On the application of additive manufacturing methods for auxetic structures: a review

Investigating the Effect of Design Parameters on the Mechanical Performance of Contact Wave Springs Designed for Additive Manufacturing

Additive manufacturing (AM) enables design freedom to fabricate functionally graded wave springs designed by varying design parameters, which are not possible in traditional manufacturing. AM also enables optimization of the wave spring design for specific load-bearing requirements. Existing wave springs are manufactured by metal with constant dimensions (width and thickness of the strip, diameter) using customized traditional machines in which design variations are almost impossible. This study aims to investigate the effect of wave height, the overlap between the two consecutive coils, and the number of waves per coil on the mechanical properties, for example, load-bearing capacity, stiffness, and energy absorption of contact wave springs. Two designs, that is, rectangular and variable thickness wave springs, were chosen and the design of experiment was devised using Minitab software, resulting in 24 samples. HP MultiJet Fusion (MJF) printer was used to manufacture the samples for performing uniaxial compression tests up to 10 cycles and 90% of the compressible distance to study the variation in mechanical properties due to changes in parameters. Experimental and simulation results showed that variable thickness wave springs have better load bearing, stiffness, and energy absorption compared with the rectangular counterparts. In addition to that, the number of waves per coil and the overlap are directly proportional to the load-bearing capacity as well as stiffness of the wave springs, while the constant wave height is responsible for more uniformly distributed stresses throughout the coils. Load-bearing capacity was increased by 62%, stiffness by 37%, and energy absorption by 20% once the number of waves per coil is increased from 5 to 6 in rectangular wave springs. Overall, the parametric variations significantly affect the performance of wave springs; thus, designers can choose the optimized values of investigated parameters to design customized wave springs for specific applications as per load/stiffness requirements.

Exploiting nonlinearities through geometric engineering to enhance the auxetic behaviour in re-entrant honeycomb metamaterials

Classical approaches to enhance auxeticity quite often involve exploring or designing newer architectures. In this work, simple geometrical features at the member level are engineered to exploit non-classical nonlinearities and improve the auxetic behaviour. The structural elements of the auxetic unit cell are here represented by thin strip-like beams, or thin-walled tubular beams. The resulting nonlinear stiffness enhances the auxeticity of the lattices, especially under large deformations. To quantify the influence of the proposed structural features on the resulting Poisson's ratio, we use here variational asymptotic method (VAM) and geometrically exact beam theory. The numerical examples reveal that 2D re-entrant type micro-structures made of thin strips exhibit an improvement in terms of auxetic behaviour under compression. For the auxetic unit cell with thin circular tubes as members, Brazier's effect associated with cross-sectional ovalisation improves the auxetic behaviour under tension; the enhancement is even more significant for the 3D re-entrant geometry. Thin strip-based auxetic unit cells were additively manufactured and tested under compression to verify the numerical observations. The experimentally measured values of the negative Poisson's ratio are in close agreement with the numerical results, revealing a 66% increase due to the nonlinearity. Simulation results showcase these alternative approaches to improve the auxetic behaviour through simple geometric engineering of the lattice ribs.

A Unit Compound Structure Design: Poisson's Ratio Is Autonomously Adjustable from Negative to Positive

The shape memory polymer (SMP) is a new type of smart material that can produce a shape memory effect through the stimulation of the external environment. In this article, the viscoelastic constitutive theory of the shape memory polymer and the mechanism of the bidirectional memory effect of the shape memory polymer are described. A chiral poly cellular circular concave auxetic structure based on a shape memory polymer made of epoxy resin is designed. Two structural parameters, α and β, are defined, and the change rule of Poisson's ratio under different structural parameters is verified by ABAQUS. Then, two elastic scaffolds are designed to assist a new type of cellular structure made of a shape memory polymer to autonomously adjust bidirectional memory under the stimulation of the external temperature, and two processes of bidirectional memory are simulated using ABAQUS. Finally, when a shape memory polymer structure implements the bidirectional deformation programming process, a conclusion is drawn that changing the ratio β of oblique ligament and ring radius has a better effect than changing the angle α of oblique ligament and horizontal in achieving the autonomously adjustable bidirectional memory effect of the composite structure. In summary, through the combination of the new cell and the bidirectional deformation principle, the autonomous bidirectional deformation of the new cell is achieved. The research can be used in reconfigurable structures, tuning symmetry, and chirality. The adjusted Poisson's ratio achieved by the stimulation of the external environment can be used in active acoustic metamaterials, deployable devices, and biomedical devices. Meanwhile, this work provides a very meaningful reference for the potential application value of metamaterials.

