Tunable Poisson's Ratio Research Articles

Shape Morphing of Re‐Entrant Honeycomb Metamaterials for Linear Auxetic Behaviors

A re‐entrant honeycomb structure stands out as one of the most prevalent auxetic metamaterials, characterized by its negative Poisson's ratio. While re‐entrant auxetic structures are capable of achieving tunable Poisson's ratios, they tend to vary with the magnitude of applied strain, thereby exhibiting nonlinear auxetic behaviors. This study proposes a novel re‐entrant structure aimed at achieving linear auxetic behavior by mathematically modifying the shape of a re‐entrant cell. To achieve this objective, a sigmoid‐based shape morphing function is introduced to modify the morphology of the hinge connections within the re‐entrant honeycomb cell. The deformation behavior of the shape‐morphed re‐entrant cell is investigated using finite element analysis (FEA), with variations in the morphing parameter. Two FEA models, namely the unconstrained and constrained models, are developed for fundamental analysis of cell deformation and experimental validation, respectively. Compared to the pure re‐entrant honeycomb structure, the proposed shape morphing reduces the relative variation of Poisson's ratio by 70%, while maintaining its magnitude higher than 1.0. This achievement of linear auxetics with a high Poisson's ratio has the potential to broaden the applications of the proposed auxetic structures to various functional components, including sensors with high linear sensitivity and soft actuators with tunable deformation characteristics.

Optimization of vibration and sound insulation in GPLRC honeycomb structures based on circle chaos mapping and Levy flight-enhanced YDSE with constraints

Utilizing the first-order shear deformation theory (FSDT) and Hamilton's principle, dynamic equations for tunable Poisson's ratio metamaterial honeycomb sandwich panels have been derived. These panels include petal-shaped, star-shaped, and butterfly-shaped designs. The acoustic response of these panels when subjected to plane harmonic sound waves has been formulated, treating them as fluid-structure interaction systems. To enhance the structural vibration and sound propagation attributes, traditional metallic aluminum has been replaced with graphene platelet-reinforced composites (GPLRC). Through computational analysis and finite element simulation data, the natural frequencies and sound transmission loss (STL) characteristics of the panels have been determined. An improved heuristic algorithm called the circle chaos mapping and levy flight enhanced Young's double-slit experiment optimizer (CLYDSE) has been introduced to optimize their vibrational and acoustic properties. This algorithm builds upon Young's double-slit experiment optimizer (YDSE) by incorporating circle chaos mapping for initializing a monochromatic light source and utilizing the levy flight principle for more accurate search results. These enhancements allow the CLYDSE algorithm to avoid local optima and improve convergence velocity. A penalty function method was employed to establish mass and equivalent elastic modulus as optimization constraints, aiming to achieve superior specific stiffness. Finally, structural optimization using the proposed CLYDSE method was conducted to enhance the vibrational and acoustic performance of the three types of honeycomb sandwich panels. The results validate the effectiveness of the theoretical model in predicting vibration and acoustic response, as well as the improved performance of the CLYDSE algorithm in terms of convergence velocity and optimization accuracy. This demonstrates the algorithm's efficacy in refining the acoustic and vibrational qualities of these advanced honeycomb structures.

A novel 3D tetra-missing rib auxetic meta-structure with tension/compression-twisting coupling effect

Three-dimensional (3D) tunable auxetic meta-structures find widespread applications across various domains. Nevertheless, the existing meta-structures have constrained tunability in their elastic constants, preventing the simultaneous attainment of high stiffness and a prominent auxetic effect. Based on a previously designed 2D tetra-missing rib (TMR) auxetic meta-structure, a novel 3D TMR honeycomb meta-structure was proposed with a tension/compression-twisting coupling effect in this work. To investigate the underlying deformation mechanism of the proposed design, a mechanics model of the elastic constants is formulated by adopting an energy-based approach. The accuracy of the theoretical formulations was then validated both experimentally and numerically. The results indicate the proposed design concurrently exhibits high stiffness and a noticeable auxetic effect. Moreover, tunable Poisson's ratios and elastic modulus within a relative wide range can be obtained by adjusting the geometrical parameters, enabling it adoptable for precise requirements in practical applications.

