Biocompatible and shape-morphing metallic structures have been proposed for musculoskeletal applications to provide structural support to bony tissues. However, fabricating these structures to conform to a wide range of curvatures, including both single and double curvatures, remains a significant challenge. In this study, we present and analyze structures featuring a regular tiling network connected by spherical joints, forming a chain mail-like mechanism capable of adapting to complex geometries with clay-like flexibility. Simulations using a multibody kinematics model show that parameters such as unit cell shape, dimension ratios, and substrate curvature affect the shape-matching abilities of the structure. Experimental validation using specimens additively manufactured through laser-based powder bed fusion (from Ti6Al4V) and full-field strain measurements performed through digital image correlation confirms the simulation results, demonstrating that reducing structural density (i.e., fewer bodies, struts, and joints per unit area) improves shape adaptability. However, the improved shape morphing capability often comes at the expense of mechanical strength under uni-axial tensile loads. These findings provide a framework for optimizing structures designed to achieve efficient surface conformance and adaptability in load-bearing applications.

Incorporating shape-morphing capability into 3D microprinting enables the fabrication of 4D-printed microarchitectures as proof-of-concept actuators for potential use in soft robotics and microfluidic systems. The ability of these 3D microstructures to actuate rapidly and reversibly enables precise, non-invasive, and controllable deformation. In this study, we investigated the programmable shape-morphing behavior of 3D microarchitectures fabricated using two-photon polymerization (2PP) of a well-established temperature-responsive hydrogel, poly(N-isopropylacrylamide) (pNIPAM). We first systematically studied how 2PP 3D printing parameters (e.g., laser power, scanning speed) and the chemical composition of pNIPAM, including monomer and crosslinker, influence the shape morphing of bilayer microstructures within a temperature range of ~ 32 °C to 60 °C. The (thermo)mechanical properties of the hydrogels, including the Young’s modulus, thermal expansion coefficients, and angular deflection, were also measured at different laser doses and temperatures. Based on these experimental measurements, we calibrated a thermomechanical model capable of predicting the shape morphing of 4D-printed microarchitectures. These microarchitectures served as proof-of-concept actuators, demonstrating the potential of programmable microscale soft robotics and microfluidic systems. The findings provide design guidelines for engineering stimuli-responsive 3D microstructures, highlighting limitations and opportunities for future integration into functional soft robotic or microfluidic systems made of a single material.

The development of high-fidelity three-dimensional (3D) tissue models can minimize the need for animal models in clinical medicine and drug development. However, physical limitations regarding the distances within which diffusion processes are effective impose limitations on the size of such constructs. That is because larger-size constructs experience necrosis, especially in their centers, due to the cells residing deep inside such constructs not receiving enough oxygen and nutrients. This hampers the sustained in vitro growth of the tissues which is required for achieving functional microtissues. To address this challenge, we used three types of 3D printing technologies to create perfusable networks at different length scales and integrate them into such constructs. Toward this aim, networks incorporating porous conduits with increasingly complex configurations were designed and fabricated using fused deposition modeling, stereolithography, and two-photon polymerization while optimizing the printing conditions for each of these technologies. Furthermore, following network embedding in hydrogels, contrast agent-enhanced micro-computed tomography and confocal fluorescence microscopy were employed to characterize one of the essential network functionalities, namely the diffusion function. The investigations revealed the effects of various design parameters on the diffusion behavior of the porous conduits over 24 h. We found that the number of pores exerts the most significant influence on the diffusion behavior of the contrast agent, followed by variations in the pore size and hydrogel concentration. The analytical approach and the findings of this study establish a solid base for a new technological platform to fabricate perfusable multiscale 3D porous networks with complex designs while enabling the customization of diffusion characteristics to meet specific requirements for sustained in vitro tissue growth. Statement of significance: This study addresses an essential limitation of current 3D tissue engineering, namely, sustaining tissue viability in larger constructs through optimized nutrient and oxygen delivery. By utilizing advanced 3D printing techniques this research proposes the fabrication of perfusable, multiscale and customizable networks that enhance diffusion and enable cell access to essential nutrients throughout the construct. The findings highlighted the role of network characteristics on the diffusion of a model compound within a hydrogel matrix. This work represents a promising technological platform for creating advanced in vitro 3D tissue models that can reduce the use of animal models in research involving tissue regeneration, disease models and drug development.

In this study, by mimicking bone tissue adaptation, we introduce a hierarchical design approach to optimize the mechanical performance of auxetic metamaterials. Using a multi-material voxel-based 3D printer, we rationally position soft and hard phases at the voxel level based on a bone-inspired remodeling algorithm that maintains the homeostasis of strain energy density. This process introduces an additional length scale within the structure, leading to (1) a significant expansion of the envelope of achievable elastic properties, (2) more homogeneous strain energy distributions, and (3) up to 78 % stronger metamaterials compared to initial designs. Our results demonstrate that this bone-mimicking design approach enables the emergence of an intermediate length scale between the unit cell and voxel scales, which is responsible for the observed improvements in mechanical performance. Taken together, these findings highlight the potential of biomimetic remodeling for the rational design of stress-worthy, multiscale mechanical metamaterials that combine unusual elastic properties with high mechanical performance.

