Cellular biomaterials offer unique properties for diverse biomedical applications. However, their complex viscoelastic behavior requires careful consideration for design optimization. This study explores the effective viscoelastic response of two promising unit cell designs (tetrahedron-based and octet-truss) suitable for high porosity and strong mechanics. The asymptotic homogenization (AH) method was employed to determine effective longitudinal and shear moduli, as well as Poisson’s ratio, across various relative densities. Finite element simulations (ABAQUS) validated the AH results, demonstrating good agreement (<10% discrepancies). Additionally, analytical models and compression tests on 3D-printed lattice structures supported the theoretical predictions. The study revealed a strong correlation between relative density and the effective modulus of both designs. Notably, the tetrahedron-based design exhibited superior modulus, making it favorable for high loading levels, particularly when used as a high-density configuration. Both designs demonstrated minimal time-dependent elastic modulus changes and a near-constant Poisson’s ratio (0.34–0.349 for octet-truss, 0.316–0.326 for tetrahedron) across a 5–50% relative density range. While minimal, time-dependent modulus reduction needs to be considered in longer-term simulations (𝑡>107 s). This study provides valuable insights into the viscoelastic behavior of these unit cells using the homogenization method, with potential applications in various biomedical fields.@en

Material-extrusion-based 3D printing with polylactic acid (PLA) has transformed the production of lightweight lattice structures with a high strength-to-weight ratio for various industries. While PLA offers advantages such as eco-friendliness, affordability, and printability, its mechanical properties degrade due to environmental factors. This study investigated the impact resistance of PLA lattice structures subjected to material degradation under room temperature, humidity, and natural light exposure. Four lattice core types (auxetic, negative-to-positive (NTP) gradient in terms of Poisson’s ratio, positive-to-negative (PTN) gradient in terms of Poisson’s ratio, and honeycomb) were analyzed for variations in mechanical properties due to declines in yield stress and failure strain. Mechanical testing and numerical simulations at various yield stress and failure strain levels evaluated the degradation effect, using undegraded material as a reference. The results showed that structures with a negative Poisson’s ratio exhibited superior resistance to local crushing despite material weakening. Reducing the material’s brittleness (failure strain) had a greater impact on impact response compared to reducing its yield stress. This study also revealed the potential of gradient cores, which exhibited a balance between strength (maintaining similar peak force to auxetic cores around 800 N) and energy absorption (up to 40% higher than auxetic cores) under moderate degradation (yield strength and failure strain at 60% and 80% of reference values). These findings suggest that gradient structures with varying Poisson’s ratios employing auxetic designs are valuable choices for AM parts requiring both strength and resilience in variable environmental conditions@en

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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The aim of the present work is to design active acoustic metamaterial consisting of an array of Helmholtz resonators and fabricating them using an additive manufacturing technique in order to assist in a reduction in noise levels in aerospace applications. To this aim, initially, a passive metamaterial consisting of an array of 64 Helmholtz resonator unit cells is designed and tested to establish the effectiveness and region of performance. The selected design variable for change is identified as the resonator cavity depth through the frequency response for each parameter of the Helmholtz resonance equation and randomized to achieve a broadband frequency range of the passive metamaterial. An active model of this design (actuated by a stepper motor) is fabricated and tested. The metamaterials are tested under two acoustic set-ups: a closed system aimed at recreating the environment of a soundproof room and an open-system aimed to recreate the condition of an active liner. For the case of passive system, the metamaterial gave sound attenuation of 18 dB (for f = 150 Hz) in open system configuration and 33 dB (f = 350 Hz) in closed system configuration. The attenuation obtained for the active model was 10–15 dB over the mean line performance for the case of closed system and 15–20 dB for the case of open system. The closed system was also tested for performance at multiple cavity depths by setting two wall depths at 10 mm and three walls at 50 mm. This test yielded an attenuation of 15 dB at 180 Hz, the frequency corresponding to 50 mm cavity depth, and 10 dB at 515 Hz, corresponding to 10 mm cavity depth.

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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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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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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.

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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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Auxetic materials, materials demonstrating negative Poisson's ratio, have revolutionized the use of materials in industries, as they demonstrate superb acoustic response, fracture resistance, and energy absorption. For the first time, this study embraces the free vibration of conical shells consisting of an auxetic core with and without ring support under various boundary conditions. First, the material characteristics of the auxetic core are calculated by means of a micromechanical approach. Afterwards, the kinematic motion equations of the conical shell are derived utilizing the first-order shear deformation theory. Finally, the governing equations are solved using the powerful generalized differential quadrature element method (GDQEM). The primary goal of this paper is to study the role of implementing an auxetic core as well as ring support in determining the vibrational behavior of the structure. The results of the study showed that the honeycomb interior angle and the presence of ring support can significantly affect the natural frequency of the structure. Lower frequencies can be reached as the interior angle increases. The importance of ring position is found to be highly dependent on the longitudinal mode shapes of vibration. The impact of ring position on natural frequencies is affected by the semi-vertex angle of the cone, and a shift in frequency peaks can be observed by increasing the semi-vertex angle.

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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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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

Study of porous materials, in particular closed-cell foams, has always attracted researchers’ interest due to the advantages these materials offer in applications where low weight, buoyancy, insulation, or energy absorption is of importance. In this study, quasi-static compressive experimental tests are conducted for low-, medium-, and high-density aluminum foams and their mechanical properties are obtained. In addition, two types of lattice structures based on regular repeating unit cells (Kelvin and Weaire–Phelan) are modelled and their suitability for predicting the mechanical behavior of closed-cell foams in quasi-static configuration is evaluated and compared. Due to the irregular structure of cast foams, it is computationally very expensive to reproduce numerical models with similar structural topology. Using tessellation method can be a step forward in investigating various parameters affecting the properties of closed-cell foams. The results indicated that as compared to Kelvin models, the Weaire–Phelan models better mimic the deformation of manufactured specimens. On the contrary, as compared to the Weaire–Phelan models, the mechanical properties obtained from the Kelvin models are in general closer to the experimental results. The study results also showed that as the foam density increases, the densification strain decreases, while all other mechanical properties (elastic modulus, yield stress, plateau stress, and energy absorption capacity) increase.

