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The paper presents an analysis of rotating rigid unit (RRU) auxetic structures, the special property of which is negative Poisson's ratio. The crucial features of such modified structures are the well-functioning linkages of the square units at their pivot points. This ensures the stable functioning of such structures in tension or compression. The presented geometrical analysis of these auxetic structures may facilitate their adequate construction and allow one to determine the expected values of their expansion as well as the desired porosity. The results are confirmed based on the behaviour of physical models produced by the assembly of square units. The change in the dimensions of the physical models when moving from a closed to an open position is consistent with the predictions of the geometric models. By modifying the well-known 'rotating squares' model, physical structures with auxetic properties are obtained that can be utilised in industrial conditions, where a simultaneous change of linear dimensions is needed—either in compression or in tension. The assembly method may prove efficient in building such structures, given the abilities of assembly robots to regularly arrange the unit cells in lines and rows and to connect them with rings at the designated positions (evenly spaced perforations). The presented auxetic structures might find their potential application in, e.g., expansion joints or structures in which the porosity is mechanically changed, such as mesoscale structures. The tested structures subjected to high compressive forces buckle when the yield strength of the rigid unit material is exceeded. [ABSTRACT FROM AUTHOR]

This paper aims at to improve the vibration behavior of the train floor panel by the use of a cellular auxetic layer. A field measurement is performed to obtain the vibrational frequency content of the body floor moving on the tangent track. Using acceleration sensors, the vibrational response is measured on the bogie (as the input excitation) and on the floor panel (as the observation response). Finite Element modeling for the floor panel is accomplished and measurement data are used for both the input excitation and the verification of the numerical results. The floor panel is a sandwich panel containing multiple layers. In this study, the conventional wooden layer of the panel is substituted with a cellular auxetic one with a re-entrant hexagonal pattern. Then, an optimization problem is defined while the topological parameters of the auxetic layer are the design variables and the dynamic performance of the panel is the objective function. The parameter of power–mass–ratio (PMR) is defined taking the effects of both weight and dynamic response amplitude into calculation. It is found that the PMR is reduced to almost 0.6 by replacing the wooden layer with an auxetic one, and after topological optimization, it is reduced to 0.35. [ABSTRACT FROM AUTHOR]

This paper analyzes the basic geometric and kinematic characteristics of auxetic structures. The geometric principles are then transferred to a family of new possible forms. We investigate and elaborate auxetic behavior in a purely geometric way which is based on the kinematic movement of different frameworks. We then demonstrate its usefulness by analyzing the involved geometry with computer software but without computer simulations or numerical approximations. Instead, using cut flat material and, depending on the cuts and the material used, we enable the kinematical movement of the structures. We also analyze monostable auxetic structures whose movements can be described as geometrically precise, as well as bistable ones. Based on geometric considerations, we combine rigid materials and composites and select appropriate joint connections to allow the application of this system in an architectural scale in, for example, facades, screens or shading systems. [ABSTRACT FROM AUTHOR]

Three-dimensional (3D) fabrics with negative Poisson's ratio (NPR) are known as 3D auxetic fabrics. They expand (or contract) in the direction perpendicular to stretch (or compression) under uniaxial tensile (or compressing) conditions. Many enhanced properties come with this unusual auxetic behaviour, such as shear modulus, indentation resistance, fracture toughness, energy absorption, synclastic curvature, etc. Therefore, these 3D auxetic metamaterials have a broad prospect in applications like personal protective equipment as a replacement of polyurethane foams, fabric-reinforced composites with improved ballistic and impact resistance, and women's brassiere paddings with perfect shape-ability. This paper presents a review on 3D fabrics with NPR produced with different fabric technologies, including weaving, knitting, nonwoven, and other techniques. [ABSTRACT FROM AUTHOR]

