The authors regret that the affiliation of Joseph Ahn was incorrectly listed in the original article. The correct affiliation is:

Independent Researcher, Hwaseong-si, South Korea

This error has now been corrected in the online version of the article.

The authors would like to apologise for any inconvenience caused.@en

High-performance soft–hard interfaces are inherently difficult to fabricate due to the dissimilar mechanical properties of both materials, especially when connecting extremely soft biomaterials, such as hydrogels, to much harder biomaterials, such as rigid polymers. Nevertheless, there is significant clinical demand for synthetic soft–hard interfaces. Here, soft–hard interface geometries are proposed, designed with the aid of computational analyses and fabricated as 3D-printed hydrogel-to-polylactide (PLA) structures. Two primary interlocking geometries (i.e., anti-trapezoidal (AT) and double-hook (DH)) are used to study the envelope of 2.5D geometric interlocking designs, fabricated through hybrid 3D printing, combining pneumatic extrusion with fused deposition modeling. Finite-element analysis, uniaxial tensile tests, and digital image correlation (DIC) are used to characterize the geometries and identify parameters that significantly influence their mechanical performance. These findings reveal significant differences between geometric designs, where DH geometries performed significantly better than AT geometries, exhibiting a 190% increase in the maximum force, F_max, and a 340% increase in the fracture toughness, W. Compared to the control groups (i.e., flat, inset, and 90° interfaces), F_max and W values increased by 500%–990% and 350%–1200%, respectively. The findings of this study can serve as a guideline for the design and fabrication of efficient soft–hard interfaces with performances close to predicted values.

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The existing 3D printing methods exhibit certain fabrication-dependent limitations for printing curved constructs that are relevant for many tissues. Four-dimensional (4D) printing is an emerging technology that is expected to revolutionize the field of tissue engineering and regenerative medicine (TERM). 4D printing is based on 3D printing, featuring the introduction of time as the fourth dimension, in which there is a transition from a 3D printed scaffold to a new, distinct, and stable state, upon the application of one or more stimuli. Here, we present an overview of the current developments of the 4D printing technology for TERM, with a focus on approaches to achieve temporal changes of the shape of the printed constructs that would enable biofabrication of highly complex structures. To this aim, the printing methods, types of stimuli, shape-shifting mechanisms, and cell-incorporation strategies are critically reviewed. Furthermore, the challenges of this very recent biofabrication technology as well as the future research directions are discussed. Our findings show that the most common printing methods so far are stereolithography (SLA) and extrusion bioprinting, followed by fused deposition modelling, while the shape-shifting mechanisms used for TERM applications are shape-memory and differential swelling for 4D printing and 4D bioprinting, respectively. For shape-memory mechanism, there is a high prevalence of synthetic materials, such as polylactic acid (PLA), poly(glycerol dodecanoate) acrylate (PGDA), or polyurethanes. On the other hand, different acrylate combinations of alginate, hyaluronan, or gelatin have been used for differential swelling-based 4D transformations. TERM applications include bone, vascular, and cardiac tissues as the main target of the 4D (bio)printing technology. The field has great potential for further development by considering the combination of multiple stimuli, the use of a wider range of 4D techniques, and the implementation of computational-assisted strategies.

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The Poisson's ratio and elastic modulus are two parameters determining the elastic behavior of biomaterials. While the effects of elastic modulus on the cell response is widely studied, very little is known regarding the effects of the Poisson's ratio. The micro-architecture of meta-biomaterials determines not only the Poisson's ratio but also several other parameters that also influence cell response, such as porosity, pore size, and effective elastic modulus. It is, therefore, very challenging to isolate the effects of the Poisson's ratio from those of other micro-architectural parameters. Here, we computationally design meta-biomaterials with controlled Poisson's ratios, ranging between -0.74 and +0.74, while maintaining consistent porosity, pore size, and effective elastic modulus. The 3D meta-biomaterials were additively manufactured at the micro-scale using two-photon polymerization (2PP), and were mechanically evaluated at the meso‑scale. The response of murine preosteoblasts to these meta-biomaterials was then studied using in vitro cell culture models. Meta-biomaterials with positive Poisson's ratios resulted in higher metabolic activity than those with negative values. The cells could attach and infiltrate all meta-biomaterials from the bottom to the top, fully covering the scaffolds after 17 days of culture. Interestingly, the meta-biomaterials exhibited different cell-induced deformations (e.g., shrinkage or local bending) as observed via scanning electron microscopy. The outcomes of osteogenic differentiation (i.e., Runx2 immunofluorescent staining) and matrix mineralization (i.e., Alizarin red staining) assays indicated the significant potential impact of these meta-biomaterials in the field of bone tissue engineering, paving the way for the development of advanced bone meta-implants. Statement of significance: We studied the influence of Poisson's ratio on bone cell response in meta-biomaterials. While elastic modulus effects are well-studied, the impact of Poisson's ratio, especially negative values found in architected biomaterials, remains largely unexplored. The complexity arises from intertwined micro-architectural parameters, such as porosity and elastic modulus, making it challenging to isolate the Poisson's ratio. To overcome this limitation, this study employed rational computational design to create meta-biomaterials with controlled Poisson's ratios, alongside consistent effective elastic modulus, porosity, and pore size. The study reveals that two-photon polymerized 3D meta-biomaterials with positive Poisson's ratios displayed higher metabolic activity, while all the developed meta-biomaterials supported osteogenic differentiation of preosteoblasts as well as matrix mineralization. The outcomes pave the way for the development of advanced 3D bone tissue models and meta-implants.

