Both 2D and 3D re-entrant designs are among the well-known prevalent auxetic structures exhibiting negative Poisson's ratio. The present study introduces novel analytical relationships for 2D re-entrant hexagonal honeycombs for both negative and positive ranges of the cell interior angle θ (θ<0 showing a negative Poisson's ratio). The derived analytical solutions are validated against finite element method (FEM) and experimental results. The results show that, compared to the analytical solutions available in the literature, the analytical relationships presented in this study provide the most accurate results for elastic modulus, Poisson's ratio, and yield stress. The analytical/computational tools are then implemented for designing Kinesio taping (KT) structures applicable to treatment of Achilles tendon injuries. One of the main features of the Achilles tendon is a natural auxetic behavior. Poisson's ratio distribution of an Achilles tendon is obtained using longitudinal and transverse strains and are then used to design and 3D print thermoplastic polyurethane (TPU) KT structures with non-uniform distribution of auxetic unit cells. The presented novel KT shows that it is capable of replicating the deformation and global and local Poisson's ratio distributions, similar to those of the Achilles tendon. Due to the absence of similar formulations and procedures in the literature, the results are expected to be instrumental for designing and 3D printing of flexible implants with unusual auxeticity.@en

Mechanical metamaterials are man-made rationally-designed structures that present un-precedented 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 experi-mentally. 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 agree-ment 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. Never-theless, 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.@en

Additive manufacturing (AM), as one of the most powerful manufacturing methods, is fabricating a three-dimensional (3D) structure using computer-aided design (CAD) data by adding material layer by layer. In contrast to traditional manufacturing processes that start from raw block material and remove waste materials, the AM process can demonstrate better aspects such as freedom of design, reduced postprocessing, and waste reduction. With emerging smart materials such as shape memory polymers, the 3D printing technology has upgraded to a technology that is called four-dimensional (4D) printing, in which the fourth dimension expresses time. In this technology, by using active materials, the printed structure can reshape its configuration and also change its mechanical properties in the presence of external stimuli such as temperature, magnetic field, and/or electric field. The fabrication and modeling of 4D-printed structures are considered due to their extensive applications in various areas such as biomedical and robotic. In this chapter, initially based on thermomechanical properties of smart materials, the constitutive modeling is presented for the shape memory feature. Subsequently, the fabrication of 4D-printed elements based on the FDM process is described, and a simple finite element method (FEM) is introduced to predict their self-morphing features. Finally, the fabricated self-morphing and adaptive structures are presented and the proposed model is calibrated based on them. Following model calibration, some smart structures such as grippers, adaptive dynamic structures, and smart composites are presented as case studies, and their behavior under external stimuli is investigated.@en

Acoustic metamaterials are synthetic materials, made of repeating unit cells that are designed to address an acoustic problem, through the rational design of their micro-feature@en

Stress shielding and micromotions are the most significant problems occurring at the bone-implants interface due to a mismatch of their mechanical properties. Mechanical 3D metamate-rials, with their exceptional behaviour and characteristics, can provide an opportunity to solve the mismatch of mechanical properties between the bone and implant. In this study, a new porous femoral hip meta-implant with graded Poisson’s ratio distribution was introduced and its results were compared to three other femoral hip implants (one solid implant, and two porous meta-implants, one with positive and the other with a negative distribution of Poisson’s ratio) in terms of stress and micromotion distributions. For this aim, first, a well-known auxetic 3D re-entrant structure was studied analytically, and precise closed-form analytical relationships for its elastic modulus and Poisson’s ratio were derived. The results of the analytical solution for mechanical properties of the 3D re-entrant structure presented great improvements in comparison to previous analytical studies on the structure. Moreover, the implementation of the re-entrant structure in the hip implant provided very smooth results for stress and strain distributions in the lattice meta-implants and could solve the stress shielding problem which occurred in the solid implant. The lattice meta-implant based on the graded unit cell distribution presented smoother stress-strain distribution in comparison with the other lattice meta-implants. Moreover, the graded lattice meta-implant gave minimum areas of local stress and local strain concentration at the contact region of the implants with the internal bone surfaces. Among all the cases, the graded meta-implant also gave micromotion levels which are the closest to values reported to be desirable for bone growth (40 µm).@en