In this paper, a pseudo-rigid body model is proposed for the analysis of a spatial mechanical metamaterial and its application is demonstrated. Using this model, the post-buckling behavior of the mechanical metamaterial can be determined without the need to consider the whole elastic structure, e.g., using finite-element procedures. This is done by analyzing a porous cylindrical mechanical metamaterial using a rigid body mechanism, consisting of rigid squares that are connected at their corners. Stiffness in this model comes from torsion springs placed at the connections between rigid parts. The theory of the model is presented and the results of two versions of this model are compared through experiments. One version describes the metamaterial in the free state, while the other, more extended, version includes clamped boundaries, matching the conditions of the experimental set-up. It is shown that the mechanical behavior of the spatial metamaterial is captured by the models and that the shape of the metamaterial in the deformed state can be obtained from the more extended model. [ABSTRACT FROM AUTHOR]

• The proposed design exhibits better energy absorption characteristics. • Reinforcing ligaments ensure uniform deformation and improved stability. • The proposed design maintains a constant Poisson's ratio under relatively large deformation. • The theoretical derivation is simple and applicable to other auxetic structures. The traditional anti-tetra-missing rib structure often suffers from uneven stress deformation and poor energy absorption, which limits its engineering applications. To address these limitations, this paper proposed a novel windmill-shaped auxetic structure by incorporating reinforcing ligaments into the traditional anti-tetra-missing rib structure. The incorporation of these reinforcing ligaments ensures that both the outer and inner ligaments of the windmill-shaped auxetic structure are adequately supported, leading to more uniform structural deformation and enhanced energy absorption capabilities. Further modifications, such as reducing the length of the outer and inner ligaments and increasing their thickness within a reasonable range, significantly enhance the energy absorption capacity. These findings provide a theoretical basis for the design and practical application of auxetic metamaterials. [Display omitted] [ABSTRACT FROM AUTHOR]

Designing a particular change in a system structure to achieve the desired elastic properties of materials for a given task is challenging. Recent studies of purely geometrical atomic models have shown that structural modifications on a molecular level can lead to interesting and desirable elastic properties. Still, the result of such changes is usually difficult to predict. The present work concerns the impact of nanolayer inclusion ordering in hard sphere crystals on their elastic properties, with special attention devoted to their auxetic properties. Two sets of representative models, based on cubic crystals consisting of 6 × 6 × 6 unit cells of hard spheres and containing either neighboring or separated layers of spheres of another diameter, oriented orthogonally to the [001] direction, have been studied by Monte Carlo simulations in the isothermal–isobaric (NpT) ensemble. Their elastic constants have been evaluated using the Parinello–Rahman approach. The Monte Carlo simulations showed that introducing the layer inclusions into a pure face-centered cubic (FCC) structure leads to the system's symmetry changes from cubic symmetry to tetragonal in both cases. Essential changes in the elastic properties of the systems due to layer ordering were found both for neighboring and separated inclusions. It has been found that the choice of a set of layer inclusions allows one to tune the auxetic properties in two crystallographic directions ( [ 110 ] [ 1 1 ¯ 0 ] and [ 101 ] [ 1 ¯ 01 ] ). In particular, this study revealed that the change in layer ordering (from six separated layers to six neighboring ones) allows for, respectively: (i) enhancing auxeticity of the system in the [ 101 ] [ 1 ¯ 01 ] direction with almost loss of auxetic properties in the [ 110 ] [ 1 1 ¯ 0 ] direction in the case of six separated layers, while (ii) in the case of six neighboring layers, keeping the auxetic properties in both auxetic directions independently of the size of spheres constituting inclusions. [ABSTRACT FROM AUTHOR]

The flowing, jamming, and avalanche behavior of granular materials is satisfyingly universal and vexingly hard to tune: A granular flow is typically intermittent and will irremediably jam if too confined. Here, we show that granular metamaterials made from particles with a negative Poisson's ratio yield more easily and flow more smoothly than ordinary granular materials. We first create a collection of auxetic grains based on a re-entrant mechanism and show that each grain exhibits a negative Poisson's ratio regardless of the direction of compression. Interestingly, we find that the elastic and yielding properties are governed by the high compressibility of granular metamaterials: At a given confinement, they exhibit lower shear modulus, lower yield stress, and more frequent, smaller avalanches than materials made from ordinary grains. We further demonstrate that granular metamaterials promote flow in more complex confined geometries, such as intruder and hopper geometries, even when the packing contains only a fraction of auxetic grains. Moreover, auxetic granular metamaterials exhibit enhanced impact absorption. Our findings blur the boundary between complex fluids and metamaterials and could help in scenarios that involve process, transport, and reconfiguration of granular materials. [ABSTRACT FROM AUTHOR]