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The aim of present work is to address nonlinear dynamic thermal buckling of shallow spherical functionally graded porous shells subjected to transient thermal loading using the first order shear deformation theory (FSDT). A power-law distribution as well as cosine-type porosity distribution are used to model the variation of constituents through the shell thickness. Thermomechanical properties are assumed to be temperature dependent. Using Crank–Nicolson time marching scheme, an iterative procedure is employed to solve nonlinear transient heat conduction equation. For thermal boundary conditions, the outer surface of shells is kept at a reference temperature, while the inner surface experiences a sudden temperature rise. Geometrical type of nonlinearity in the sense of von-Karman is taken into account. The highly coupled nonlinear governing equations of motion are extracted by constructing the appropriate weak form and also using multi-term Ritz–Chebyshev method. The resulting ODEs are then reduced to a system of nonlinear algebraic equations by employing the well-known Newmark family of time integration schemes. The latter equations are solved by means of Newton–Raphson iteration procedure. Budiansky criterion is used to recognize critical parameters of dynamic instability of shells due to applied thermal shocks. Some comparison studies are conducted in order to verify the accuracy of results of the present work. Moreover, various parametric studies are performed to assess the influence of involved parameters.

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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.

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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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Triply periodic minimal surfaces (TPMS) metamaterials and shape-memory polymer (SMP) smart materials are known for their beneficial attributes in novel scientific and industrial fields. Through TPMS designs, low weight accompanied by high surface area are achievable, which are known as crucial parameters in many fields, such as tissue engineering. Moreover, SMPs are well-suited to generate force or to recover their permanent shape by means of an external stimulus. Combining these properties is possible by fabricating TPMS-based metamaterials made out of SMPs, which can be applicable in numerous applications. By considering different level volume fraction of four types of TPMS-based lattices (diamond, gyroid, IWP, and primitive), we focus on the effect of micro-architecture on shape-memory characteristics (i.e., shape recovery, shape fixity, and force recovery) as well as mechanical properties (elastic modulus and Poisson's ratio) of these smart metamaterials. For this purpose, shape-memory effect (SME) is simulated employing thermo-visco-hyperelastic constitutive equations coupled with the time-temperature superposition principle. It is observed that by increasing the level volume fraction of each lattice type, the elastic modulus, shape fixity, and force recovery increase, while the shape recovery diminishes. Such behaviors can be attributed to different deformation modes (flexural or uniaxial) in SMP TPMS-based metamaterials. Furthermore, it is shown that the Poisson's ratio has a nonlinear behavior in these structures. The smart metamaterials introduced in this study have the advantage of providing the possibility of designing implants, especially in bone defects tailored with different micro-architectures depending on each patient's specific need.

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Bird strikes are one major accident for aircraft engines and can inflict heavy casualties and economic losses. In this study, a smoothed particle hydrodynamics (SPH) mallard model has been used to simulate bird impact to rotary aero-engine fan blades. The simulations were performed using the finite element method (FEM) at LS-DYNA. The reliability of the material model and numerical method was verified by comparing the numerical results withWilberk’s experimental results. The effects of impact and bearing parameters, including bird impact location, bird impact orientation, initial bird velocity, fan rotational speeds, stiffness of the bearing, and the damping of the bearing on the bird impact to aero-engine fan blade are studied and discussed. The results show that both the impact location and bird orientation have significant effects on the bird strike results. Bird impact to blade roots is the most dangerous scenario causing the impact force to reach 390 kN. The most dangerous orientation is the case where the bird’s head is tilted 45° horizontally, which leads to huge fan kinetic energy loss as high as 64.73 kJ. The bird’s initial velocity affects blade deformations. The von Mises stress during the bird strike process can reach 1238 MPa for an initial bird velocity of 225 m/s. The fan’s rotational speed and the bearing stiffness affect the rotor stability significantly. The value of bearing damping has little effect on the bird strike process. This paper gives an idea of how to evaluate the strength of fan blades in the design period.

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Materials with a negative Poisson's ratio, also known as auxetics, have attracted a lot attention as they have shown innovation potential in applications for energy damping, modern fasteners, biomedical implants, piezoelectric sensors, and soft actuators. In this study, we introduce different patterns of graded distribution of unit cells with positive and negative Poisson's ratio in tubular configurations. Seven types of patterns are programmed into the fabric of the metamaterial to create desired shape changes upon applying far-field external loads. Two of the patterns demonstrate near-zero Poisson's ratio even at axial strains as high as 44%. Other pattern distributions convert the initially cylindrical shape of the tubes to vase, barrel, hourglass, nonsymmetrical vase, and nonsymmetrical hourglass geometries. The experimental Poisson's ratio values for the linear negative-to-positive-to-negative gradient (resulting in hourglass shape) and linear positive-to-negative-to-positive gradient (resulting in barrel shape) cases are +0.53 and -0.47, respectively. The measured Poisson's ratio values at tube level are in good accordance with the analytical values of +0.5 and -0.5. Benefits of the proposed designs in applications such as action-at-a-distance actuators and wrinkle-free jointless hinges in both 3D and 2D configurations are demonstrated.

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