Vibro-acoustic response and sound transmission loss of sandwich plates with tunable Poisson's ratio core in a hygrothermal environment

In this study, vibro-acoustic response and sound transmission loss of sandwich plates with tunable Poisson's ratio (TPR) core in a hygrothermal environment are investigated. The sandwich plate is taken as a moderately thick plate and various plate theories are used to examine the vibroacoustic behavior. First, the equations of motion of a sandwich plate in the hygrothermal environment are derived based on Hamilton's principle. Then, the solution to free vibration for a simply supported sandwich plate is presented. Next, we obtain the sound power level (SPL) for the point harmonic force exerted on the surface of the sandwich plate using the Rayleigh integral and the sound transmission loss (STL) as the harmonic sound wave is incident on the plate surface. Finally, numerical examples are conducted and discussed. The effects of the core-to-thickness ratio, plate theories, parameters of the TPR core, hygrothermal environment, and incident elevation angle on the SPL and STL of the sandwich plate are analyzed. This study will contribute to the design and manufacturing of lightweight structures in the aviation industry.

Study on design and impact energy absorption of Voronoi porous structure with tunable Poisson's ratio

As the inner core of crash box, the porous structure could cushion impact load through its own deformation. The aims of this study were to propose a series of Voronoi porous structures with tunable Poisson's ratio (VP-VPS) by using the periodic array of unit cells based on Voronoi-Tessellation and to develop crash boxes filled with porous structures for strong crashworthiness and high energy absorption. VP-VPS structures through the periodic arrays of unit cells were constructed according to 4 independent unit cell design factors. The quasi-static and dynamic compressive mechanical responses of VP-VPS structures prepared by selective laser melting (SLM) were studied through the combinations of mechanical test and simulation. Relationships between VP-VPS unit cell design factors and mechanical properties of structures were determined by establishing regression equations using the response surface method (RSM). Finally, the energy absorption of new crash boxes filled with VP-VPS structures was investigated through simulation. Results showed that VP-VPS structures had high load-bearing capacities and energy absorption under quasi-static and dynamic compressive conditions. Regression equations based on RSM could well predict mechanical properties of structures. The mechanical properties of VP-VPS structures were enhanced with the increase of global strain rate, which showed different deformation modes at low and high global strain rates. Compared with typical crash boxes filled with negative Poisson's ratio (NPR) inner cores, new type VP-VPS crash boxes had stronger impact resistance and higher energy absorption. This investigation provided a feasible design solution and theoretical basis for the construction and engineering application of impact resistance protective structures.

4D Printing of Chiral Mechanical Metamaterials with Modular Programmability using Shape Memory Polymer

AbstractThe rational design of mechanical metamaterials endows them with unusual properties inaccessible by conventional materials. In this study, compression–twist coupling building blocks with embedded chirality are fabricated by multimaterial 4D printing of shape memory polymers. Each chiral unit can be programmed individually by mechanical compression at a selected high temperature, whose temporary shape is self‐maintained at the reduced temperature when the load is removed. With these building blocks, lattice‐like architectures can be constructed in planar and layer‐to‐layer assemblies. Such modular design overcomes the limitation of conventional material arrangement by allowing on‐demand re‐programmability of chirality‐defined structural heterogeneity. Using this strategy, metamaterials with tunable Poisson's ratio and shape‐morphing metastructures are developed by harnessing the cooperative deformation of spatially heterogenous tessellation that undergoes local shrinkage or expansion, depending on the encoded Poisson response. An untethered multimodal soft gripper is assembled by chiral metastructures with distinct morphing modes, capable of unscrewing up a bottle cap attributed by the programmed functionality at module‐level. The present modular chiral metamaterials with embedded chirality and flexible deployability may promote the applications of mechanical metamaterials in active shape‐morphing structures and functional soft machines.

