffness unit cells, so-called soft and stiff re-entrant unit cells. The variability in unit cells’ stiffness is caused by the specific design of the unit cells. A finite element analysis (FEA) is employed to simulate the deformation patterns of the ZPRs. Following that, meta-structures are fabricated with 3D printing of TPU as hyperelastic materials to validate the FEA results. A good correlation is observed between FEA and experimental results. The experimental and numerical results show that due to the presence of multi-stiffness re-entrant unit cells, the deformation mechanisms and the unit cells’ densifications are adjustable under quasi-static compression. Also, the structure designed based on the DNA molecule’s base pairs, so-called structure F''', exhibits the highest energy absorption capacity. Apart from the diversity in metamaterial unit cells’ designs, the effect of multi-thickness cell walls is also evaluated. The results show that the diversity in cell wall thicknesses leads to boosting the energy absorption capacity. In this regard, the energy absorption capacity of structure ‘E’ enhances by up to 33% than that of its counterpart with constant cell wall thicknesses. Finally, a comparison in terms of energy absorption capacity and stability between the newly designed ZPRs, traditional ZPRs, and auxetic metamaterial is performed, approving the superiority of the newly designed ZPR metamaterials over both traditional ZPRs and auxetic metamaterials.

Kinematics of the Morph Origami Pattern and its Hybrid States

2020 ◽  
Author(s):  
Phanisri P. Pratapa ◽  
Ke Liu ◽  
Glaucio H. Paulino
Keyword(s):  
Configuration Space ◽  
Poisson’S Ratio ◽  
Plane Deformation ◽  
Mode Locking ◽  
Unit Cell ◽  
Poisson's Ratio ◽  
Form Complex ◽  
Mountain Valley ◽  
Characteristic Modes ◽  
Unit Cells

Abstract A new degree-four vertex origami, called the Morph pattern, has been recently proposed by the authors (Pratapa, Liu, Paulino, Phy. Rev. Lett. 2019), which exhibits interesting properties such as extreme tunability of Poisson’s ratio from negative infinity to positive infinity, and an ability to transform into hybrid states through rigid origami kinematics. We look at the geometry of the Morph unit cell that can exist in two characteristic modes differing in the mountain/valley assignment of the degree-four vertex and then assemble the unit cells to form complex tessellations that are inter-transformable and exhibit contrasting properties. We present alternative and detailed descriptions to (i) understand how the Morph pattern can smoothly transform across all its configuration states, (ii) characterize the configuration space of the Morph pattern with distinguishing paths for different sets of hybrid states, and (iii) derive the condition for Poisson’s ratio switching and explain the mode-locking phenomenon in the Morph pattern when subjected to in-plane deformation as a result of the inter-play between local and global kinematics.

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 Regularly configured structures with polygonal prisms for three-dimensional auxetic behaviour

2017 ◽  
Vol 473 (2202) ◽  
pp. 20160926 ◽  
Author(s):  
Junhyun Kim ◽  
Dongheok Shin ◽  
Do-Sik Yoo ◽  
Kyoungsik Kim
Keyword(s):  
Poisson’S Ratio ◽  
Three Dimensional ◽  
Unit Cell ◽  
Poisson's Ratio ◽  
Numerical Verification ◽  
Geometric Conditions ◽  
Unit Cells ◽  
Negative Poisson's Ratio ◽  
Poisson's Ratios ◽  
Poisson’S Ratios

We report here structures, constructed with regular polygonal prisms, that exhibit negative Poisson’s ratios. In particular, we show how we can construct such a structure with regular n -gonal prism-shaped unit cells that are again built with regular n -gonal component prisms. First, we show that the only three possible values for n are 3, 4 and 6 and then discuss how we construct the unit cell again with regular n -gonal component prisms. Then, we derive Poisson’s ratio formula for each of the three structures and show, by analysis and numerical verification, that the structures possess negative Poisson’s ratio under certain geometric conditions.