Auxetics are materials, metamaterials or structures which expand laterally in at least one cross-sectional plane when uniaxially stretched, that is, have a negative Poisson's ratio. Over these last decades, these systems have been studied through various methods, including simulations through finite elements analysis (FEA). This simulation tool is playing an increasingly significant role in the study of materials and structures as a result of the availability of more advanced and user-friendly commercially available software and higher computational power at more reachable costs. This review shows how, in the last three decades, FEA proved to be an essential key tool for studying auxetics, their properties, potential uses and applications. It focuses on the use of FEA in recent years for the design and optimisation of auxetic systems, for the simulation of how they behave when subjected to uniaxial stretching or compression, typically with a focus on identifying the deformation mechanism which leads to auxetic behaviour, and/or, for the simulation of their characteristics and behaviour under different circumstances such as impacts. [ABSTRACT FROM AUTHOR]

A novel two-dimensional (2D) mechanical metamaterial with highly programmable mechanical response under compressive load is presented in this paper by introducing hierarchical rotating structures, in which flexible structures are used to replace the rigid part in conventional rotating rigid structures. Multi-step deformation pathways and negative Poisson's ratio were observed in in situ compression experiments and finite element simulations, suggesting that the mechanical behavior of the hierarchical metastructure is highly ordered and can be programmed by constraining angles of the proposed metamaterial. This work offers new insights to create mechanical metamaterial using hierarchical rotating structures for flexible devices and crashworthiness applications. [ABSTRACT FROM AUTHOR]

[Display omitted] • Deflection behaviour of existing auxetic re-entrant beams compared with traditional beam designs. • Overlooked factors of placement and orientation of auxetic clusters utilized for enhancement. • Two new improved auxetic beam designs proposed with minimal deflection and 64% reduction in material. • Usefulness of the proposed designs brought out by application into lightweight foot bridge design. Auxetic materials have gained popularity in engineering applications owing to their unique deformation response mechanism. However, they have not been exploited to their full potential in engineering load bearing applications. The current paper, therefore, is focused on exploring and improving the deflection behaviour of auxetic beam structures. Initially, a single re-entrant unit cell and an array of auxetic clusters are modelled using Finite Element Method (FEM). These numerical models are then verified for its Poisson's ratio and deflection behaviour using theoretical formulations. Subsequently, in the next phase, a comparison of the deflection characteristics of the in-use common beams with that of the conventional auxetic beam design is carried out. Much overlooked factors such as orientation and placements of auxetic clusters are introduced in beam designs and are exploited to improve the deflection characteristics of conventional auxetic beams. Through this assessment, the paper proposes two novel design concepts of Oriented Re-entrant Structures (ORS) and Assorted Re-entrant Structures (ARS) for improved load bearing response. Novel designs of ORS and ARS beams are observed to perform significantly better than the conventional auxetic and honeycomb beams. The newly proposed beam designs exhibit a 64% reduction in mass in comparison to the homogeneous beam. The usefulness of these designs are brought out by introducing the ARS auxetic beams into a real-world lightweight foot bridge design. The bridge designs with ARS cross beams demonstrates a better behaviour in comparison to the bridge designs with conventional cross beams in terms of both deformation and material usage. This work highlights the potential use of unconventional mechanical metamaterial structures in engineering load bearing problems to address the demands of green engineering and sustainability without compromising on its structural integrity. [ABSTRACT FROM AUTHOR]