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Temporomandibular joint (TMJ) replacement prostheses often face limitations in accommodating translational movements, leading to unnatural kinematics and loading conditions, which affect functionality and longevity. Here, we investigate the potential of functionally graded materials (FGMs) in TMJ prostheses to enhance mandibular kinematics and reduce joint reaction forces. We develop a functionally graded artificial cartilage for the TMJ implant and evaluate five FGM designs: hard, hard-soft, and three FGM gradients with gradual transitions from 90% hard material to 0%, 10%, and 20%. These designs are 3D printed, mechanically tested under quasi-static compression, and simulated under physiological conditions. Results from computational modeling and experiments are compared to an intact mandible during incisal clenching and left group biting. The FGM design with a transition from 90% to 0% hard material improves kinematics by 19% and decreases perfomance by 3%, reduces joint reaction forces by 8% and 10%, and increases mandibular movement by 20% and 88% during incisal clenching and left group biting, respectively. These findings provide valuable insights for next-generation TMJ implants.

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Take a thin cylindrical shell and twist it; it will buckle immediately. Such unavoidable torsional buckling can lead to systemic failure, for example by disrupting the blood flow through arteries. In this study, we prevent this torsional buckling instability using a combination of auxeticity and orthotropy in cylindrical metamaterial shells with a holey pattern. When the principal axes of the orthotropic meta-shell are relatively aligned with that of the compressive component of the applied stress during twisting, the meta-shell uniformly shrinks in the radial direction as a result of a local buckling instability. This shrinkage coincides with a softening-stiffening transition that leads to ordered stacking of unit cells along the compressive component of the applied stress. These transitions due to local instabilities circumvent the usual torsional instability even under a large twist angle. This study highlights the potential of tailoring anisotropy and programming instabilities in metamaterials, with potential applications in designing mechanical elements for soft robotics, biomechanics or fluidics. As an example of such applications, we demonstrate soft torsional compressor for generating pulsatile flows through a torsion release mechanism.

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Emerging 4D printing techniques have enabled the realization of smart materials whose shape or properties can change with time. Two important phenomena play important roles in the 4D printing of shape memory polymeric materials. First, the anisotropic deformation of the printed filaments due to residual stresses can be harnessed to create out-of-plane shape transformations. Second, the unavoidable formation of micro-defects during the printing processes often affects the programmability of the printed object. Here, we propose a design approach that harnesses these two effects occurring during fused deposition modeling to create tailor-made curved geometries from initially 2D flat disks. We first determined the size and distribution of the imperfections formed within printed structures by varying two printing parameters namely the printing speed and the number of printed materials. Spatially varying the printing speed and combining polylactic acid filaments with a softer material without shape memory properties allowed us to cover a variety of shapes from negative to positive values of the mean and Gaussian curvature. We propose an analytical model to calculate the magnitude of the maximum out-of-plane deformation from the anisotropic expansion factor of the constituting microstructures. Furthermore, we develop computational models to predict the complex shape-changing of thermally actuated 4D printed structures given the distribution of rationally introduced imperfections and we demonstrate the potential applications of such defect-based metamaterials in drug delivery systems.