Fused Deposition Modelling of Polymeric Auxetic Structures: A Review

Additive Manufacturing (AM) techniques have recently attracted the attention of scientists for the development of prototypes with complex or particular geometry in a fast and cheap way. Among the different AM processes, the Fused Deposition Modelling process (FDM) offers several advantages in terms of costs, implementation features and design freedom. Recently, it has been adopted to realise auxetic structures, which are characterised by negative Poisson ratio, enhanced mechanical properties, and a higher compression resistance than conventional structures. This review outlines the use of AM processes, in particular FDM, to design and obtain auxetic structures, with the final aim to exploit their applications in different fields. The first part of this work presents a brief classification of auxetic structures and materials. Subsequently, a summary of additive manufacturing processes is presented, focusing on the use of FDM and its limitations. Finally, the studies on the use of additive manufacturing to produce auxetic structures are shown, evidencing the potential of the concurrent combination of a fast prototyping technique such as FDM and the characteristics of polymer- and/or composite-based auxetic structures. Indeed, this new technological field opens the possibility of realising novel structures with integrated smart behaviour, multifunctional properties, compression resistance, and a tailored microstructure and shape.

Development and Prospect of Smart Materials and Structures for Aerospace Sensing Systems and Applications

The rapid development of the aviation industry has put forward higher and higher requirements for material properties, and the research on smart material structure has also received widespread attention. Smart materials (e.g., piezoelectric materials, shape memory materials, and giant magnetostrictive materials) have unique physical properties and excellent integration properties, and they perform well as sensors or actuators in the aviation industry, providing a solid material foundation for various intelligent applications in the aviation industry. As a popular smart material, piezoelectric materials have a large number of application research in structural health monitoring, energy harvest, vibration and noise control, damage control, and other fields. As a unique material with deformation ability, shape memory materials have their own outstanding performance in the field of shape control, low-shock release, vibration control, and impact absorption. At the same time, as a material to assist other structures, it also has important applications in the fields of sealing connection and structural self-healing. Giant magnetostrictive material is a representative advanced material, which has unique application advantages in guided wave monitoring, vibration control, energy harvest, and other directions. In addition, giant magnetostrictive materials themselves have high-resolution output, and there are many studies in the direction of high-precision actuators. Some smart materials are summarized and discussed in the above application directions, aiming at providing a reference for the initial development of follow-up related research.

Evaluation of the Orthotropic Behavior in an Auxetic Structure Based on a Novel Design Parameter of a Square Cell with Re-Entrant Struts

In this research, a three-dimensional auxetic configuration based on a known re-entrant cell is proposed. The 3D auxetic cell is configured from a new design parameter that produces an internal rotation angle to its re-entrant elements to study elastic properties in its three orthogonal directions. Through a topological analysis using Timoshenko beam theory, the bending of its re-entrant struts is modeled as a function of the new design parameter to manipulate Poisson's ratio and Young's modulus. Experimental samples were fabricated using a fused filament fabrication system using ABS and subsequently tested under quasi-static compression and bending tests. Additionally, an orthotropy factor is applied that allows for measuring the deviation between the mechanical properties of each structure. The experimental results validate the theoretical design and show that this new unit cell can transmit an orthotropic mechanical behavior to the macrostructure. In addition, the proposed structure can provide a different bending stiffness behavior in up to three working directions, which allows the application under different conditions of external forces, such as a prosthetic ankle.

Strength enhancement and modulus modulation in auxetic meta-biomaterials produced by selective laser melting

Meta-biomaterials are applied to orthopedic implants to avoid stress shielding effects; however, there is no reason for the yield strength to be comparable to that of human bone. In this study, a composite unit cell was designed by combining the positive Poisson's ratio (PPR) and negative Poisson's ratio (NPR) unit cells, inspired by the second-phase strengthening theory. The purpose was to increase the strength while maintaining the elastic modulus. All structures were successfully fabricated from Ti-6Al-4V via selective laser melting. The relative density is between 0.08 and 0.24, which falls within the optimal range for bone growth. Mechanical tests indicated that the center of the inclined rod fractured in a stepwise fracture mode, which was consistent with the predictions of the Johnson-Cook model. The elastic modulus ranged from 0.652 ± 0.016 to 5.172 ± 0.021 GPa, and the yield strength varied from 10.62 ± 0.112 to 87.158 ± 2.215 MPa. An improved Gibson-Ashby law was proposed to facilitate the design of gradient structures. When the re-entrant angle was 40°, a hybrid body-centered cubic NPR structure was formed, resulting in a significant improvement in the mechanical properties. Importantly, the yield strength of the proposed composite structures increased by 43.23%, and the compression strength increased by 44.70% under the same elastic modulus. The strengthening mechanism has been proven to apply to other bending-dominated structures. Overall, this imparts unprecedented mechanical performance to auxetic meta-biomaterials and provides insights into improving the reported porous structures. STATEMENT OF SIGNIFICANCE: : Auxetic meta-biomaterials exhibit auxetic properties that can improve the contact between the bone-implant interface and reduce the risk of aseptic failure. To avoid the stress shielding effect, the elastic modulus has traditionally been decreased by increasing the porosity. However, the strength is simultaneously reduced. Therefore, a composite unit cell was proposed to increase strength rather than modulus by combining the positive and negative Poisson's ratio unit cells, inspired by the second-phase strengthening theory. We observed a 43.23% increase in the yield strength of the composite structure without increasing the elastic modulus. This strengthening mechanism has been proven to apply to other bending-dominated structures. Our approach provides insights into improving other bending-dominated structures and broadening their applications for bone implantation.