The subject of the work is analysis, which presents a renowned auxetic structure based on so-called rotating polygons, which has been subject to modification. This modification entails introducing pivot points on unit cell surfaces near rectangle corners. This innovative system reveals previously unexplored correlations between Poisson's ratio, the ratio of rectangle side lengths, pivot point placement, and structural opening. Formulas have been derived using geometric relationships to compute the structure's linear dimensions and Poisson's ratio. The obtained findings suggest that Poisson's ratio is intricately tied to the structure's opening degree, varying as the structure undergoes stretching. Notably, there are critical parameter limits beyond which Poisson's ratio turns positive, leading to the loss of auxetic properties. For elongated rectangles, extremely high negative Poisson's ratio values are obtained, but only for small opening angles, while with further stretching, the structure loses its auxetic properties. This observed trend is consistent across a broad category of structures comprised of rotating rectangles. [ABSTRACT FROM AUTHOR]

Production of piezo‐resistive auxetic sensors is usually carried out through mixing and coating methods. Although these methods are beneficial, Young's modulus of mixed sensors becomes high because of using a high percentage of sensing elements while the durability of coated sensors gets low due to the separation of sensing elements from the sensor surface. This article presents a new core–shell metamaterial model to address the mentioned problems. The shell and the core are produced of polydimethylsiloxane (PDMS) rubber and a mixture of PDMS/graphite powders (73.45 wt% graphite powders), respectively. A finite element model is developed via COMSOL software to predict the electromechanical behaviors of the created sensor and verified by an experimental study. Scanning electron microscope imaging is conducted to detect the separations of the graphite particles. The main important feature of this meta‐sensor is to possess a linear sensitivity due to having zero Poisson's ratio. The advantage of this method is that Young's modulus of the sensor does not decrease (unlike the mixing method), and the sensor‐coated particles do not separate from the sensor after a while (unlike the coating method). The introduced model has advantages that promote potential applications such as using sensory gloves to detect, for instance, human hand movements. [ABSTRACT FROM AUTHOR]

• An efficient DNN-based design framework for functionally graded lattices is established. • Functionally graded lattices are designed using the framework, fabricated using addictive manufacturing, and evaluated using experimental tests. • The effectiveness of the design framework is demonstrated with the performances of the functionally graded lattices. • This work is inspirable to promote advanced structures/materials with tailored properties. Auxetic materials with counterintuitive negative Poisson's ratio have been of significant interest due to potential applications across diverse engineering fields. Functionally grading such auxetics further enables customization of the structural response and harnesses the potential for multi-functional applications. However, a critical challenge in designing functionally graded lattices is to efficiently determine the spatial variation of the functional gradient and the corresponding geometric designs to achieve the desired response. In this paper, a highly efficient deep learning-based inverse design framework for functionally graded tetra-petal auxetics with spatially tailored properties is presented. This framework significantly improves the efficiency of tailoring functionally graded auxetics where many unit cells need to be tailor-designed. The graded tetra-petal auxetics obtained from the inverse design framework are additively manufactured and subjected to impact tests. The results show superior impact performance compared with uniform designs, demonstrating the effectiveness of the proposed inverse design framework, which can be inspirable to promote advanced structures/materials with enhanced impact resistance. [ABSTRACT FROM AUTHOR]

The elastic properties of f.c.c. hard sphere crystals with periodic arrays of nanoinclusions filled by hard spheres of another diameter are the subject of this paper. It has been shown that a simple modification of the model structure is sufficient to cause very significant changes in its elastic properties. The use of inclusions in the form of joined (mutually orthogonal) layers and channels showed that the resulting tetragonal system exhibited a complete lack of auxetic properties when the inclusion spheres reached sufficiently large diameter. Moreover, it was very surprising that this hybrid inclusion, which can completely eliminate auxeticity, was composed of components that, alone, in these conditions, enhanced the auxeticity either slightly (layer) or strongly (channel). The study was performed with computer simulations using the Monte Carlo method in the isothermal-isobaric ( N p T ) ensemble with a variable box shape. [ABSTRACT FROM AUTHOR]