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Meta-biomaterials, engineered materials with distinctive combinations of mechanical, physical, and biological properties stemming from their micro-architecture, have emerged as a promising domain within biomedical engineering. Correspondingly, meta-implants, which serve as the device counterparts of meta-biomaterials, offer exceptional functionalities, holding great potential for addressing complex skeletal diseases. This paper presents a comprehensive overview of the various types of meta-implants, including hybrid, shape-morphing, metallic clay, and deployable meta-implants, highlighting their unprecedented properties and recent achievement in the field. This paper also delves into the potential future developments of meta-implants, addressing the exploration of multi-functionalities in meta-biomaterials and their applications in diverse biomedical fields.

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The currently available treatments for inner ear disorders often involve systemic drug administration, leading to suboptimal drug concentrations and side effects. Cochlear implants offer a potential solution by providing localized and sustained drug delivery to the cochlea. While the mechanical characterization of both the implants and their constituent material is crucial to ensure functional performance and structural integrity during implantation, this aspect has been mostly overlooked. This study proposes a novel methodology for the mechanical characterization of our recently developed cochlear implant design, namely, rectangular and cylindrical, fabricated using two-photon polymerization (2 PP) with a novel photosensitive resin (IP-Q™). We used in silico computational models and ex silico experiments to study the mechanics of our newly designed implants when subjected to torsion mimicking the foreseeable implantation procedure. Torsion testing on the actual-sized implants was not feasible due to their small size (0.6 × 0.6 × 2.4 mm³). Therefore, scaled-up rectangular cochlear implants (5 × 5 × 20 mm³, 10 × 10 × 40 mm³, and 20 × 20 × 80 mm³) were fabricated using stereolithography and subjected to torsion testing. Finite element analysis (FEA) accurately represented the linear behavior observed in the torsion experiments. We then used the validated Finite element analysis models to study the mechanical behavior of real-sized implants fabricated from the IP-Q resin. Mechanical characterization of both implant designs, with different inner porous structures (pore size: 20 μm and 60 μm) and a hollow version, revealed that the cylindrical implants exhibited approximately three times higher stiffness and mechanical strength as compared to the rectangular ones. The influence of the pore sizes on the mechanical behavior of these implant designs was found to be small. Based on these findings, the cylindrical design, regardless of the pore size, is recommended for further research and development efforts.@en

4D (bio-)printing endows 3D printed (bio-)materials with multiple functionalities and dynamic properties. 4D printed materials have been recently used in biomedical engineering for the design and fabrication of biomedical devices, such as stents, occluders, microneedles, smart 3D-cell engineered microenvironments, drug delivery systems, wound closures, and implantable medical devices. However, the success of 4D printing relies on the rational design of 4D printed objects, the selection of smart materials, and the availability of appropriate types of external (multi-)stimuli. Here, this work first highlights the different types of smart materials, external stimuli, and design strategies used in 4D (bio-)printing. Then, it presents a critical review of the biomedical applications of 4D printing and discusses the future directions of biomedical research in this exciting area, including in vivo tissue regeneration studies, the implementation of multiple materials with reversible shape memory behaviors, the creation of fast shape-transformation responses, the ability to operate at the microscale, untethered activation and control, and the application of (machine learning-based) modeling approaches to predict the structure–property and design–shape transformation relationships of 4D (bio)printed constructs.

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Thin-wall structures, particularly thin-walled tubes, play a critical role in load-bearing structures. Enhancing their ability to withstand crushing loads can significantly improve the overall damping efficiency of the system. Functionally graded thickness (FGT) is a promising approach for enhancing the load-bearing properties of thin-walled tubes by enabling control over material usage and localized deformation patterns within the structure. In this study, we proposed a novel theoretical model that analyzes the crushing behavior of hollow and foam-filled FGT thin-walled circular tubes by considering four primary failure mechanisms that contribute to energy dissipation: (1) bending of plastic hinges, (2) membrane stretching, (3) axial foam crushing, and (4) the interaction between foam and the tube's wall. We validated our model against experimental results from previous researchers and observed a good agreement. Additionally, we conduct a comprehensive study to examine the effects of various geometrical parameters, such as power-law functions and normalized wall thickness ratio, on the crushing behavior of FGT structures. Our results demonstrate the accuracy and reliability of our theoretical model and highlight the potential of FGT structures to enhance the performance of thin-walled tubes in a range of load-bearing applications.

