Data-Driven Structural Design Optimization for Petal-Shaped Auxetics Using Isogeometric Analysis

Focusing on the structural optimization of auxetic materials using data-driven methods,a back-propagation neural network(BPNN)based design framework is developed for petal-shaped auxetics using isogeometric analysis.Adopting a NURBSbased parametric modelling scheme with a small number of design variables,the highly nonlinear relation between the input geometry variables and the effective material properties is obtained using BPNN-based fitting method,and demonstrated in this work to give high accuracy and efficiency.Such BPNN-based fitting functions also enable an easy analytical sensitivity analysis,in contrast to the generally complex procedures of typical shape and size sensitivity approaches.

Auxetics in Biomedical Applications: A Review

Materials exhibiting auxetic properties have a negative Poisson’s ratio, which intrigued researchers to understand the behavior of auxetic structure. Several researchers focused on the different auxetic cell designs, while others focused on the auxetic applications. With the advance of additive manufacturing methods, computer-aided design and finite element analysis in recent decades, auxetics have been explored. One of the interesting applications is in the field of biomedical devices or implants, especially for certain natural biomedical organs such as tissues, certain ligaments that have auxetic properties. This paper is an overview of auxetic design approaches and biomedical applications.

Dynamic response of honeycomb-FGS shells subjected to the dynamic loading using non-polynomial higher-order IGA

The main goal of this study is to use higher-order isogeometric analysis(IGA)to study the dynamic response of sandwich shells with an auxetic honeycomb core and two different functionally graded materials(FGM)skin layers(namely honeycomb-FGS shells)subjected to dynamic loading.Touratier's non-polynomial higher-order shear deformation theory(HSDT)is used due to its simplicity and performance.The governing equation is derived from Hamilton's principle.After verifying the present approach,the effect of input parameters on the dynamic response of honeycomb-FGS shells is carried out in detail.

Dynamics of a rotating ring-stiffened sandwich conical shell with an auxetic honeycomb core

The free vibration analysis of a rotating sandwich conical shell with a reentrant auxetic honeycomb core and homogenous isotropic face layers reinforced with a ring support is studied.The shell is modeled utilizing the first-order shear deformation theory(FSDT)incorporating the relative,centripetal,and Coriolis accelerations alongside the initial hoop tension created by the rotation.The governing equations,compatibility conditions,and boundary conditions are attained using Hamilton’s principle.Utilizing trigonometric functions,an analytical solution is derived in the circumferential direction,and a numerical one is presented in the meridional direction via the differential quadrature method(DQM).The effects of various factors on the critical rotational speeds and forward and backward frequencies of the shell are studied.The present work is the first theoretical work regarding the dynamic analysis of a rotating sandwich conical shell with an auxetic honeycomb core strengthened with a ring support.

Bending results of graphene origami reinforced doubly curved shell

The present work investigates higher order stress,strain and deformation analyses of a shear deformable doubly curved shell manufactures by a Copper(Cu)core reinforced with graphene origami auxetic metamaterial subjected to mechanical and thermal loads.The effective material properties of the graphene origami auxetic reinforced Cu matrix are developed using micromechanical models cooperate both material properties of graphene and Cu in terms of temperature,volume fraction and folding degree.The principle of virtual work is used to derive governing equations with accounting thermal loading.The numerical results are analytically obtained using Navier's technique to investigate impact of significant parameters such as thermal loading,graphene amount,folding degree and directional coordinate on the stress,strain and deformation responses of the structure.The graphene origami materials may be used in aerospace vehicles and structures and defence technology because of their low weight and high stiffness.A verification study is presented for approving the formulation,solution methodology and numerical results.

