Pentamodes (first conceived theoretically by Milton and Cherkaev) are a very interesting class of mechanical metamaterials that can be used as building blocks of structures withdecoupled bulk and shear moduli. The pentamodes usually are composed of double cone-shaped struts with the middle diameter being large and the end diameters being tiny (ideally approaching zero). The cubic diamond geometry was proposed by Milton and Cherkaev as a suitable geometry for the unit cell and has since been used in the majority of the works on pentamodes. In this work, we aim to evaluate the degree to which the base unit cell design contributes to high bulk to shear modulus ratio, also known as Figure Of Merit(FOM). In addition to the diamond unit cell, three other well-known unit cell types are considered, and the effect of small diameter size and the ratio of large-to-small diameter, α, on the FOM is evaluated. The results showed that regardless of the base unit cell shape, the FOM value is highly dependent on the d (the smaller diameter size of double-cone) value, while its dependence on the D (the greater diameter of double-cone) value is very weak. For d/h∝0.05 (h representing the linkage length), figures of merit in the range of 10³ could be reached for all the studied topologies.

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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.

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Due to payload weight limitations and human vulnerability to harsh space conditions, it is preferable that the potential landing location for humans has an already constructed habitat preferably made from in situ materials. Therefore, the prospect of utilizing a readily available Martian material, such as regolith, in an easily programmable manufacturing method, such as 3D printing, is very lucrative. The goal of this research is to explore a mixture containing Martian regolith for the purposes of 3D printing in unfavorable conditions. A binder consisting of water and sodium silicate is used. Martian conditions are less favorable for the curing of such a mixture because of low temperature and pressure on the surface of the planet. In order to evaluate mechanical properties of the mixture, molding and 3D printing were conducted at various curing conditions and the mechanical and physical characteristics were compared. Due to the combination of low reaction speed at low temperature (2 °C) and rapid water evaporation at low pressure (0.1–0.01 bar), curing of the specimens in Martian conditions yielded unsatisfactory results. The reaction medium (water) evaporated before the curing reaction could progress enough to form a proper geopolymer. The specimens cured at high temperatures (60 °C) showed satisfactory results, with flexural strength up to 9 MPa when cured at a temperature of 60 °C and pressure of 1 bar. The specimens manufactured by 3D printing showed ultimate flexural strength that was 20% lower than that of equivalent molded specimens. Exploring potential mixture modifications and performing improved tests using the basis laid in this research can lead to an effective and realistic way of utilizing Martian regolith for unmanned 3D-printing purposes with minimal investment.

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Heavily resource-reliant transportation and harsh living conditions, where humans cannot survive without a proper habitat, have prevented humans from establishing colonies on the Moon and Mars. Due to the absence of an atmosphere, potential habitats on the Moon or Mars require thick and strong structures that can withstand artificially produced internal pressure, potential meteoroid strikes, and the majority of incoming radiation. One promising way to overcome the noted challenges is the use of additive manufacturing (AM), also known as 3D printing. It allows producing structures from abundant materials with minimal material manipulation as compared to traditional constructing techniques. In addition to constructing the habitat itself, 3D printing can be utilized for manufacturing various tools that are useful for humans. Recycling used-up tools to compensate for damaged or unfunctional devices is also possible by melting down a tool back into raw material. While space 3D printing sounds good on paper, there are various challenges that still have to be considered for printing-assisted space missions. The conditions in space are drastically different from those on Earth. This includes factors such as the absence of gravity, infinitesimal pressure, and rapid changes in temperature. In this paper, a literature study on the prospects of additive manufacturing in space is presented. There are a variety of 3D printing techniques available, which differ according to the materials that can be utilized, the possible shapes of the final products, and the way solidification of the material occurs. In order to send humans to other celestial bodies, it is important to account for their needs and be able to fulfill them. An overview of requirements for potential space habitats and the challenges that arise when considering the use of additive manufacturing in space are also presented. Finally, current research progress on 3D printing Lunar and Martian habitats and smaller items is reviewed.