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Shape morphing is the ability of objects to adapt to different shapes and reduce stress concentrations through increased contact area. This is a common trait of natural and engineered objects and has several applications in, among others, soft robotics and orthopedic implants. Shape morphing is achieved through flexible materials or rigid components with either kinematic or compliant joints. An additional step, namely shape locking, is needed for sustained load support. Activation of a locking mechanism can be done with any energy, among which magnetism is one. Here, we present the implementation of a magnetic locking mechanism for kinematically deformable metamaterial structures that maintain shape and support loads upon locking. The structure consists of 3D printed rigid magnetic and non-magnetic components connected by hinges. We created several prototypes of the proposed designs using two additive manufacturing methods (i.e., material extrusion and multi-material jetting) and demonstrated its application in a closed-loop grid for arbitrary shapes. Moreover, we characterized the performance of the prototypes using mechanical tests and multibody kinematic system simulations. This work highlights the viability of the locking concept and provides design considerations for future applications. Further improvement and optimizations are needed for increased efficiency and effectiveness.

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This paper presents an analytical model to investigate the static behaviour of sandwich plates comprised of two isotropic face sheets and a honeycomb core. Through-thickness transverse shear stresses were considered using a unified displacement field with which various plate theories were implemented, i.e., exponential, third-order, hyperbolic, sinusoidal, fifth-order, Mindlin, and the classic plate theory. The equilibrium equations of a simply-supported sandwich panel were derived using the principle of virtual work and Navier solution was obtained under static transverse loading. After validating of the model, various mechanical and geometrical parameters were varied to characterise the behaviour of the structure under regular and auxetic response. It was found that the auxeticity of the core strongly affects the mechanical response, e.g., in controlling deflection, in-plane anisotropy, and Poisson’s ratio. Cell wall angle was found to be most critical parameter that can be used to adjust anisotropy, out-of-plane shear modulus, transverse shear stress distribution, and deflection of the panel. Also the cell aspect ratio controls the sensitivity of the core response to other geometrical variations. In terms of the higher-order theories, the deflection-dependent parameter of the unified formulation seems to have more control of maximum deflection compared to independent rotations. Auxeticity of the core showed some benefits in controlling anisotropy, deflection and providing additional out-of-plane shear rigidity. Overall, since there is not one-to-one relationship between specific values of Poisson’s ratio, anisotropy, and shear rigidity, careful design considerations must be invested to obtain a correct mechanical response.

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Shape-morphing structures have the ability to adapt to various target shapes, offering significant advantages for many applications. However, predicting their behavior presents challenges. Here, we present a method to assess the shape-matching behavior of shape-morphing structures using a multibody systems approach wherein the structure is represented by a collection of nodes and their associated constraints. This representation preserves the kinematic properties of the original structure while allowing for a rigorous treatment of the shape-morphing behavior of the underlying metamaterial. We assessed the utility of the proposed method by applying it to a wide range of 2D/3D sample shape-morphing structures. A modular system of joints and links was also 3D printed for the experimental realization of the systems under study. Both our simulations and the experiments confirmed the ability of the presented technique to capture the true shape-morphing behavior of complex shape-morphing metamaterials.

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In orthopedic surgery, patient-specific bone plates are used for fixation when conventional bone plates do not fit the specific anatomy of a patient. However, plate failure can occur due to a lack of properly established design parameters that support optimal biomechanical properties of the plate. This review provides an overview of design parameters and biomechanical properties of patient-specific bone plates, which can assist in the design of the optimal plate. A literature search was conducted through PubMed and Embase, resulting in the inclusion of 78 studies, comprising clinical studies using patient-specific bone plates for fracture fixation or experimental studies that evaluated biomechanical properties or design parameters of bone plates. Biomechanical properties of the plates, including elastic stiffness, yield strength, tensile strength, and Poisson’s ratio are influenced by various factors, such as material properties, geometry, interface distance, fixation mechanism, screw pattern, working length and manufacturing techniques. Although variations within studies challenge direct translation of experimental results into clinical practice, this review serves as a useful reference guide to determine which parameters must be carefully considered during the design and manufacturing process to achieve the desired biomechanical properties of a plate for fixation of a specific type of fracture. Graphical Abstract: [Figure not available: see fulltext.]

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Bone-to-soft tissue interfaces are responsible for transferring loads between tissues with significantly dissimilar material properties. The examples of connective soft tissues are ligaments, tendons, and cartilages. Such natural tissue interfaces have unique microstructural properties and characteristics which avoid the abrupt transitions between two tissues and prevent formation of stress concentration at their connections. Here, we review some of the important characteristics of these natural interfaces. The native bone-to-soft tissue interfaces consist of several hierarchical levels which are formed in a highly specialized anisotropic fashion and are composed of different types of heterogeneously distributed cells. The characteristics of a natural interface can rely on two main design principles, namely by changing the local microarchitectural features (e.g., complex cell arrangements, and introducing interlocking mechanisms at the interfaces through various geometrical designs) and changing the local chemical compositions (e.g., a smooth and gradual transition in the level of mineralization). Implementing such design principles appears to be a promising approach that can be used in the design, reconstruction, and regeneration of engineered biomimetic tissue interfaces. Furthermore, prominent fabrication techniques such as additive manufacturing (AM) including 3D printing and electrospinning can be used to ease these implementation processes. Biomimetic interfaces have several biological applications, for example, to create synthetic scaffolds for osteochondral tissue repair.