This study proposed a novel continuous roll-forming process of elastomer molds, which can control the deformation of the mold using the rolling belt stack combination method. This study analyzed various rolling belt combinations, assembled the system based on simulation and experimental data according to the deformation requirement design, and obtained a controllable microstructure mold rolling belt with tensile deformation. Mold thickness and microstructure size are key microstructure mold deformation parameters. This study designed and assembled a controllable microstructure mold rolling belt-type imprint molding system and conducted a series of experiments. The impact and application of different experimental system operation procedures and fabrication methods of the auxetic structure rolling belt on replication molding were analyzed. The innovative controllable microstructure mold rolling belt-type imprint replication molding technique proposed in this study had a stable and controllable mold deformation mechanism. It can control and replicate molding. [ABSTRACT FROM AUTHOR]

• Introducing dual-material auxetic meta-sandwiches by 4D printing technology. • Arranging soft hyper-elastic polymers and elasto-plastic hard shape memory polymers. • Proposing reversible energy absorbers by leveraging instability and elasto-plasticity. • Implementing finite element methods to predict experimental observations. • Showing high capability of reversible meta-sandwiches for dissipating energy. The aim of this paper is to introduce dual-material auxetic meta-sandwiches by four-dimensional (4D) printing technology for reversible energy absorption applications. The meta-sandwiches are developed based on an understanding of hyper-elastic feature of soft polymers and elasto-plastic behaviors of shape memory polymers and cold programming derived from theory and experiments. Dual-material lattice-based meta-structures with different combinations of soft and hard components are fabricated by 4D printing fused deposition modelling technology. The feasibility and performance of reversible dual-material meta-structures are assessed experimentally and numerically. Computational models for the meta-structures are developed and verified by the experiments. Research trials show that the dual-material auxetic designs are capable of generating a range of non-linear stiffness as per the requirement of energy absorbing applications. It is found that the meta-structures with hyper-elastic and/or elasto-plastic features dissipate energy and exhibit mechanical hysteresis characterized by non-coincident compressive loading-unloading curves. Mechanical hysteresis can be achieved by leveraging elasto-plasticity and snap-through-like mechanical instability through compression. Experiments also reveal that the mechanically induced plastic deformation and dissipation processes are fully reversible by simply heating. The material-structural model, concepts and results provided in this paper are expected to be instrumental towards 4D printing tunable meta-sandwiches for reversible energy absorption applications. Image, graphical abstract [ABSTRACT FROM AUTHOR]

Rational design of artificial micro-structured metamaterials with advanced mechanical and physical properties that are not accessible in nature materials is challenging and important. In our paper, mechanical designs of 2D and 3D chiral mechanical metamaterials are reviewed, and their mechanical behaviors and deformation mechanisms can be investigated through equilibrium principle, strain energy analysis, micropolar elasticity and homogenization theories. Afterwards, multifunctional properties of chiral mechanical metamaterials are elaborated, such as: vibration attenuation, impact energy absorption and negative coefficient of thermal expansion (CTE). Finally, several successful industrial applications of chiral mechanical metamaterials are demonstrated, such as: morphing airfoil smart deployable antenna and reconfigurable structures, auxetic stent, chiral flexible electronics and phase transforming metastructures, etc. Finally, perspectives and challenges on chiral mechanical metamaterials are discussed. Rational design of artificial micro-structured metamaterials with advanced mechanical and physical properties that are not accessible in nature materials is challenging and important. In the past several years, making use of the node rotation and ligament bending deformation features of chiral elements, various types of 2D and 3D chiral mechanical metamaterials are designed and proposed for industrial application. In our paper, mechanical designs of 2D and 3D chiral mechanical metamaterials are reviewed, and their mechanical behaviors and deformation mechanisms can be investigated through force and momentum equilibrium principle, strain energy analysis, micropolar elasticity and homogenization theories. Afterwards, multifunctional properties of chiral mechanical metamaterials are elaborated, such as: vibration attenuation and bandgap features, impact energy absorption and negative coefficient of thermal expansion (CTE). Finally, several successful industrial applications of chiral mechanical metamaterials are demonstrated, such as: morphing airfoil with chiral core configuration, shape memorial smart deployable antenna and reconfigurable structures, auxetic stent for biomedical application, chiral flexible electronics and phase transforming metastructures with shape switching abilities, etc. Unlabelled Image • Design of chiral mechanical metamaterials are reviewed, theoretical models are elaborated for exploring the deformation mechanisms. • Multifunctional mechanical benefits and limitations of chiral mechanical metamaterials are reviewed and discussed. • Industrial applications of chiral mechanical metamaterials are reviewed, perspectives and challenges are discussed. [ABSTRACT FROM AUTHOR]