This paper presents nonlinear finite element (FE) models to predict time-and tempera-ture-dependent responses of shape memory polymer (SMP) foams in the large deformation regime. For the first time, an A SMP foam constitutive model is implemented in the ABAQUS FE package with the aid of a VUMAT subroutine to predict thermo-visco-plastic behaviors. A phenomenological constitutive model is reformulated adopting a multiplicative decomposition of the deformation gradient into thermal and mechanical parts considering visco-plastic SMP matrix and glass micro-sphere inclusions. The stress split scheme is considered by a Maxwell element in parallel with a hyper-elastic rubbery spring. The Eyring dashpot is used for modelling the isotropic resistance to the local molecular rearrangement such as chain rotation. A viscous flow rule is adopted to prescribe shear viscosity and stress. An evolution rule is also considered for the athermal shear strengths to simulate macroscopic post-yield strain-softening behavior. In order to validate the accuracy of the model as well as the solution procedure, the numerical results are compared to experimental responses of Styrene and Polyurethane SMP foams at different temperatures and under different strain rates. The results show that the introduced FE modelling procedure is capable of capturing the major phenomena observed in experiments such as elastic and elastic-plastic behaviors, softening plateau regime, and densification.@en

Bonded patches are widely used in several industry sectors for repairing damaged plates, cracks in metallic structures, and reinforcement of damaged structures. Composite patches have optimal properties such as high strength‐to‐weight ratio, easiness in being applied, and high flexibility. Due to recent rapid growth in the aerospace industry, analyses of adhesively bonded patches applicable to repairing cracked structures have become of great significance. In the present study, the fatigue behavior of the aluminum alloy, repaired by a double‐sided glass/epoxy composite patch, is studied numerically. More specifically, the effect of applying a double‐sided composite patch on the fatigue life improvement of a damaged aluminum 6061‐T6 is analyzed. 3D finite element numerical modeling is performed to analyze the fatigue performance of both repaired and unrepaired aluminum plates using the Abaqus package. To determine the fatigue life of the aluminum 6061‐T6 plate, first, the hysteresis loop is determined, and afterward, the plastic strain amplitude is calculated. Finally, by using the Coffin‐Manson equation, fatigue life is predicted and validated against the available experimental data from the literature. Results reveal that composite patches increase the fatigue life of cracked structures significantly, ranging from 55% to 100% for different applied stresses.@en

Origami structures are a traditional Japanese art that have recently found their way into engineering applications due to their powerful capability to transform flat 2D structures into complex 3D structures along their creases. This has given a rise to their application as designer materials with unprecedented mechanical characteristics, also known as metamaterials. Herein, gradient Miura-ori origami metamaterials are introduced as a method to preprogram out-of-plane curvatures. Several types of unit cell distributions in the origami lattice structure including checkered, linear gradient, concave radial gradient, convex radial gradient, and striped are considered. The results show that these distributions of Miura-ori origami can create single- or double curvatures including twisting, saddling, bending, local inflation, local twisting, local bending, and wavy shapes, when the origami metamaterial is loaded in compression. All the Gaussian curvatures (negative, positive, and zero) can be achieved using the proposed models. The approach helps tailoring complex preprogrammed surface geometries by employing linearly varying gradient distributions of Miura-ori origami.@en

This paper presents a concise state-of-the-art review on the use of Fiber Reinforced Polymers (FRPs) in bridge engineering. The paper is organized into commonly used FRP bridge components, and different materials/manufacturing techniques used for repairing and construction of FRP bridges. Efforts have been made to give a clear and concise view of FRP bridges using the most relevant literature. FRPs have certain desired properties like high strength to weight ratio, and high corrosion and fatigue resistance that make them a sustainable solution for bridges. However, as FRPs are brittle and susceptible to damage, when safety is concerned, critical parts of the bridges are made as hybrids of FRP and conventional materials. Despite significant studies, it has been found that a comprehensive effort is still required on better understanding the long term performance and end-of-life recycling, developing cost-effective and flexible manufacturing processes such as 3D printing, and developing green composites to take full advantages of FRPs.@en

