The development of engineered cell microenvironments for fundamental cell mechanobiology, in vitro disease modeling, and tissue engineering applications increased exponentially during the last two decades. In such context, in vitro radiobiology is a field of research aiming at understanding the effects of ionizing radiation (e.g., X-rays/photons, high-speed electrons, and high-speed protons) on biological (cancerous) tissues and cells, in particular in terms of DNA damage leading to cell death. Herein, the perspective provides a comparative assessment overview of scaffold-free, scaffold-based, and organ-on-a-chip models for radiobiology, highlighting opportunities, limitations, and future pathways to improve the currently existing approaches toward personalized cancer medicine.

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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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The effect of mechanical cues on cellular behaviour has been reported in multiple studies so far, and a specific aspect of interest is the role of mechanotransductive proteins in neuronal development. Among these, yes-associated protein (YAP) is responsible for multiple functions in neuronal development such as neuronal progenitor cells migration and differentiation while myocardin-related transcription factor A (MRTFA) facilitates neurite outgrowth and axonal pathfinding. Both proteins have indirectly intertwined fates via their signalling pathways. There is little literature investigating the roles of YAP and MRTFA in vitro concerning neurite outgrowth in mechanically confined microenvironments. Moreover, our understanding of their relationship in immature neurons cultured within engineered confined microenvironments is still lacking. In this study, we fabricated, via two-photon polymerization (2PP), 2.5D microgrooves and 3D polymeric microchannels, with a diameter range from 5 to 30 μm. We cultured SH-SY5Y cells and differentiated them into immature neuron-like cells on both 2.5D and 3D microstructures to investigate the effect of mechanical confinement on cell morphology and protein expression. In 2.5D microgrooves, both YAP and MRTFA nuclear/cytoplasmic (N/C) ratios exhibited maxima in the 10 μm grooves indicating a strong relation with mechanical-stress-inducing confinement. In 3D microchannels, both proteins’ N/C ratio exhibited minima in presence of 5 or 10 μm channels, a behaviour that was opposite to the ones observed in the 2.5D microgrooves and that indicates how the geometry and mechanical confinement of 3D microenvironments are unique compared to 2.5D ones due to focal adhesion, actin, and nuclear polarization. Further, especially in presence of 2.5D microgrooves, cells featured an inversely proportional relationship between YAP N/C ratio and the average neurite length. Finally, we also cultured human induced pluripotent stem cells (hiPSCs) and differentiated them into cortical neurons on the microstructures for up to 2 weeks. Interestingly, YAP and MRTFA N/C ratios also showed a maximum around the 10 μm 2.5D microgrooves, indicating the physiological relevance of our study. Our results elucidate the possible differences induced by 2.5D and 3D confining microenvironments in neuronal development and paves the way for understanding the intricate interplay between mechanotransductive proteins and their effect on neural cell fate within engineered cell microenvironments.

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In the present study, the influence of topographic and mechanical cues on neuronal growth cones (NGCs) and network directionality in 3D-engineered cell culture models is explored. Two-photon polymerization (2PP) is employed to fabricate nanopillar arrays featuring tunable effective shear modulus. Large variations in mechanical properties are obtained by altering the aspect ratio of the nanostructures. The nanopillar arrays are seeded with different neuronal cell lines, including neural progenitor cells (NPCs) derived from human induced pluripotent stem cells (iPSCs), I³Neurons, and primary hippocampal neurons. All cell types exhibit preferential orientations according to the nanopillar topology, as shown by neurites creating a high number of oriented orthogonal networks. Furthermore, the differentiation and maturation of NPCs are affected by the topographic and mechanical properties of the nanopillars, as shown by the expression of the mature neuronal marker Synapsin I. Lastly, NGCs are influenced by effective shear modulus in terms of spreading area, and stochastic optical reconstruction microscopy (STORM) is employed to assess the cytoskeleton organization at nanometric resolution. The developed approach, involving laser-assisted 3D microfabrication, neuro-mechanobiology, and super-resolution microscopy, paves the way for prospective comparative studies on the evolution of neuronal networks and NGCs in healthy and diseased (e.g., neurodegenerative) conditions.

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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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Micro/nanoscale additive manufacturing provides a powerful tool for advanced materials and structures with complex and precise features. For instance, the feature resolution of two-photon polymerization (2PP) can reach 200 nm. At this scale, materials properties can change, and the influence of the size effect cannot be ignored. Therefore, it is necessary to assess changes in the material mechanical properties considering size effects. In this work, several micrometric polymeric specimens are printed via 2PP, and their mechanical properties are assessed using compression tests. Detailed printing and testing procedures and the effects of parameter settings are provided. The experimental results show that the changes in the microstructures size have a direct effect on Young s modulus. In particular, a large surface-volume ratio results in a higher Young s modulus. In other words, the smaller the structure size, the higher the stiffness. The reported findings play a significant role in the development of fabrication strategies for polymeric microstructures where high stiffness accuracy is fundamental.