Transient responses of double-curved sandwich two-layer shells resting on Kerr's foundations with laminated three-phase polymer/GNP/fiber surface and auxetic honeycomb core subjected to the blast load

This work uses refined first-order shear theory to analyze the free vibration and transient responses of double-curved sandwich two-layer shells made of auxetic honeycomb core and laminated three-phase polymer/GNP/fiber surface subjected to the blast load.Each of the two layers that make up the double-curved shell structure is made up of an auxetic honeycomb core and two laminated sheets of three-phase polymer/GNP/fiber.The exterior is supported by a Kerr elastic foundation with three characteristics.The key innovation of the proposed theory is that the transverse shear stresses are zero at two free surfaces of each layer.In contrast to previous first-order shear deformation theories,no shear correction factor is required.Navier's exact solution was used to treat the double-curved shell problem with a single title boundary,while the finite element technique and an eight-node quadrilateral were used to address the other boundary requirements.To ensure the accuracy of these results,a thorough comparison technique is employed in conjunction with credible statements.The problem model's edge cases allow for this kind of analysis.The study's findings may be used in the post-construction evaluation of military and civil works structures for their ability to sustain explosive loads.In addition,this is also an important basis for the calculation and design of shell structures made of smart materials when subjected to shock waves or explosive loads.

Non-Fourier heat conduction induced thermal shock fracture behavior of multi-crack auxetic honeycomb structures

The investigation of non-Fourier thermal shock fracture behavior in multicrack auxetic honeycomb structures(HSs) is presented. By employing a non-Fourier heat conduction model, the corresponding temperature and thermal stress fields are established. Subsequently, a thermal stress intensity factor(TSIF) model for the auxetic HSs,accounting for multi-crack interactions, is developed. Finally, using the fracture-based failure criterion, the non-Fourier multi-crack critical temperature of the auxetic HSs is determined. This investigation thoroughly examines the effects of the non-Fourier effect(NFE), auxetic property, crack spacing, and crack location on the thermal shock fracture behavior of the auxetic HSs. Results indicate that a stronger NFE leads to weaker thermal shock resistance in auxetic HSs. Regardless of the presence of the NFE, the auxetic property consistently increases the multi-crack critical temperature of the HSs.Additionally, the interaction of multi-crack inhibits thermal shock crack propagation in HSs.

Thermoelastic Damping in Auxetic Plate

The paper deals with the thermoelastic damping in a rectangular auxetic plate during its free and forced vibrations.Contrary to existing descriptions the relaxation properties of the thermal field as well as the negative material(auxetic-material of negative Poisson′s ratio)properties are taken into considerations.

Architectural Design and Additive Manufacturing of Mechanical Metamaterials:A Review

Mechanical metamaterials can be defined as a class of architected materials that exhibit unprecedented mechanical properties derived from designed artificial architectures rather than their constituent materials.While macroscale and simple layouts can be realized by conventional top-down manufacturing approaches,many of the sophisticated designs at various length scales remain elusive,due to the lack of adequate manufacturing methods.Recent progress in additive manufacturing(AM)has led to the realization of a myriad of novel metamaterial concepts.AM methods capable of fabricating microscale architectures with high resolution,arbitrary complexity,and high feature fidelity have enabled the rapid development of architected meta materials and drastically reduced the design-computation and experimental-validation cycle.This paper first provides a detailed review of various topologies based on the desired mechanical properties,including stiff,strong,and auxetic(negative Poisson’s ratio)metamaterials,followed by a discussion of the AM technologies capable of fabricating these metamaterials.Finally,we discuss current challenges and recommend future directions for AM and mechanical metamaterials.

Auxetic mechanical metamaterials: from soft to stiff

Auxetic mechanical metamaterials are artificially architected materials that possess negative Poisson’s ratio,demonstrating transversal contracting deformation under external vertical compression loading.Their physical properties are mainly determined by spatial topological configurations.Traditionally,classical auxetic mechanical metamaterials exhibit relatively lower mechanical stiffness,compared to classic stretching dominated architectures.Nevertheless,in recent years,several novel auxetic mechanical metamaterials with high stiffness have been designed and proposed for energy absorption,load-bearing,and thermal-mechanical coupling applications.In this paper,mechanical design methods for designing auxetic structures with soft and stiff mechanical behavior are summarized and classified.For soft auxetic mechanical metamaterials,classic methods,such as using soft basic material,hierarchical design,tensile braided design,and curved ribs,are proposed.In comparison,for stiff auxetic mechanical metamaterials,design schemes,such as hard base material,hierarchical design,composite design,and adding additional load-bearing ribs,are proposed.Multi-functional applications of soft and stiff auxetic mechanical metamaterials are then reviewed.We hope this study could provide some guidelines for designing programmed auxetics with specified mechanical stiffness and deformation abilities according to demand.