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Mechanical and morphological design parameters, such as stiffness or porosity, play important roles in creating orthopedic implants and bone substitutes. However, we have only a limited understanding of how the microarchitecture of porous scaffolds contributes to bone regeneration. Meta-biomaterials are increasingly used to precisely engineer the internal geometry of porous scaffolds and independently tailor their mechanical properties (e.g., stiffness and Poisson's ratio). This is motivated by the rare or unprecedented properties of meta-biomaterials, such as negative Poisson's ratios (i.e., auxeticity). It is, however, not clear how these unusual properties can modulate the interactions of meta-biomaterials with living cells and whether they can facilitate bone tissue engineering under static and dynamic cell culture and mechanical loading conditions. Here, we review the recent studies investigating the effects of the Poisson's ratio on the performance of meta-biomaterials with an emphasis on the relevant mechanobiological aspects. We also highlight the state-of-the-art additive manufacturing techniques employed to create meta-biomaterials, particularly at the micrometer scale. Finally, we provide future perspectives, particularly for the design of the next generation of meta-biomaterials featuring dynamic properties (e.g., those made through 4D printing).

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This broad review summarizes recent advances and "hot"research topics in nanophononics and elastic, acoustic, and mechanical metamaterials based on results presented by the authors at the EUROMECH 610 Colloquium held on April 25-27, 2022 in Benicássim, Spain. The key goal of the colloquium was to highlight important developments in these areas, particularly new results that emerged during the last two years. This work thus presents a "snapshot"of the state-of-the-art of different nanophononics- and metamaterial-related topics rather than a historical view on these subjects, in contrast to a conventional review article. The introduction of basic definitions for each topic is followed by an outline of design strategies for the media under consideration, recently developed analysis and implementation techniques, and discussions of current challenges and promising applications. This review, while not comprehensive, will be helpful especially for early-career researchers, among others, as it offers a broad view of the current state-of-the-art and highlights some unique and flourishing research in the mentioned fields, providing insight into multiple exciting research directions.

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Additive manufacturing (AM) technologies, particularly those based on powder bed fusion (PBF), most notably, selective laser melting (SLM) for metals, have in recent years emerged as unique fabrication methods for patient-specific implants made of metals and their alloys. The ability to manufacture complex geometries together with the other features of PBF has resulted in successful fabrication of previously unseen functional implants with reliable, reproducible, and predictable properties. The capability of SLM to manufacture a wide range of metals has made this process the most favored one in the manufacturing of implants, mostly for orthopedic applications. As such, it has received tremendous attention from both academia and industry to speed up the achievement of technological maturity, which is demonstrated by the ability to ensure the desired quality of SLM implants and reproducibility in a cost-effective manner. We will, in this chapter, address some of the critical aspects of PBF, particularly those of SLM, including the effects of geometrical design, process parameters, and material type on the quality and properties of AM implants. Finally, we will conclude this chapter with a discussion on the limitations, challenges, and outlook of SLM for implants.

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Durable interfacing of hard and soft materials is a major design challenge caused by the ensuing stress concentrations. In nature, soft-hard interfaces exhibit remarkable mechanical performance, with failures rarely happening at the interface. Here, we mimic the strategies observed in nature to design efficient soft-hard interfaces. We base our geometrical designs on triply periodic minimal surfaces (i.e., Octo, Diamond, and Gyroid), collagen-like triple helices, and randomly distributed particles. A combination of computational simulations and experimental techniques, including uniaxial tensile and quad-lap shear tests, are used to characterize the mechanical performance of the interfaces. Our analyses suggest that smooth interdigitated connections, compliant gradient transitions, and either decreasing or constraining strain concentrations lead to simultaneously strong and tough interfaces. We generate additional interfaces where the abovementioned toughening mechanisms work synergistically to create soft-hard interfaces with strengths approaching the upper achievable limit and enhancing toughness values by 50%, as compared to the control group.

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