An optimization approach to design deformation patterns in perforated mechanical metamaterials using distributions of Poisson’s ratio-based unit cells

2021 ◽  
pp. 115015
Author(s):  
Jianfei Yao ◽  
Yongfei Su ◽  
Fabrizio Scarpa ◽  
Yan Li
Keyword(s):  
Poisson’S Ratio ◽  
Poisson's Ratio ◽  
Optimization Approach ◽  
Mechanical Metamaterials ◽  
Unit Cells ◽  
Deformation Patterns

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.

scholarly journals Auxetic metamaterials from disordered networks

2018 ◽  
Vol 115 (7) ◽  
pp. E1384-E1390 ◽  
Author(s):  
Daniel R. Reid ◽  
Nidhi Pashine ◽  
Justin M. Wozniak ◽  
Heinrich M. Jaeger ◽  
Andrea J. Liu ◽  
...  
Keyword(s):  
Poisson’S Ratio ◽  
Theoretical Work ◽  
Realistic Model ◽  
Poisson's Ratio ◽  
Local Responses ◽  
Mechanical Responses ◽  
Mechanical Metamaterials ◽  
Recent Theoretical Work ◽  
Pruning Strategy ◽  
Disordered Networks

Recent theoretical work suggests that systematic pruning of disordered networks consisting of nodes connected by springs can lead to materials that exhibit a host of unusual mechanical properties. In particular, global properties such as Poisson’s ratio or local responses related to deformation can be precisely altered. Tunable mechanical responses would be useful in areas ranging from impact mitigation to robotics and, more generally, for creation of metamaterials with engineered properties. However, experimental attempts to create auxetic materials based on pruning-based theoretical ideas have not been successful. Here we introduce a more realistic model of the networks, which incorporates angle-bending forces and the appropriate experimental boundary conditions. A sequential pruning strategy of select bonds in this model is then devised and implemented that enables engineering of specific mechanical behaviors upon deformation, both in the linear and in the nonlinear regimes. In particular, it is shown that Poisson’s ratio can be tuned to arbitrary values. The model and concepts discussed here are validated by preparing physical realizations of the networks designed in this manner, which are produced by laser cutting 2D sheets and are found to behave as predicted. Furthermore, by relying on optimization algorithms, we exploit the networks’ susceptibility to tuning to design networks that possess a distribution of stiffer and more compliant bonds and whose auxetic behavior is even greater than that of homogeneous networks. Taken together, the findings reported here serve to establish that pruned networks represent a promising platform for the creation of unique mechanical 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 Double-Negative Mechanical Metamaterials Displaying Simultaneous Negative Stiffness and Negative Poisson's Ratio Properties

2016 ◽  
Vol 28 (46) ◽  
pp. 10116-10116 ◽  
Author(s):  
Trishan A. M. Hewage ◽  
Kim L. Alderson ◽  
Andrew Alderson ◽  
Fabrizio Scarpa
Keyword(s):  
Poisson’S Ratio ◽  
Negative Stiffness ◽  
Poisson's Ratio ◽  
Double Negative ◽  
Negative Poisson’S Ratio ◽  
Mechanical Metamaterials ◽  
Negative Poisson's Ratio

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.

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.

Qualitative Analysis and Design of Mechanical Metamaterials

2017 ◽  
Author(s):  
Sreekalyan Patiballa ◽  
Girish Krishnan
Keyword(s):  
Qualitative Analysis ◽  
Poisson’S Ratio ◽  
Compliant Mechanisms ◽  
Flow Behavior ◽  
Load Flow ◽  
Poisson's Ratio ◽  
Negative Poisson’S Ratio ◽  
Analysis And Design ◽  
Mechanical Metamaterials ◽  
Negative Poisson's Ratio

This paper presents a new mechanics-based framework for the qualitative analysis and conceptual design of mechanical meta-materials. The methodology is inspired by recent advances in the insightful synthesis of compliant mechanisms by visualizing a kinetostatic field of forces that flow through the mechanism geometry. The framework relates load flow behavior in the microstructure geometry to the global behavior of the materials, such as auxetic (negative poisson’s ratio), high bulk modulus, and high shear modulus. This understanding is used to synthesize and demonstrate novel planar microstructures that exhibit negative poisson’s ratio behavior. Furthermore, the paper identifies three unique classes of qualitative design problems for planar mechanical microstructures that can be potentially solved using this framework.

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.

scholarly journals Auxetic mechanical metamaterials

RSC Advances ◽  
2017 ◽  
Vol 7 (9) ◽  
pp. 5111-5129 ◽  
Author(s):  
H. M. A. Kolken ◽  
A. A. Zadpoor
Keyword(s):  
Young’S Modulus ◽  
Poisson’S Ratio ◽  
Young's Modulus ◽  
Poisson's Ratio ◽  
Property Relationship ◽  
Mechanical Metamaterials

We review the topology–property relationship and the spread of Young's modulus–Poisson's ratio duos in three main classes of auxetic metamaterials.

scholarly journals Idealized 3D Auxetic Mechanical Metamaterial: An Analytical, Numerical, and Experimental Study

Materials ◽  
2021 ◽  
Vol 14 (4) ◽  
pp. 993
Author(s):  
Naeim Ghavidelnia ◽  
Mahdi Bodaghi ◽  
Reza Hedayati
Keyword(s):  
Mechanical Properties ◽  
Finite Element ◽  
Poisson’S Ratio ◽  
Element Model ◽  
Industrial Applications ◽  
Poisson's Ratio ◽  
Geometrical Parameters ◽  
Mechanical Metamaterials ◽  
Strength And Stiffness ◽  
The One

Mechanical metamaterials are man-made rationally-designed structures that present unprecedented mechanical properties not found in nature. One of the most well-known mechanical metamaterials is auxetics, which demonstrates negative Poisson’s ratio (NPR) behavior that is very beneficial in several industrial applications. In this study, a specific type of auxetic metamaterial structure namely idealized 3D re-entrant structure is studied analytically, numerically, and experimentally. The noted structure is constructed of three types of struts—one loaded purely axially and two loaded simultaneously flexurally and axially, which are inclined and are spatially defined by angles θ and φ. Analytical relationships for elastic modulus, yield stress, and Poisson’s ratio of the 3D re-entrant unit cell are derived based on two well-known beam theories namely Euler–Bernoulli and Timoshenko. Moreover, two finite element approaches one based on beam elements and one based on volumetric elements are implemented. Furthermore, several specimens are additively manufactured (3D printed) and tested under compression. The analytical results had good agreement with the experimental results on the one hand and the volumetric finite element model results on the other hand. Moreover, the effect of various geometrical parameters on the mechanical properties of the structure was studied, and the results demonstrated that angle θ (related to tension-dominated struts) has the highest influence on the sign of Poisson’s ratio and its extent, while angle φ (related to compression-dominated struts) has the lowest influence on the Poisson’s ratio. Nevertheless, the compression-dominated struts (defined by angle φ) provide strength and stiffness for the structure. The results also demonstrated that the structure could have zero Poisson’s ratio for a specific range of θ and φ angles. Finally, a lightened 3D re-entrant structure is introduced, and its results are compared to those of the idealized 3D re-entrant structure.

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