Optimal design of a novel cylindrical sandwich panel with double arrow auxetic core under air blast loading

The increasing threat of explosions on the battle field and the terrorist action requires the development of more effective blast resistance materials and structures.Curved structure can support the external loads effectively by virtue of their spatial curvature.In review of the excellent energy absorption property of auxetic structure,employing auxetic structure as core material in curved sandwich shows the potential to improve the protection performance.In this study,a novel cylindrical sandwich panel with double arrow auxetic(DAA) core was designed and the numerical model was built by ABAQUS.Due to the complexity of the structure,systematic parameter study and optimal design are conducted.Two cases of optimal design were considered,case1 focuses on reducing the deflection and mass of the structure,while case2 focuses on reducing the deflection and increasing the energy absorption per unit mass.Parameter study and optimal design were conducted based on Latin Hypercube Sampling(LHD)method,artificial neural networks(ANN) metamodel and the nondominated sorting genetic algorithm(NSGA-Ⅱ).The Pareto front was obtained and the cylindrical DAA structure performed much better than its equal solid panel in both blast resistance and energy absorption capacity.Optimization results can be used as a reference for different applications.

Elastic properties of chiral,anti-chiral,and hierarchical honeycombs:A simple energy-based approach

The effects of two geometric refinement strategies widespread in natural structures, chirality and self-similar hierarchy, on the in-plane elastic response of two-dimensional honeycombs were studied systematically. Simple closed-form expressions were derived for the elastic moduli of several chiral, anti- chiral, and hierarchical honeycombs with hexagon and square based networks. Finite element analysis was employed to validate the analytical estimates of the elastic moduli. The results were also compared with the numerical and experimental data available in the literature. We found that introducing a hier- archical refinement increases the Young＇s modulus of hexagon based honeycombs while decreases their shear modulus. For square based honeycombs, hierarchy increases the shear modulus while decreasing their Young＇s modulus. Introducing chirality was shown to always decrease the Young＇s modulus and Poisson＇s ratio of the structure. However, chirality remains the only route to auxeticity. In particular, we found that anti-tetra-chiral structures were capable of simultaneously exhibiting anisotropy, auxeticity, and remarkably low shear modulus as the magnitude of the chirality of the unit cell increases.

Dynamic crushing behavior and energy absorption of hybrid auxetic metamaterial inspired by Islamic motif art

Auxetic honeycomb structures are promising metamaterials with outstanding mechanical properties,and can be potentially used in energy absorption applications.In this study,a novel modified re-entrant hybrid auxetic metamaterial inspired by Islamic motif art is designed by integrating four-pointed double re-entrant motifs with symmetric semi-hexagonal unit cells to achieve a high energy absorption capacity(EAC).Theoretical analyses and numerical simulations are performed to examine the dynamic crushing behavior of the four-pointed double re-entrant combined structure(FDRCS).The developed finite element models(FEMs)are validated by the experiments under quasi-static compression.The deformation mode and stress-strain curves are further studied under low,medium,and high crushing velocities.The theoretically predicted plateau stress of the FDRCS under different crushing velocities is consistent with the numerical simulation results.The crushing stress and the EAC of the FDRCS are influenced by the geometric parameters and crushing velocities.The FDRCS exhibits a negative Poisson's ratio(NPR),owing to the four-point re-entrant structure(RES).Moreover,the specific energy absorption(SEA)of these structures is higher than that of nonauxetic hexagonal and auxetic re-entrant structures,owing to the generation of more plastic hinges that dissipate more energy during dynamic crushing.