Effect of Variation in Poisson’s Ratio on Plastic Tensile Instability

1967 ◽  
Vol 89 (1) ◽  
pp. 35-39 ◽  
Author(s):  
C. W. Bert ◽  
E. J. Mills ◽  
W. S. Hyler
Keyword(s):  
Classical Theory ◽  
Poisson’S Ratio ◽  
Biaxial Tension ◽  
Tensile Specimen ◽  
Poisson's Ratio ◽  
Uniaxial Tensile ◽  
Plastic Range ◽  
A Value ◽  
Tensile Instability ◽  
Experimental Values

Using the concept of the tensile-instability mechanism which determines the ultimate strength of most of the ductile materials under uniaxial or biaxial tension conditions, two new analyses are carried out. In these are considered an effect previously neglected: Variation of Poisson’s ratio (based on total strain) with strain in the plastic range. One analysis treats a uniaxial tensile specimen, and the predicted results are generally in better agreement with experimental values for seven alloys of aerospace structural importance than the results of classical theory, in which Poisson’s ratio is assumed to remain constant at a value of 1/2 in the plastic range. The other considers a thin-walled spherical shell subject to internal pressure, and the predicted result is again closer to the experimental value than that predicted by classical theory.

scholarly journals In-Plane Behavior of Auxetic Non-Woven Fabric Based on Rotating Square Unit Geometry under Tensile Load

Polymers ◽  
2019 ◽  
Vol 11 (6) ◽  
pp. 1040 ◽  
Author(s):  
Polona Dobnik Dubrovski ◽  
Nejc Novak ◽  
Matej Borovinšek ◽  
Matej Vesenjak ◽  
Zoran Ren
Keyword(s):  
Poisson’S Ratio ◽  
Testing Machine ◽  
Tensile Load ◽  
Woven Fabric ◽  
Poisson's Ratio ◽  
Plane Rotation ◽  
High Definition ◽  
Equal Distribution ◽  
Out Of Plane ◽  
Unit Cells

This paper reports the auxetic behavior of modified conventional non-woven fabric. The auxetic behavior of fabric was achieved by forming rotating square unit geometry with a highly ordered pattern of slits by laser cutting. Two commercial needle-punched non-woven fabric used as lining and the reinforcement fabric for the footwear industry were investigated. The influence of two rotating square unit sizes was analyzed for each fabric. The original and modified fabric samples were subjected to quasi-static tensile load by using the Tinius Olsen testing machine to observe the in-plane mechanical properties and deformation behavior of tested samples. The tests were recorded with a full high-definition (HD) digital camera and the video recognition technique was applied to determine the Poisson’s ratio evolution during testing. The results show that the modified samples exhibit a much lower breaking force due to induced slits, which in turn limits the application of such modified fabric to low tensile loads. The samples with smaller rotating cell sizes exhibit the highest negative Poisson’s ratio during tensile loading through the entire longitudinal strain range until rupture. Non-woven fabric with equal distribution and orientation of fibers in both directions offer better auxetic response with a smaller out-of-plane rotation of rotating unit cells. The out-of-plane rotation of unit cells in non-homogenous samples is higher in machine direction.

scholarly journals Dynamic Measurements for Determining Poisson’s Ratio of Young Concrete

2018 ◽  
Vol 58 (1) ◽  
pp. 95-106 ◽  
Author(s):  
Lamis Ahmed
Keyword(s):  
Poisson’S Ratio ◽  
Resonance Method ◽  
Poisson's Ratio ◽  
Early Age ◽  
A Value ◽  
Young Concrete ◽  
Impact Resonance ◽  
Set Up ◽  
The Impact ◽  
Non Destructive

Abstract Knowledge of the elastic properties of concrete at early age is often a pre-requisite for numerical calculations. This paper discusses the use of a laboratory technique for determining Poisson’s ratio at early concrete age. A non-destructive test set-up using the impact resonance method has been tested and evaluated. With the method, it has been possible to obtain results already at 7 hours of concrete age. Poisson’s ratio is found to decrease sharply during the first 24 hours to reach a value of 0.08 and then increase to approximately 0.15 after seven days.

SECONDARY ARRIVALS IN A WELL VELOCITY SURVEY

Geophysics ◽  
1943 ◽  
Vol 8 (3) ◽  
pp. 290-296
Author(s):  
C. W. Horton
Keyword(s):  
Bulk Modulus ◽  
Poisson’S Ratio ◽  
Poisson's Ratio ◽  
Secondary Wave ◽  
Transverse Waves ◽  
A Value

Seismograms obtained in a well survey of the Shell‐Longleaf Lumber Co. #1, Vernon Parish, Louisiana, showed well‐developed secondary arrivals which satisfied a velocity formula V = (2000+0.27Z) feet per second. If these arrivals are assumed to be transverse waves, a value of 0.43 for Poisson’s ratio is obtained. On this same assumption, values of the modulus of rigidity and bulk modulus are computed for various depths. It is shown that the velocity of the secondary wave does not satisfy the equation developed by Lamb for thick‐walled tube waves.

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