Experimental and numerical analysis of a bolted reinforced honeycomb with tunable Poisson's ratio

The use of large honeycomb structures is becoming increasingly widespread, with many specialized honeycomb structures being produced through additive manufacturing and laser cutting technologies. However, the high manufacturing costs and low efficiency associated with these methods limit their applicability. In this paper, reinforced honeycombs with a total length of nearly 1 m were assembled using bolts. The effects of relative thickness and corrugated plate angle on Poisson's ratio and mechanical properties were investigated both experimentally and numerically. Additionally, three design strategies - layered, internal and external, and space filling - were adopted to further regulate Poisson's ratio. The results show that relative thickness, angle, and the aforementioned design strategies can all be used to regulate Poisson's ratio. As the thickness of the reinforced plate increases, energy absorption (EA) increases, but specific energy absorption (SEA) decreases. The reinforced honeycomb structure (RHC) exhibits the best energy absorption and SEA at a 60° angle. Through hierarchical, internal, and external designs, this paper shows that the reinforced honeycomb structure with one layer of reinforcement plus one layer of non-reinforcement (1+1-RHC) has the largest negative Poisson's ratio effect. Furthermore, the transition structure between RHC and 1+1-RHC is studied through unreinforced space filling design. The fabrication method presented here promises low-cost and large-scale fabrication with the ability to program Poisson's ratio, making it suitable for applications in protective gear and smart energy absorbing devices.

Advanced Fabrication of Mechanical Metamaterials Based on Micro/Nanoscale Technology

In recent years, mechanical metamaterials have shown good mechanical properties such as ultralightness, programmable stiffness, and tunable Poisson's ratio through clever structural design of microstructures. Micro/nanotechnology has been used to ensure mechanical metamaterials’ fabrication quality and performance for use as structural substrates in multifunctional applications. Mechanical metamaterials are intentionally engineered with periodic microstructures in diverse shapes, allowing for the creation of complex structural substrates. However, this sophisticated design poses significant challenges in the fabrication process, particularly at the micro/nanoscale level, where current technology hinders mechanical metamaterials’ performance improvement and function realization. This review explores the fabrication processes of mechanical metamaterials using micro/nanotechnology and showcase recent progress and future trends. Particular attention is given to recent development, challenges, and future trends in advanced fabrication technologies for mechanical metamaterials. This survey aims to explain why mechanical metamaterials have significant benefits and are well‐suited as structural substrates for multifunctional applications, what advanced fabrication technologies at the micro/nanoscale have been introduced to prepare mechanical metamaterials and how to overcome manufacturing technology bottlenecks of mechanical metamaterials in terms of synthesis, materials, and design method.

A novel compression-torsion coupling metamaterial with tunable Poisson's ratio

In this study, a three-dimensional compression-torsion coupled negative Poisson structure was designed by combining the perforated plate with the inclined rod out of the plane. This structure can realize the selection of the positive and negative Poisson's ratio of the three-dimensional structure by changing the direction of the inclined rod. The absolute value of the Poisson's ratio of the two structures is close to the same but the positive and negative are opposite. Both structures maintain close to the same stress–strain curve. This structural characteristic can realize the selection of an ideal Poisson's ratio without changing the mechanical properties of the structure. Two 3D compression-torsion coupling structures were printed using metal 3D printing technology, and compression tests were carried out in the axial and transverse directions. Then, parametric analysis was carried out under axial compression, including energy absorption and specific energy absorption analyses. The results show that the experimental and finite element results are in good agreement and the finite element simulation is accurate. The Poisson's ratio of this negative Poisson's ratio metamaterial is selectable under both axial and lateral pressure conditions, so the structure has the excellent characteristics of selectable Poisson's ratio in three mutually perpendicular axes. The results show that the absolute value of Poisson's ratio exceeds 1 when the structure is under lateral compression, which indicates that the lateral deformation rate of the structure is greater than the axial deformation rate under this compression form. Finally, two tubular structures with different arrangements were designed by using these two structural cells, and the ball passing test was carried out. The results show that different arrangements will cause the balls to experience different resistances when passing through different positions in the tube. Research shows that the structure has potential applications in energy absorption, biomechanical devices, smart actuators, and devices with special requirements for Poisson's ratio.