A novel wavy non-uniform ligament chiral stent with J-shaped stress-strain behavior to mimic the native trachea

Tracheal stents are an important form of treatment for benign or malignant central airway obstruction.However,the mechanical behavior of current tracheal stents is significantly different from that of the native trachea,which leads to a variety of serious complications.In this study,inspired by the structure of the native trachea,a wavy non-uniform ligament chiral tracheal stent is proposed,in which J-shaped stress-strain behavior and negative Poisson's ratio response are achieved by replacing the tangential ligament of tetrachiral and anti-tetrachiral hybrid structure with a wavy non-uniform ligament.Through the combination of theoretical analysis,finite element analysis and experimental tests,a wide range of desired J-shaped stress-strain curves are explored to mimic the native porcine trachea by tailoring the stent geometry.Besides,the negative Poisson’s ratio and auxetic diameter curves versus axial strain of the stent are also studied in detail,thus contributing to the enhancement of cross-section ventilation and reducing the migration of the stent.This novel tracheal stent with a unique microstructure shows a potential to perfectly match the physiological activities of the native trachea and thereby reduce potential complications.

Hygroelasticity analysis of an elastically restrained functionally graded porous metamaterial circular plate resting on an auxetic material circular plate

The main objective of this research is to investigate the hygroelastic behavior of a non-homogeneous circular plate made up of porous metamaterial resting on an auxetic material plate.The mechanical properties of the main plate,as well as moisture concentration,vary as an exponential function in the transverse direction.Poisson’s ratio is constant.The elastic supporting medium is developed by considering the structurestructure coupling.Based on the linear hygroelasticity theory,the governing state equations in terms of displacements and moisture concentration are acquired.At first,the Fickian equation is solved to compute the nonlinear distribution of moisture through the plate thickness,and then the state equations are semi-analytically solved using the statespace(SS)method and the differential quadrature(DQ)rule to predict the elastic field quantities.A comprehensive parametric analysis is accomplished to elucidate the effects of key parameters on the steady-state response of the plate under the mechanical and hygral loads.

Analysis of the geometrical dependence of auxetic behavior in reentrant structures by finite elements

Materials with a negative Poisson＇s ratio（PR）are called auxetics;they are characterized by expansion/contraction when tensioned/compressed.Given this counterintuitive behavior,they present very particular characteristics and mechanical behavior.Geometrical models have been developed to justify and artificiall reproduce such materials＇ auxetic behavior.The focus of this study is the exploration of a reentrant model by analyzing the variation in the PR of reentrant structures as a function of geometrical and base material parameters.It is shown that,even in the presence of protruding ribs,there may not be auxetic behavior,and this depends on the geometry of each reentrant structure.Values determined for these parameters can be helpful as approximate reference data in the design and fabrication of auxetic lattices using reentrant geometries.

A new interpretation for formation of orthogonal joints in quartz sandstone

Two vertical and orthogonal systematic joint sets are generally arrayed in a grid pattern on the bedding surface,which are the significant features of flat-lying sandstone terrains.Although extensive researches are reported on this topic,many fundamental problems have still not been solved.Such mutually perpendicular opening-mode fractures are an obvious manifestation of effective tensile stresses in two orthogonal directions in the horizontal bedding plane.A good understanding of these orthogonal joint systems is a key to structural analysis,landscape interpretation,and guidance of resolving a number of very practical problems in engineering,mining and hydrologic projects.Based on an anatomic investigation on the orthogonal joints in the Potsdam sandstone of Cambrian age at Ausable Chasm(New York State,USA)and Beauharnois(Quebec,Canada),we proposed that the orthogonal joints may result from the auxetic effects of quartz-rich sandstone rather than local or regional rotation of the maximum tensile stress(σ_(3))direction by about 90°.The sandstone beds with negative Poisson's ratios are so fascinating that,when placed under vertical burial compression and layer-parallel extension in one direction(σ_(3)),it becomes stretched in the transverse direction(σ_(2)),producing two orthogonal sets of mutual abutting and intersecting joints(J1 and J2 normal toσ_(3) andσ_(2),respectively),and both are normal to the bedding surface.Joint set J1 is more closely-spaced than J2 by a factor of∼3.3,which is correlated with an average Poisson's ratio of−0.3 for the Potsdam sandstone at the time of joint formation.