The paper presents an analysis of rotating rigid unit (RRU) auxetic structures, the special property of which is negative Poisson’s ratio. The crucial features of such modified structures are the well-functioning linkages of the square units at their pivot points. This ensures the stable functioning of such structures in tension or compression. The presented geometrical analysis of these auxetic structures may facilitate their adequate construction and allow one to determine the expected values of their expansion as well as the desired porosity. The results are confirmed based on the behaviour of physical models produced by the assembly of square units. The change in the dimensions of the physical models when moving from a closed to an open position is consistent with the predictions of the geometric models. By modifying the well-known ‘rotating squares’ model, physical structures with auxetic properties are obtained that can be utilised in industrial conditions, where a simultaneous change of linear dimensions is needed—either in compression or in tension. The assembly method may prove efficient in building such structures, given the abilities of assembly robots to regularly arrange the unit cells in lines and rows and to connect them with rings at the designated positions (evenly spaced perforations). The presented auxetic structures might find their potential application in, e.g., expansion joints or structures in which the porosity is mechanically changed, such as mesoscale structures. The tested structures subjected to high compressive forces buckle when the yield strength of the rigid unit material is exceeded.

The influence of periodically distributed inclusions on elastic properties of crystals in which particles interact through Yukawa potential is discussed briefly. The inclusions in the form of channels oriented along the [001]-direction and layers orthogonal to the [010]-direction are considered. Monte Carlo simulations have shown that, depending on the type of inclusion and the concentration of inclusion particles in Yukawa crystal, qualitative changes in elastic properties occur. In selected directions, one observes appearance of auxetic properties for systems with nanolayers and enhancement of auxeticity for systems with nanochannels. [ABSTRACT FROM AUTHOR]

Auxetic materials, i.e. materials exhibiting negative Poisson's ratio, stand to answer the demand for novel materials with unique and application-tailored properties. The vast range of potential applications motivates researchers to search for new materials with such properties, or to look for ways to modify the properties of existing materials. The study of systems with structural inclusions falls into the latter category. This work reports numerical investigations of elastic properties of hard sphere f.c.c. crystal. The investigations have been focused on Monte Carlo simulations of systems with arrays of inclusions filled by hard spheres of different diameter, resulting in binary systems, i.e. systems composed of two kinds of particles that differ only in size. Two different layouts of narrow nanoinclusions have been studied in the isobaricisothermal ensemble. It has been shown that even the narrowest inclusions can significantly alter elastic properties of hard particle crystal by eliminating auxetic properties while maintaining the effective cubic symmetry. [ABSTRACT FROM AUTHOR]

Auxetic materials are endowed with a behavior that contradicts common sense, when subjected to an axial tensile load they increase their transverse dimension. In case of a compression load, they reduce their transverse dimension. Consequently, these materials have a negative Poisson's ratio in such direction. This paper reviews research related to these materials. It presents the theories that explain their deformation behavior and reveals the important role represented by the internal structure. Their mechanical properties are explored and some potential applications for these materials are shown. [ABSTRACT FROM AUTHOR]