Improved lightweight corrugated network design to auxetic perforated metamaterial

Auxetic metamaterials with peanut-shaped perforations are superior for durable morphing control applications due to its extremely low stress concentration level and controllable auxetic capability. However, there are some issues to be concerned for such metamaterials with complex cellular features, including (1) improving structure topology for higher material efficiency, (2) tunable Poisson's ratio from positive to negative, (3) characterization of full elastic properties. To this end, an improved lightweight design with orthogonal corrugated beams is proposed in this study to approximate the perforated auxetic structure and then its full anisotropic elastic constants are characterized by a distinctive computational homogenization model based on the eigenfunction expansion variational theory with simple implementation technique of periodic displacement constraints. The numerical model is verified by the experimental tests of three specimens with different geometrical topologies. Subsequently, the dependence of structural elastic responses on the microstructural configuration is highlighted towards an elevated understanding of cell-structure-property relationship. It is demonstrated that the local in-plane rotation of interconnected regions in unit cell under uniaxial loading contributes to the structural auxetic behavior. Also, it is feasible to achieve tailorable mechanical properties through flexible microstructural adjustment and a design criterion of the crucial zero Poisson's ratio is given by a polynomial in terms of the normalized amplitude and thickness of the curved beam. The results pave a way to the design and analysis of novel metamaterials with tunable mechanical properties.

Designing Amorphous Networks with Adjustable Poisson Ratio from a Simple Triangular Lattice

Materials with a negative and tunable Poisson ratio have great potential applications in fracture resistance and energy absorption. However, one material usually exhibits one specific Poisson ratio and a systematic tuning is highly desired. In this study, we design disordered networks with a wide tunable range of the Poisson ratio based on triangular analysis. By distorting the equilateral triangle lattice, the Poisson ratio can be systematically decreased due to the large area change in highly nonequilateral triangles. Analysis further shows that in a nonequilateral triangle, bonds with different lengths play distinct roles: the removal of short bonds can decrease the Poisson ratio, while the removal of long bonds does the opposite. Thus a negative Poisson ratio can be achieved by removing a small amount of short bonds. Moreover, such networks can serve as unit cells to build larger systems with a similar performance. Such auxetic networks are further experimentally realized in both spring and three-dimensionally printed systems, demonstrating the general validity of our analysis and its possible applications in building practical systems.

Design, mechanical properties and optimization of lattice structures with hollow prismatic struts

Lattice structures with hollow struts exhibit superior mechanical properties as compared to solid ones. In this study, we introduce a new type of body-centered cubic (BCC) lattice, consisting of hollow prismatic struts with mechanical properties defined by an inner hollow parameter. The mechanical properties and deformation behavior of the BCC lattice structures with different inner hollow parameters are investigated under periodic boundary conditions. It is shown that the elastic modulus of the hollow-strut BCC lattice structure improves significantly by 598%-1460% and their deformation mechanism gradually changes from bending-dominated to stretching-dominated, when the inner hollow size increases. In contrast, there are little influences on shear deformation. Interestingly, tunable Poisson's ratio and isotropic elasticity can be achieved by adjusting the inner hollow size. In addition, the BCC lattice structures with different inner hollow parameters are fabricated by digital light processing for compression tests, and the experimental results are in good agreement with the simulation with relative errors of less than 14.6%. Finally, a high-fidelity interpolation model is employed to describe the effective elastic matrix of lattice structures, and a new optimization framework is proposed to simultaneously optimize the distribution of the volume fraction and inner hollow size of hollow-strut lattice structures. This proposed approach significantly improves the stiffness (compliance decreased by 15.8% to 53.1%) of the cantilever beam as compared to traditional optimal designs, demonstrating the potential application of the proposed approach in lightweight designs.