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Damages to aircraft fuselages by ice impactors are categorized as barely visible impact damage (BVID). As the application of composite laminates in manufacturing aircraft fuselage is increasing rapidly, studying hail impact on composite laminates seems crucial. Investigation of variation of delamination area and link-up area for different impact scenarios between ice and carbon fibre prepreg composite plates is the main goal of this study. Link-up refers to joining of delaminated areas created by separate impacts at relatively close impact locations. To this aim, multiple impacts at 1 and up to 6 impact locations and with different impactor energies were simulated using SPH formulation, and delamination areas were quantified. The results showed that as the spacing L between two impact locations increases from 0 to 4R (where R denotes the impactor radius), the total delamination area first shows an increase up to a peak point (usually at R<L<2R) after which it shows a large drop, and after L≈2R, the total delamination area level remains almost constant. The large drop is related to disappearance of the link-up phenomenon beyond a certain spacing. Moreover, it was observed that increasing the number of impact locations increases the delamination area almost linearly. As for the impactor energy influence, the results showed that as the impact energy increases, the threshold spacing for link-up increases. Moreover, for the case of impact at two locations and constant total energy level, two impactors with identical energy level lead to higher delamination area as compared to impactors with non-identical energy levels.

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This special issue presents up-to-date studies on porous media with a special focus on analytical models and their capability in reconstructing numerical and experimental results. The published papers included within this special issue provide analytical and semi-analytical models for a wide range of problems including micro-polar liquid flow induced by stretching/shrinking sheet, unsteady magnetohydrodynamic flow, incompressible nanofluid flow under the effect of ohmic heating and magnetic field, free convection flow, and axisymmetric Stokes flow of couple-stress fluid. We would like to thank all the authors, reviewers, and editors for their valuable contribution to this special issue. We are also grateful for the continuous support by the Editorial Office of the Journal of Porous Media.

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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

This special issue aimed to contribute to the novelties and frontiers in porous media with a special focus on analytical models and their comparison with numerical and experimental approaches. The published papers included within this special issue help engineers and programmers to keep the models of real apparatus as simple and accurate as possible and illustrate the broad and varied applications of porous media. To conclude, we would like to thank all the contributing authors, the respected reviewers and editors, and the Editorial Office of the Journal of Porous Media.

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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.

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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).

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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.

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Bird impact on fan blades poses a serious threat to the operational safety of aircraft engines.In this study, a real bird model of mallard duck was developed using the smooth particle hydrodynamics method based on a CT scan of a mallard duck.The accuracy of the real bird model was verified by comparing the simulation results of the impact on a plate of real bird model and simplified traditional bird model with the results of Wilbeck's tests.The transient impact responses of bird body and fan blade as the bird was striking a static and a rotating fan blade were comparatively analyzed.To study the effect of fan rotational speed on the bird-impact process, 836r/min, 1984r/min, 3344r/min, and 3772r/min were selected as fan rotational speed.To study the effects of impact location on the bird-impact process, 1/6, 2/6, 3/6, 4/6 and 5/6 of the blade height were selected as impact locations.The results show that blade rotation has a direct impact on the number of bird block cuts, the mass of a single bird block, and the number of impacted blades.Without considering the blade rotation conditions, the contact force, blade root stress, and blade leading edge stress are significantly lower than that when the blade rotation conditions are considered, which makes the prediction of blade stress and damage conservative and inadequate for use in the design of blade strength.Therefore, the blade rotation motion should be considered in the study of bird impact.The interaction mode between the bird and blade at 836r/min speed obviously differs from that at other rotational speeds.The kinetic energy of the bird decreases at a rotational speed of 836r/min, and increases at other rotational speeds, and the increment of the kinetic energy of the bird increases with increases in rotational speed.The leading-edge peak stress at 836r/min is greater than that at 1984r/min;at other rotational speeds, the peak stress of the leading edge increases with increases in the rotational speed.The contact force and blade root stress increase with increases in the rotational speed.With increases in the impact height, the contact force, kinetic-energy increment of the bird body, peak stress of the blade root, kinetic energy of the bird body, and the stress on the leading edge of blade all increase first and then decrease under the combined action of the relative velocity of the impact point and twist angle of the blade.The peak stress of the leading edge and the increment of the kinetic energy of the bird are greatest when impact occurs at 3/6 blade height, and the peak stress of the blade root and the contact force are greatest when impact occurs at 4/6 blade height.