Damping Analysis and Failure Mechanism of 3D Printed Bio-Based Sandwich with Auxetic Core under Bending Fatigue Loading

Meta-sandwich composites with three-dimensional(3D)printed architecture structure are characterized by their high ability to absorb energy.In this paper,static and fatigue 3-point bending tests are implemented on a 3D printed sandwich composites with a re-entrant honeycomb core.The skins,core and whole sandwich are manufactured using the same bio-based material which is polylactic acid with flax fiber reinforcement.Experimental tests are performed in order to evaluate the durability and the ability of this material to dissipate energy.First,static tests are conducted to study the bending behaviour of the sandwich beams,as well as to determine the failure parameters and the characteristic used in fatigue tests.Then,fatigue analyses were carried out to determine the fatigue resistance of these structures.The effects of the core density on the stiffness,hysteresis loop,energy absorption and loss factor,for two loading level,are determined.Moreover,the behaviour of this sandwich composite with re-entrant honeycomb core is compared with that of sandwiches with different core topologies.The results show that sandwich with high core density dissipate more energy,which results higher loss factors.The determined properties offer the most sensitive indicators of sandwich composite damage during its lifetime.This work aims to determine the static and fatigue properties of this material,thus,study its potential applications in industry.

Modified virtual internal bond model based on deformable Voronoi particles

In last time,the series of virtual internal bond model was proposed for solving rock mechanics problems.In these models,the rock continuum is considered as a structure of discrete particles connected by normal and shear springs(bonds).It is well announced that the normal springs structure corresponds to a linear elastic solid with a fixed Poisson ratio,namely,0.25 for threedimensional cases.So the shear springs used to represent the diversity of the Poisson ratio.However,the shearing force calculation is not rotationally invariant and it produce difficulties in application of these models for rock mechanics problems with sufficient displacements.In this letter,we proposed the approach to support the diversity of the Poisson ratio that based on usage of deformable Voronoi cells as set of particles.The edges of dual Delaunay tetrahedralization are considered as structure of normal springs(bonds).The movements of particle’s centers lead to deformation of tetrahedrals and as result to deformation of Voronoi cells.For each bond,there are the corresponded dual face of some Voronoi cell.We can consider the normal bond as some beam and in this case,the appropriate face of Voronoi cell will be a cross section of this beam.If during deformation the Voronoi face was expand,then,according Poisson effect,the length of bond should be decrees.The above mechanism was numerically investigated and we shown that it is acceptable for simulation of elastic behavior in 0.1–0.3 interval of Poisson ratio.Unexpected surprise is that proposed approach give possibility to simulate auxetic materials with negative Poisson’s ratio in interval from–0.5 to–0.1.

In-Plane Impact Dynamics Analysis of Re-Entrant Honeycomb with Variable Cross-Section

Due to the unique deformation characteristics of auxetic materials(Poisson’s ratioμ<0),they have better shock resistance and energy absorption properties than traditional materials.Inspired by the concept of variable crosssection design,a new auxetic re-entrant honeycomb structure is designed in this study.The detailed design method of re-entrant honeycomb with variable cross-section(VCRH)is provided,and five VCRH structures with the same relative density and different cross-section change rates are proposed.The in-plane impact resistance and energy absorption abilities of VCRH under constant velocity are investigated by ABAQUS/EXPLICIT.The results show that the introduction of variable cross-section design can effectively improve the impact resistance and energy absorption abilities of auxetic re-entrant honeycombs.The VCRH structure has better Young’s modulus,plateau stress,and specific energy absorption(SEA)than traditional re-entrant honeycomb(RH).The influence of microstructure parameters(such as cross-section change rateα)on the dynamic impact performance of VCRH is also studied.Results show that,with the increase in impact velocity andα,the plateau stress and SEA of VCRH increase.A positive correlation is also found between the energy absorption efficiency,impact load uniformity andαunder both medium and high impact speeds.These results can provide a reference for designing improved auxetic re-entrant honeycomb structures.