A novel programmable composite metamaterial with tunable Poisson's ratio and bandgap based on multi-stable switching

Metamaterial is a new type of structure constructed by artificially designed geometries and possessing extraordinary physical properties. However, the functions of metamaterial are currently difficult to be adjusted and switched. A novel type of multi-pattern composite metamaterial with tunable Poisson's ratio and band gap is designed and fabricated using shape memory polymers based on curved-beams. The effects of geometric parameters and temperature on pattern switching and vibration performance is investigated by using theoretical analysis, finite element simulation and experiments. Based on this new metamaterial, a bionic multi-degree-of-freedom dexterous finger tube is designed and the major geometric parameters affecting its bending angle is investigated. The present intelligent regulation combining with the mechanical regulation provide a valuable contribution to the design of novel multifunctional tunable metamaterials, as well as further extending the applications in biomedical field.

Design 3D improved star-shaped honeycomb with different tip angles from 2D analytical star-shaped model

Two-dimensional star-shaped honeycombs (2D SSHs) exhibit an effective negative Poisson's ratio due to the abundant internal space and re-entrant angle, while the strength and the deformation of the three-dimensional (3D) SSHs are still limited owing to the finite tuneability of the tip angle. By adding different tip re-entrant angles into the SSH, multiple improved star-shaped honeycombs (ISSHs) with tunable Poisson's ratio are proposed. The in-plane elastic properties, including the effective Young's moduli and effective Poisson's ratio, are both derived by 2D analytical model using the energy method. The finite element simulation and compression experiment are used to verify the correctness of theoretical results. Based on the work, the deformation mechanism of the 3D ISSHs is discussed by quasi-static compression experiment and numerical simulation. The simulation results and experimental results show a great agreement with theoretical results. Different tip angles heighten the normalized Young's modulus and make the Poisson's ratio more tunable, respectively. In addition, the 3D ISSHs show an enhanced effect among higher strength and stability while bearing the compression load. This work provides a good reference for constructing 3D symmetrical multicellular structures, especially honeycombs.

Mechanical properties of 3D hybrid double arrow-head structure with tunable Poisson's ratio

In this study, three-dimensional hybrid double arrow-head (3D HDA) structure is proposed by combining the convex and concave quadrilateral components. Theoretical models for elastic constants of 3D HDA structure are established, which indicates that 3D HDA structure has tunable Young's modulus and Poisson's ratio by adjusting the complementary action of conventional and auxetic components. 3D printing technique is used to fabricate the 3D HDA specimens with supporting materials and the compression experiments are carried out after removing supporting materials manually to validate the accuracy of theoretical and numerical models. The crushing behaviors and energy absorption performances of 3D HDA structure are investigated and the influences of geometric parameters have been revealed for different crushing conditions. For quasi-static and low-velocity crushing conditions, the crushing plateau stress gets higher when the Poisson's ratio trends to the value of zero. While for high-velocity crushing condition, the crushing collapse transfers to layer-by-layer collapse which weakens the influence of Poisson's ratio effect. The value of plateau stress is positive correlated with the Young's modulus of structure. The proposed 3D HDA structure is highly designable for mechanical properties with stable collapse deformation, excellent ductility and better energy absorption performances which make the 3D HDA structure suitable for structural and functional applications in aerospace engineering.

Origami-based cellular mechanical metamaterials with tunable Poisson's ratio: Construction and analysis

Rigid origami provides great theoretical potentials for designing metamaterials with programmable mechanical properties. In this paper, a novel family of cellular mechanical metamaterials is developed based on rigid-foldable square-twist origami. Kinematics and rigid-foldability of the four types of square-twist origami patterns are investigated. A square-twist origami, which has specific kinematic characteristics, is selected to construct novel metamaterial cells in the x-y plane. During deployment, the tunable Poisson's ratios of proposed metamaterial cells are guaranteed by their rigid-foldability and no self-intersection. Two combination schemes, literally linear and plane-symmetrical combination, are proposed to stack the metamaterial cells in the z-direction for building cellular metamaterials. Influences of geometries, number of layers, assemble mode, and combination scheme on the in-plane and out-plane Poisson's ratios of the square-twist origami are then evaluated. The Poisson's ratios of the constructed mechanical metamaterials are further analyzed. Following the mapping relationship between design factors and Poisson's ratio, cellular mechanical metamaterials with tunable Poisson's ratios could be designed for engineering applications.