With dramatic increase in 3D printing applications in industry, sandwich panels with 3D printed cores have gained a lot of attention recently. In harmony with global movement towards sustainability and low-carbon emission industries, sandwich panels with easy-to-repair and cost-effective cores would be very attractive structures. In this regard, implementing separated cells for constructing lattice structures instead of using back-to-back lattice structures makes repairing local damages in the core easier and more cost-effective. Ideally, a damaged cell can be replaced with an intact new cell without the need to change the whole core structure. In this study, mechanical responses of a single truncated cube unit cell, a well-known geometry for constructing regular lattices has been studied analytically, numerically, and experimentally. Analytical relationships were derived for stiffness, yield stress, and Poisson's ratio of a single unit cell. Samples were 3D printed and tested mechanically in large deformation regime. A good agreement between results from analytical derivations, numerical simulations, and experiments was observed. It was shown that an equilateral truncated cube structure has a yield stress at least twice of that for a simple cube structure. Three types of repairable sandwich panels with different uniform core densities as well as four graded cores were studied as well. The functionally graded sandwich panels presented the best performance while considering both energy absorption capacity and mass. The best functionally graded sandwich panels (Type 4) showed an increase in specific energy absorption (SEA) by almost 21% and a decrease in maximum displacement by 2.5% with respect to the second-ranking best option.@en

Permeable porous implants must satisfy several physical and biological requirements in order to be promising materials for orthopaedic application: they should have the proper levels of stiffness, permeability, and fatigue resistance approximately matching the corresponding levels in bone tissues. This can be achieved using designer materials, which exhibit exotic properties, commonly known as metamaterials. In recent years, several experimental, numerical, and analytical studies have been carried out on the influence of unit cell micro-architecture on the mechanical and physical properties of metamaterials. Even though experimental and numerical approaches can study and predict the behaviour of different micro-structures effectively, they lack the ease and quickness provided by analytical relationships in predicting the answer. Although it is well known that Timoshenko beam theory is much more accurate in predicting the deformation of a beam (and as a result lattice structures), many of the already-existing relationships in the literature have been derived based on Euler–Bernoulli beam theory. The question that arises here is whether or not there exists a convenient way to convert the already-existing analytical relationships based on Euler–Bernoulli theory to relationships based on Timoshenko beam theory without the need to rewrite all the derivations from the start point. In this paper, this question is addressed and answered, and a handy and easy-to-use approach is presented. This technique is applied to six unit cell types (body-centred cubic (BCC), hexagonal packing, rhombicuboctahedron, diamond, truncated cube, and truncated octahedron) for which Euler–Bernoulli analytical relationships already exist in the literature while Timoshenko theory-based relationships could not be found. The results of this study demonstrated that converting analytical relationships based on Euler–Bernoulli to equivalent Timoshenko ones can decrease the difference between the analytical and numerical values for one order of magnitude, which is a significant improvement in accuracy of the analytical formulas. The methodology presented in this study is not only beneficial for improving the already-existing analytical relationships, but it also facilitates derivation of accurate analytical relationships for other, yet unexplored, unit cell types.@en