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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

Additive manufacturing (AM) techniques enable fabrication of bone-mimicking meta-biomaterials with unprecedented combinations of topological, mechanical, and mass transport properties. The mechanical performance of AM meta-biomaterials is a direct function of their topological design. It is, however, not clear to what extent the material type is important in determining the fatigue behavior of such biomaterials. We therefore aimed to determine the isolated and modulated effects of topological design and material type on the fatigue response of metallic meta-biomaterials fabricated with selective laser melting. Towards that end, we designed and additively manufactured Co-Cr meta-biomaterials with three types of repeating unit cells and three to four porosities per type of repeating unit cell. The AM meta-biomaterials were then mechanically tested to obtain their normalized S-N curves. The obtained S-N curves of Co-Cr meta-biomaterials were compared to those of meta-biomaterials with same topological designs but made from other materials, i.e. Ti-6Al-4V, tantalum, and pure titanium, available from our previous studies. We found the material type to be far more important than the topological design in determining the normalized fatigue strength of our AM metallic meta-biomaterials. This is the opposite of what we have found for the quasi-static mechanical properties of the same meta-biomaterials. The effects of material type, manufacturing imperfections, and topological design were different in the high and low cycle fatigue regions. That is likely because the cyclic response of meta-biomaterials depends not only on the static and fatigue strengths of the bulk material but also on other factors that may include strut roughness, distribution of the micro-pores created inside the struts during the AM process, and plasticity. Statement of significance: Meta-biomaterials are a special class of metamaterials with unusual or unprecedented combinations of mechanical, physical (e.g. mass transport), and biological properties. Topologically complex and additively manufactured meta-biomaterials have been shown to improve bone regeneration and osseointegration. The mechanical properties of such biomaterials are directly related to their topological design and material type. However, previous studies of such biomaterials have largely neglected the effects of material type, instead focusing on topological design. We show here that neglecting the effects of material type is unjustified. We studied the isolated and combined effects of topological design and material type on the normalized S-N curves of metallic bone-mimicking biomaterials and found them to be more strongly dependent on the material type than topological design.

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Mechanical metamaterials are a sub-category of designer materials where the geometry of the material at the small-scale is rationally designed to give rise to unusual properties and functionalities. Here, we propose the concept of "action-at-a-distance" metamaterials where a specific pattern of local deformation is programmed into the fabric of (cellular) materials. The desired pattern of local actuation could then be achieved simply through the application of one single global and far-field force. We proposed graded designs of auxetic and conventional unit cells with changing Poisson's ratios as a way of making "action-at-a-distance" metamaterials. We explored five types of graded designs including linear, two types of radial gradients, checkered, and striped. Specimens were fabricated with indirect additive manufacturing and tested under compression, tension, and shear. Full-field strain maps measured with digital image correlation confirmed different patterns of local actuation under similar far-field strains. These materials have potential applications in soft (wearable) robotics and exosuits.

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The elastic properties of mechanical metamaterials are direct functions of their topological designs. Rational design approaches based on computational models could, therefore, be used to devise topological designs that result in the desired properties. It is of particular importance to independently tailor the elastic modulus and Poisson's ratio of metamaterials. Here, we present patterned randomness as a strategy for independent tailoring of both properties. Soft mechanical metamaterials incorporating various types of patterned randomness were fabricated using an indirect additive manufacturing technique and mechanically tested. Computational models were also developed to predict the topology-property relationship in a wide range of proposed topologies. The results of this study show that patterned randomness allows for independent tailoring of the elastic properties and covering a broad area of the elastic modulus-Poisson's ratio plane. The uniform and homogenous topologies constitute the boundaries of the covered area, while topological designs with patterned randomness fill the enclosed area.