Achieving adjustable elasticity with non-affine to affine transition.

For various engineering and industrial applications it is desirable to realize mechanical systems with broadly adjustable elasticity to respond flexibly to the external environment. Here we discover a topology-correlated transition between affine and non-affine regimes in elasticity in both two- and three-dimensional packing-derived networks. Based on this transition, we numerically design and experimentally realize multifunctional systems with adjustable elasticity. Within one system, we achieve solid-like affine response, liquid-like non-affine response and a continuous tunability in between. Moreover, the system also exhibits a broadly tunable Poisson's ratio from positive to negative values, which is of practical interest for energy absorption and for fracture-resistant materials. Our study reveals a fundamental connection between elasticity and network topology, and demonstrates its practical potential for designing mechanical systems and metamaterials.

Study on a Chiral Structure with Tunable Poisson's Ratio.

A chiral structure with a negative Poisson’s ratio containing a hollow circle with varying diameters was designed, and the finite element method was used to investigate the variation in the Poisson’s ratio when the hollow circle diameter was varied (d = 0, 1, 2, 3, and 4 mm). The simulation results showed that the Poisson’s ratio was sensitive to the hollow circle diameter, and the minimum Poisson’s ratio was −0.43. Three specimens with different hollow circle diameters (d′ = 0, 1, and 3 mm) were 3D-printed from thermoplastic polyurethane, and the Poisson’s ratio and equivalent elastic modulus were measured. In the elastic range, the Poisson’s ratio increased and the equivalent elastic modulus decreased as the hollow circle diameter increased. The simulation and experimental results showed good agreement. The proposed structure is expected to be applicable to protective sports gear owing to its high energy absorption and the fact that its properties can be modified as required by adjusting the geometric parameters of the unit cell.

A novel 3-D structure with tunable Poisson's ratio and adjustable thermal expansion

Abstract： A novel 3-D structure is proposed by adding the reinforcing rods into the original 2-D star-shaped structure to obtain more obvious negative Poisson's ratio effect. The influence of length parameter, thickness parameter, angle parameters and material combination on the effective Poisson's ratio, effective Young's modulus and effective shear modulus of the novel 3-D structure is systematically investigated using cell-based finite element modeling. Additionally, the change rule of material combination sequence and length parameter of the structure's thermal expansion is also studied. The results show that the novel 3-D structure can achieve positive, zero and negative Poisson's ratio, as well as positive, zero and negative thermal expansion when appropriate material combination is adopted. Moreover, the negative Poisson's ratio effect of the novel 3-D structure is distinctly enhanced, and the effective Young's modulus is slightly increased through comparing with other two 3-D star-shaped structures. By selecting material combinations and structural geometry parameters, metamaterials with special properties can be designed for different application fields.

A novel 3D structure with tunable Poisson’s ratio and tailorable coefficient of thermal expansion based on a tri-material triangle unit

Auxetic materials and negative thermal expansion materials show great application potential in many important fields. In this paper, a novel three-dimensional truss structure with a tunable Poisson's ratio and tailorable coefficient of thermal expansion was developed. Since the deformation of each rod was dominated by axial tension or compression, the structure showed high stiffness. Equations regarding equivalent elasticity parameters and coefficients of thermal expansion of the structure were obtained by displacement and unit force methods. A numerical simulation verification was performed by ANSYS 16.0 software. The verification results indicated that the formulas have high precision and wide application scope. Through parametric analysis, we obtained the conditions for achieving a negative Poisson's ratio and negative thermal expansion coefficient. We also concluded that this material could realize a three-dimensional negative Poisson's ratio and bidirectional negative thermal expansion simultaneously by choosing reasonable geometric parameters and material combinations.