This Roadmap surveys the diversity of different approaches for characterising, modelling and designing metamaterials. It contains articles covering the wide range of physical settings in which metamaterials have been realised, from acoustics and electromagnetics to water waves and mechanical systems. In doing so, we highlight synergies between the many different physical domains and identify commonality between the main challenges. The articles also survey a variety of different strategies and philosophies, from analytic methods such as classical homogenisation to numerical optimisation and data-driven approaches. We highlight how the challenging and many-degree-of-freedom nature of metamaterial design problems call for techniques to be used in partnership, such that physical modelling and intuition can be combined with the computational might of modern optimisation and machine learning to facilitate future breakthroughs in the field.

Two-photon polymerization (2PP) is an additive manufacturing technology capable of producing polymeric 3D nano- to mesoscale structures with design flexibility and sub-micron resolution. This study investigates the influence of 2PP printing parameters on the morphology and mechanical properties of solid and porous microstructures fabricated from three commercial resins: IP-Q, IP-S, and IP-polydimethylsiloxane (IP-PDMS). To evaluate micromechanical behavior, micropillar compression tests are conducted using IP-Q, which has not been extensively characterized. Porous structures retained 80–85% of the stiffness of solids for IP-Q and IP-S, and 50% for IP-PDMS. Fourier transform infrared spectroscopy showed degrees of conversion of 38% for IP-Q and 61% for IP-S and IP-PDMS. The optimal printing parameters for IP-Q micropillars were a laser power of 50 mW, slicing distance (s) of 1.2 μm, and hatching distance (h) of 1 μm. These settings correspond to a peak laser intensity of 1.58 × 10⁻¹¹ W cm⁻², a focal spot diameter (dxy) of 3.17 μm, a Rayleigh length (zR) of 10.13 μm, and a voxel overlap (δ) of 0.6. These conditions yielded a Young's modulus of 3.7 GPa and yield strength of 75.21 MPa. Overall, the findings emphasize the challenges of parameter optimization when introducing porosity and comparing materials. The results provide a systematic framework for tailoring 2PP processing to guide biomedical microdevice design.

Acetabular defects pose significant challenges in orthopedic surgery, particularly in revision total hip arthroplasty (THA). Here, we design, additively manufacture, and evaluate shape-morphing porous implants with kinematic structures to address these defects. Three defect types were examined using synthetic hemipelvis models: posterior wall, cranial-posterior combination, and central-posterior defects. The implants were secured with screws and bone cement, and their surface conformity was assessed through micro computed tomography (µCT). Biomechanical performance was evaluated under quasi-static compression and cyclic loading conditions. Results demonstrated high surface conformity of the flexible mesh across all defect types, with minimal differences from healthy acetabula (< 10 mm). The mesh implants exhibited strong load-bearing capacity, with failures occurring only in the pubic region of the hemipelvis, while both the implants and mesh-cement interfaces remained intact. The implants withstood cyclic loading simulating half the body weight of a 80 kg patient for >1000,000 loading cycles with no evidence of fatigue failure, further confirming their durability. These findings suggest that the flexible mesh implant provides a potential solution for complex acetabular defects, offering anatomical conformity and mechanical stability, even in cases where conventional mesh grafts might be inadequate. Future studies, including cadaveric testing and clinical trials, are necessary to further validate these results in (pre-)clinical settings. Statement of significance: This study addresses the need for adaptable solutions to complex acetabular defects in revision total hip arthroplasty (THA). Traditional implants struggle to conform to severe bone loss and irregular geometries, risking suboptimal fit, and implant migration. We introduce a 3D-printed, shape-morphing porous implant with kinematic structures, offering high anatomical conformity, mechanical robustness, and support for bone graft integration. Combining the adaptability of patient-specific implants with the efficiency of standard designs, this implant reduces lead times while enabling a tailored fit. This innovative approach provides a reliable solution for managing complex defects, addressing limitations of conventional implants, and improving outcomes in orthopedic reconstruction.