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Additively manufactured (AM) porous structures are a new class of biomaterials with many advantages as compared to conventionally produced biomaterials. The goal of this study was to find out how the laser processing parameters including laser power and exposure time affect the mechanical properties, topology, and microstructure of porous biomaterials AM using a novel vector-based approach. Several cylindrical porous specimens were additively manufactured using a wide range of exposure time and laser power. The effects of those parameters on the surface roughness, strut diameter, relative density, hardness, elastic modulus, yield stress, first maximum stress, and plateau stress of the porous structures were studied. The results showed that the rate of change in mechanical and topological properties with respect to exposure time was non-linear while it was linear with respect to the laser power. The results also showed that the effects of laser power and exposure time on the mechanical properties and topology of AM porous structures could be decoupled from each other, enabling derivation of predictive emperical relationships. The emperical and experimental curves showed very good agreement, which further validates the validity of the separation method used for obtaining the emperical relationships. The analytical relationships for elastic modulus and yield stress that we had obtained in a previous study could predict the elastic modulus and yield stress of the porous strucutres when the energy input was high enough (i.e. exposure times ≥ 450 μs), because the local mechanical properties of the matrix material decreased for the lower levels of energy input. The change in the mechanical properties of the bulk material due to change in laser processing parameters should thus be taken into account.@en

Nature uses various activation mechanisms to program complex transformations in the shape and functionality of living organisms. Inspired by such natural events, we aimed to develop initially flat (i.e. two-dimensional) programmable materials that, when triggered by a stimulus such as temperature, could self-transform their shape into a complex three-dimensional geometry. A two-dimensional starting point enables full access to the surface, e.g. for (nano-)patterning purposes, which is not available in most other manufacturing techniques including additive manufacturing techniques and molding. We used different arrangements of bi- and multi-layers of a shape memory polymer (SMP) and hyperelastic polymers to program four basic modes of shape-shifting including self-rolling, self-twisting (self-helixing), combined self-rolling and self-wrinkling, and wave-like strips. The effects of various programming variables such as the thermomechanical properties of the hyperelastic layer, dimensions of the bi- and multi-layer strips, and activation temperature on the morphology of the resulting three-dimensional objects were studied experimentally and were found to cause as much as 10-fold change in the relevant dimensions. Some of the above-mentioned modes of shape-shifting were then integrated into other two-dimensional constructs to obtain self-twisting DNA-inspired structures, programmed pattern development in cellular solids, self-folding origami, and self-organizing fibers. Furthermore, the possibility of incorporating multiple surface patterns into one single piece of shape-transforming material is demonstrated using ultraviolet-cured photopolymers. @en

Honeycomb structures have found numerous applications as structural and biomedical materials due to their favourable properties such as low weight, high stiffness, and porosity. Application of additive manufacturing and 3D printing techniques allows for manufacturing of honeycombs with arbitrary shape and wall thickness, opening the way for optimizing the mechanical and physical properties for specific applications. In this study, the mechanical properties of honeycomb structures with a new geometry, called octagonal honeycomb, were investigated using analytical, numerical, and experimental approaches. An additive manufacturing technique, namely fused deposition modelling, was used to fabricate the honeycomb from polylactic acid (PLA). The honeycombs structures were then mechanically tested under compression and the mechanical properties of the structures were determined. In addition, the Euler-Bernoulli and Timoshenko beam theories were used for deriving analytical relationships for elastic modulus, yield stress, Poisson's ratio, and buckling stress of this new design of honeycomb structures. Finite element models were also created to analyse the mechanical behaviour of the honeycombs computationally. The analytical solutions obtained using Timoshenko beam theory were close to computational results in terms of elastic modulus, Poisson's ratio and yield stress, especially for relative densities smaller than 25%. The analytical solutions based on the Timoshenko analytical solution and the computational results were in good agreement with experimental observations. Finally, the elastic properties of the proposed honeycomb structure were compared to those of other honeycomb structures such as square, triangular, hexagonal, mixed, diamond, and Kagome. The octagonal honeycomb showed yield stress and elastic modulus values very close to those of regular hexagonal honeycombs and lower than the other considered honeycombs.

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