Magneto-/ electro-responsive polymers (MERPs) are a class of stimuli-responsive materials that are actuated when triggered by external magnetic/ electric fields. MERPs exhibit rapid, reversible, and safe multi-functional and dynamic (i.e., changing with time) properties, which can effectively be manipulated at different length scales. These features make MERPs very attractive particularly in biomedical engineering (e.g., drug delivery systems and tissue engineering), soft matter engineering (e.g., soft robotics), and structural design of smart materials with unprecedented properties (e.g., complex shape morphing). Due to the recent progress in the design and development of MERPs, here, we highlighted the current advances in fabricating MERPs using various manufacturing methods including 3D/ 4D printing and conventional techniques. We also summarized the methods used for the characterization of MERPs and discussed their important structure-property relationship. We also highlighted the potential applications of MERPs in biomedical engineering, soft robotic, and the design of smart materials and systems. MERPs show great potentials for creating smart materials with predictable dynamic properties. More studies are necessary to investigate the biological responses of MERP both in-vivo and in-vitro, which is essential for biomedical engineering applications.@en

In the present study, the fatigue behavior and tensile strength of A6061-T4 aluminum al-loy, joined by friction stir spot welding (FSSW), are numerically investigated. The 3D finite element model (FEM) is used to analyze the FSSW joint by means of Abaqus software. The tensile strength is determined for FSSW joints with both a probe hole and a refilled probe hole. In order to calculate the fatigue life of FSSW joints, the hysteresis loop is first determined, and then the plastic strain amplitude is calculated. Finally, by using the Coffin-Manson equation, fatigue life is predicted. The results were verified against available experimental data from other literature, and a good agree-ment was observed between the FEM results and experimental data. The results showed that the joint’s tensile strength without a probe hole (refilled hole) is higher than the joint with a probe hole. Therefore, re-filling the probe hole is an effective method for structures jointed by FSSW subjected to a static load. The fatigue strength of the joint with a re-filled probe hole was nearly the same as the structure with a probe hole at low applied loads. Additionally, at a high applied load, the fatigue strength of joints with a refilled probe hole was slightly lower than the joint with a probe hole.@en

The main objective of this research is to provide a general nonlinear model of adjustable piezoelectric microwires with the ability to tune the stability conditions. In order to increase the controllability and improve system characteristics, only a part of the substrate is electrostatically actuated and the piezoelectric voltage is also applied. The governing equation of equilibrium (EOE) is derived from the principle of minimum total potential energy. The influences of the surface layer, size dependency, piezoelectricity, and dispersion forces are also included simultaneously. To solve the nonlinear differential equation, a numerical method is implemented and the obtained results are validated with available experimental and numerical results. Afterward, a set of parametric studies is carried out to examine the coupled effects of piezo-voltage, length/position of non-actuated pieces, nonlinear curvature, and molecular forces on the microresonators. It is found that the beam deflection and the pull-in voltage have sensitive-dependence on the system behavior. Furthermore, the beam deflection can increase or decrease with consideration of different positions of non-actuated pieces. This research is expected to fill a gap in the state of the art of the piezoelectric microstructures and present relevant results that are instrumental in the investigation of advanced actuated microdevices.@en

Modeling and analyzing the sports equipment for injury prevention, reduction in cost, and performance enhancement have gained considerable attention in the sports engineering community. In this regard, the structure study of on-water sports board (surfboard, kiteboard, and skimboard) is vital due to its close relation with environmental and human health as well as performance and safety of the board. The aim of this paper is to advance the on-water sports board through various bio-inspired core structure designs such as honeycomb, spiderweb, pinecone, and carbon atom configuration fabricated by three-dimensional (3D) printing technology. Fused deposition modeling was employed to fabricate complex structures from polylactic acid (PLA) materials. A 3D-printed sample board with a uniform honeycomb structure was designed, 3D printed, and tested under three-point bending conditions. A geometrically linear analytical method was developed for the honeycomb core structure using the energy method and considering the equivalent section for honeycombs. A geometrically non-linear finite element method based on the ABAQUS software was also employed to simulate the boards with various core designs. Experiments were conducted to verify the analytical and numerical results. After validation, various patterns were simulated, and it was found that bio-inspired functionally graded honeycomb structure had the best bending performance. Due to the absence of similar designs and results in the literature, this paper is expected to advance the state of the art of on-water sports boards and provide designers with structures that could enhance the performance of sports equipment.@en