Medical devices contribute to the carbon footprint generated by the healthcare sector. The development of implants and biomaterials using recycled waste materials promotes sustainable advances in tissue engineering. Additively manufactured (AM) bone-substituting biomaterials with multifunctional properties, e.g., biodegradability, antibacterial and osteogenic potential, can contribute to sustainable healthcare. Biodegradable biomaterials eliminate secondary surgeries to remove implants, reduce post-surgical complications, and enhance patient recovery, thus decreasing the energy usage and waste associated with medical treatments. Herein, we present porous iron (Fe) scaffolds incorporating 20 vol% waste-derived eggshell particles for bone substitution. The Fe-eggshell scaffolds were fabricated using direct ink writing (DIW) technique and underwent post-AM heat treatment. During sintering, the eggshell's main component – CaCO₃, transformed into CaO. Atomic diffusion between α-Fe and CaO phases resulted in the formation of Ca₂Fe₂O₅ phase at the interface. The scaffolds were 70 % porous and displayed a biodegradation rate of 0.11 mm/year. The mechanical properties were comparable to trabecular bone and the scaffolds endured 3 million loading cycles at 0.7σ_y in r-SBF. The scaffolds showed apatite-forming ability, evidenced by the formation of (carbonaceous) hydroxyapatite, which are conducive to preosteoblast adhesion, proliferation, and differentiation. RT-qPCR analysis confirmed the osteogenic potential of the specimens as evidenced by the upregulated expression of osteopontin and osteocalcin as compared to Ti6Al4V controls. Furthermore, the scaffolds exhibited bactericidal activity (>3.9-log CFU reduction) against methicillin-sensitive and multidrug-resistant strains of Staphylococcus aureus and delayed their biofilm formation. Our research showcases the exceptional multifunctionality of DIW Fe-eggshell composite scaffolds for the sustainable development of orthopedic biomaterials. Statement of significance: We aim to improve the biofunctionalities and sustainability of biodegradable bone substitutes, by developing the extrusion-based 3D printed porous Fe composite scaffolds containing eggshell-derived CaO bioceramics. Our results demonstrated that Fe-eggshell scaffolds exhibited hydroxyapatite-forming ability in simulated body fluid, having mechanical properties in the range of trabecular bone even after 4 weeks biodegradation, supported the proliferation of preosteoblasts and upregulated the expression of osteogenic genes. Moreover, the scaffolds were bactericidal against methicillin-sensitive and multi-drug resistant strains Staphylococcus aureus and delayed their biofilm formation.

Lattice structures are widely used in biomedical engineering, primarily due to their exceptional properties which results from their unique microstructural features. The variability in geometric parameters of the lattice microstructure, enables property adjustment to meet different needs. In this paper, the mechanical properties of lattice structures are investigated with respect to unit cell type, porosity, and presence of an infiltrated resin, which simulates bone tissue within the scaffold. Digital image correlation technique was employed to assess deformation modes in in-filled structures. Three different architectures, including Diamond, FCC and Gyroid with three distinct relative densities of 15 %, 25 %, and 35 % have been designed and fabricated using Ti-6Al-4 V biomaterial. Results showed that the Gyroid lattice structures demonstrated superior mechanical properties compared to Diamond and FCC lattices under quasi-static compression tests. Distinct failure behavior was also observed across the structures. At higher relative densities, Diamond and FCC lattices formed 45° macro-cracks, whereas Gyroid samples compressed severely without macro-cracks. Furthermore, in-filled structures, demonstrated up to 1.3 times higher strength compared to their as-built counterparts. Notably, a unified master curve was developed to facilitate the prediction of fatigue lives of all geometries. These findings support the development of implants with enhanced longevity and performance.

Recent developments in metal additive manufacturing (AM) processes have resulted in the fabrication of functional parts with reliable, reproducible, and predictable properties. Powder bed fusion (PBF) (e.g., selective laser melting and electron beam melting) and directed energy deposition (DED) techniques are the most common categories of AM technologies used for processing metals and their alloys. While the PBF processes can manufacture complex parts with structural gradations, the DED process offers advantages toward multi-material structures. Solid-state AM processes are also being developed for specific applications where sheet metals are readily available. This chapter addresses some critical aspects of various AM techniques, including processing parameters, material types, and geometrical design effects on the final productʼs quality, functionality, and properties. Finally, we discuss the challenges, limitations, and future outlooks for AM of metallic materials.

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.

Magnetic particles (MPs), due to their unique physical and chemical properties, have emerged as promising tools in bone tissue engineering. Their incorporation into scaffolds or uptake by bone cells, combined with exposure to external magnetic fields, has been shown in various studies to enhance cell adhesion, proliferation, and osteogenic differentiation. In this review, the state-of-the-art is presented on the synthesis processes of magnetized cells (MCs) and magnetized scaffolds (MSs), as well as the biological and mechanical effects of scaffold-free MCs, cell-seeded MSs, and MC-seeded MSs under externally applied magnetic fields on bone tissue engineering. Furthermore, the specific applications of these systems is highlighted, such as non-contact mechanical stimulation, and discuss their application to advance bone tissue engineering strategies.

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.

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.

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.

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.

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.

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.

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.

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.