• Effectiveness of re-entrant auxetic structure under close-in and far-field blasts. • Evaluation of protective efficacy of auxetic honeycomb-core sandwich panel. • Performance comparison with equivalent conventional honeycomb. This paper aims to scrutinise the effectiveness of a re-entrant auxetic honeycomb-core sandwich panel (AHSP) to protect reinforced concrete (RC) slab under close-in and far-field detonations of high explosive. A series of quarter symmetric 3D comprehensive numerical models were developed by using Arbitrary Lagrangian Eulerian (ALE) formulation in LS-DYNA hydrocode. Strain rate effects of the rate sensitive materials were employed in the model to consider dynamic behaviour of the materials during blast loading. The developed numerical model was validated with the documented experimental results. Deformation patterns, energy absorption, overpressure damping, blast pressure deflection, and stress-transmission to the protected structure were investigated with the computational models. Furthermore, the performance of AHSP sacrificial protective structure was compared with an equivalent areal density conventional honeycomb-core sandwich panel (CHSP) structure. The results showed that AHSP not only absorbed higher blast energy but also acted as a pressure deflector by forming a densified concave depression under close-in blast load. AHSP damped higher magnitude of blast overpressure in both close-in and far-field blasts. Moreover, a uniform redistribution of the stress on the protected structure was observed with AHSP protection. The overall response of AHSP was found to be better than CHSP to protect the RC slab. [ABSTRACT FROM AUTHOR]

• Novel auxetic topology computation with an objective of energy absorption maximisation for the first time. • Derivation of analytical design parameters of the novel auxetic structures with consideration of fabrication practicality. • Examination of mechanical properties and energy absorption of the developed auxetic structures to evaluate protective performance based on peak elastic stress, plateau stress, onset of the densification strain and energy absorption capability. This paper aims to develop lightweight high-performance auxetic structures for protective applications such as blast and impact energy absorption. In this study, novel auxetic topologies were computed with an objective of energy absorption maximisation through the topology optimisation method. Analytical design formulations with the consideration of fabrication practicality were derived for the novel auxetic structures; named as the hourglass structure (HGS), braced cross-petal structure (BCPS) and cross-petal structure (CPS). Based on the formulated design parameters, rectangular scaffolds of each structure were designed to investigate bulk mechanical properties and energy absorption under a compressive load. Validated nonlinear finite element (FE) models developed in LS-DYNA FE code were used to examine the mechanical performance of the novel structures. The FE simulations revealed the deformation mechanism, negative Poisson's ratio, stress-strain behaviour and energy absorption. The protective performances of the developed auxetic structure were evaluated with respect to the peak elastic stress, plateau stress, onset of the densification strain and energy absorption capacity. The HGS outperformed the other structures in term of the protective performance. In addition, comparison of specific energy absorption at the onset of densification showed that the HGS, BCPS and CPS possessed superior energy absorption capacities than the conventional auxetic structures. [Display omitted] [ABSTRACT FROM AUTHOR]

The paper discusses the realization of high dimensional stability of products, including minimization of thermal strains by the use of additives having negative coefficient of linear thermal expansion, as well as auxetics having negative Poisson’s ratio. Mechanisms of change of thermal stress state of the porous, dispersion-reinforced and layered materials are established during heating and cooling, depending on elasticity moduli, the size of inclusions, a parity of rigidity of the matrix and the filler as well as boundary conditions. The results of structural design make it possible to improve dimensional stability and reduce residual stresses of microelectronics elements, precise equipment for aerospace engineering and measuring instruments.

The implementation of periodic boundary conditions (PBCs) is one of the most important and difficult steps in the computational analysis of structures and materials. This is especially true in cases such as mechanical metamaterials which typically possess intricate geometries and designs which makes finding and implementing the correct PBCs a difficult challenge. In this work, we analyze one of the most common PBCs implementation technique, as well as implement and validate an alternative generic method which is suitable to simulate any possible 2D microstructural geometry with a quadrilateral unit cell regardless of symmetry and mode of deformation. A detailed schematic of how both these methods can be employed to study 3D systems is also presented. [ABSTRACT FROM AUTHOR]