Mechanical performance of additively manufactured cobalt-chromium-molybdenum auxetic meta-biomaterial bone scaffolds

Auxetic meta-biomaterials offer unconventional strain behaviour owing to their negative Poisson's ratio (-υ) leading to deformation modes and mechanical properties different to traditional cellular biomaterials. This can lead to favourable outcomes for load-bearing tissue engineering constructs such as bone scaffolds. Emerging early-stage studies have shown the potential of auxetic architecture in increasing cell proliferation and tissue reintegration owing to their -υ. However, research on the development of CoCrMo auxetic meta-biomaterials including bone scaffolds or implants is yet to be reported. In this regard, this paper proposes a potential framework for the development of auxetic meta-biomaterials that can be printed on demand while featuring porosity requirements suitable for load-bearing bone scaffolds. Overall, the performance of five CoCrMo auxetic meta-biomaterial scaffolds characterised under two scenarios for their potential to offer near-zero and high negative Poisson's ratio is demonstrated. Ashby's criterion followed by prototype testing was employed to evaluate the mechanical performance and failure modes of the auxetic meta-biomaterial scaffolds under uniaxial compression. The best performing scaffold architectures are identified through a multi-criteria decision-making procedure combining 'analytic hierarchy process' (AHP) and 'technique for order of preference by similarity to ideal solution' (TOPSIS). The results found the Poisson's ratio for the meta-biomaterial architectures to be in the range of -0.1 to -0.24 at a porosity range of 73-82%. It was found that the meta-biomaterial scaffold (AX1) that offered the highest auxeticity also showed the highest elastic modulus, yield, and ultimate strength of 1.66 GPa, 56 MPa and 158 MPa, respectively. The study demonstrates that the elastic modulus, yield stress, and Poisson's ratio of auxetic meta-biomaterials are primarily influenced by the underlying meta-cellular architecture followed by relative density offering a secondary influence.

Investigation of Modified Auxetic Structures from Rigid Rotating Squares

Auxetic structures exhibit unusual changes in size, expanding laterally upon stretching instead of contracting. This paper presents this effect in a failsafe mode in structures made of rigid squares. We applied the concept of auxetic structures made of rigid rotating squares (from Grima and Evans) and offer a novel solution for connecting them. By introducing axes of rotation on the surface of the squares, a reliable working system is obtained, free from stress, in which the squares can come into contact with each other and completely cover the surface of the structure, or, in the open position, form regularly arranged pores. Herein, we present a new 2D auxetic metamaterial that is mathematically generated based on a theoretical relationship of the angle between the edges of a square and the position of the axis of rotation. Physical models were generated in the form of a planar structure and in the form of a circular closed structure. Such physical models confirmed our initial considerations and the geometrical relationships, offering new application possibilities. The novel structure that was designed and manufactured for the purpose of the paper can be considered as a new proposal in the market of auxetic materials.

Auxetic Metamaterials for Biomedical Devices: Current Situation, Main Challenges, and Research Trends

Auxetic metamaterials are characterized by a negative Poisson ratio (NPR) and display an unexpected property of lateral expansion when stretched and densification when compressed. Auxetic properties can be achieved by designing special microstructures, hence their classification as metamaterials, and can be manufactured with varied raw materials and methods. Since work in this field began, auxetics have been considered for different biomedical applications, as some biological tissues have auxetic-like behaviour due to their lightweight structure and morphing properties, which makes auxetics ideal for interacting with the human body. This research study is developed with the aim of presenting an updated overview of auxetic metamaterials for biomedical devices. It stands out for providing a comprehensive view of medical applications for auxetics, including a focus on prosthetics, orthotics, ergonomic appliances, performance enhancement devices, in vitro medical devices for interacting with cells, and advanced medicinal clinical products, especially tissue engineering scaffolds with living cells. Innovative design and simulation approaches for the engineering of auxetic-based products are covered, and the relevant manufacturing technologies for prototyping and producing auxetics are analysed, taking into consideration those capable of processing biomaterials and enabling multi-scale and multi-material auxetics. An engineering design rational for auxetics-based medical devices is presented with integrative purposes. Finally, key research, development and expected technological breakthroughs are discussed.

Organismal Design and Biomimetics: A Problem of Scale

Organisms and their features represent a complex system of solutions that can efficiently inspire the development of original and cutting-edge design applications: the related discipline is known as biomimetics. From the smallest to the largest, every species has developed and adapted different working principles based on their relative dimensional realm. In nature, size changes determine remarkable effects in organismal structures, functions, and evolutionary innovations. Similarly, size and scaling rules need to be considered in the biomimetic transfer of solutions to different dimensions, from nature to artefacts. The observation of principles that occur at very small scales, such as for nano- and microstructures, can often be seen and transferred to a macroscopic scale. However, this transfer is not always possible; numerous biological structures lose their functionality when applied to different scale dimensions. Hence, the evaluation of the effects and changes in scaling biological working principles to the final design dimension is crucial for the success of any biomimetic transfer process. This review intends to provide biologists and designers with an overview regarding scale-related principles in organismal design and their application to technical projects regarding mechanics, optics, electricity, and acoustics.