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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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In our original article, an affiliation is missing for the first author of the paper (Beatriz N. L. Costa). The correct affiliation information for Beatriz N. L. Costa is as follows: INL−International Iberian Nanotechnology Laboratory, Ultrafast Bio- and Nanophotonics Group, Av. Mestre JoséVeiga S/n 4715-330 Braga, Portugal; CMEMS-UMinho, University of Minho, DEI, Campus de Azurem, ́ Guimarães 4800-058, Portugal; Faculty of Mechanical, Maritime, and Materials Engineering (3mE), Department of Precision and Microsystems Engineering (PME), Delft University of Technology, Mekelweg 2, Delft 2628 CD, The Netherlands; Escola de Enxeñarí a de Minas e Enerxí a, University of Vigo, 36310 Vigo, Pontevedra, Spain. All other affiliations and the present address are the same as in the original article. This addition of the affiliation does not alter the conclusions, results, or interpretations presented in the original article. We regret the omission of this affiliation and apologize for any confusion or inconvenience this may have caused.

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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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The most widely employed approach by cell biologists to performing in vitro cell culture assays is the one using 2D plastic culture ware systems, which allows reproducibility and ease of use. Moreover, this method is cost-effective. However, in most cases, these flat surfaces lead to the formation of unrealistic 2D cell monolayers, which do not reproduce the complex configuration characteristics of native tissues in terms of dimensionality, rigidity, and topography. For this reason, a new generation of interdisciplinary scientists, working across microengineering and cell biology has started to develop engineered cell microenvironments (Huang et al., 2017) by employing advanced materials and fabrication approaches (Fan et al., 2019) over the last two decades. Depending on the level of resolution of the adopted manufacturing technique, the geometrical features of these structures can reach micrometric or even sub-micrometric dimensions comparable to the ones of cellular somas or cellular filopodia, therefore fostering cell-biomaterial interactions. The developed structures are pivotal for a better investigation of fundamental mechanobiology (Lemma et al., 2019), the optimization of in vitro disease modeling, drug/treatment screening (Gao et al., 2021), and tissue engineering (Mani et al., 2022).@en

Glioblastoma (GBM) is a devastating cancer of the brain with an extremely poor prognosis. While X-ray radiotherapy and chemotherapy remain the current standard, proton beam therapy is an appealing alternative as protons can damage cancer cells while sparing the surrounding healthy tissue. However, the effects of protons on in vitro GBM models at the cellular level, especially when co-cultured with endothelial cells, the building blocks of brain micro-vessels, are still unexplored. In this work, novel 3D-engineered scaffolds inspired by the geometry of brain microvasculature are designed, where GBM cells cluster and proliferate. The architectures are fabricated by two-photon polymerization (2PP), pre-cultured with endothelial cells (HUVECs), and then cultured with a human GBM cell line (U251). The micro-vessel structures enable GBM in vivo-like morphologies, and the results show a higher DNA double-strand breakage in GBM monoculture samples when compared to the U251/HUVECs co-culture, with cells in 2D featuring a larger number of DNA damage foci when compared to cells in 3D. The discrepancy in terms of proton radiation response indicates a difference in the radioresistance of the GBM cells mediated by the presence of HUVECs and the possible induction of stemness features that contribute to radioresistance and improved DNA repair.

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Two-photon polymerization (2PP) has provided the field of cell biology with the opportunity to fabricate precisely designed microscaffolds for a wide range of studies, from mechanobiology to in vitro disease modelling. However, a multitude of commercial and in-house developed photosensitive materials employed in 2PP suffers from high auto-fluorescence in multiple regions of the spectrum. In the context of in vitro cell biological studies, this is a major problem since one of the main methods of characterization is fluorescence microscopy of immuno-stained cells. This undesired auto-fluorescence of microscaffolds affects the efficiency of such an analysis as it often overlaps with fluorescent signals of stained cells rendering them indistinguishable from the scaffolds. Here, we propose two effective solutions to suppress this auto-fluorescence and compare them to determine the superiority of one over the other: photo-bleaching with a powerful UV point source and auto-fluorescence quenching via Sudan Black B (SBB). The materials used in this study were all commercially available, namely IP-L, IP-Dip, IP-S, and IP-PDMS. Bleaching was shown to be 61.7–92.5% effective in reducing auto-fluorescence depending on the material. On the other hand, SBB was shown to be 33–95.4% effective. The worst result in presence of SBB (33%) was in combination with IP-PDMS since the adsorption of the material on IP-PDMS was not sufficient to fully quench the auto-fluorescence. However, auto-fluorescence reduction was significantly enhanced when activating the IP-PDMS structures with oxygen plasma for 30 s. Moreover, we performed a cell culture assay using a human neuroblastoma cell line (SH-SY5Y) to prove the effectiveness of both methods in immunofluorescence characterization. SBB presented a lower performance in the study especially in presence of 2PP-fabricated microchannels and microcages, within which the differentiated SH-SY5Y cells migrated and extended their axon-like processes, since the SBB obstructed the fluorescence of the stained cells. Therefore, we concluded that photo-bleaching is the optimal way of auto-fluorescence suppression. In summary, this study provides a systematic comparison to answer one of the most pressing issues in the field of 2PP applied to cell biology and paves the way to a more efficient immunofluorescence characterization of cells cultured within engineered in vitro microenvironments.

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The mechanical properties of two-photon-polymerised (2PP) polymers are highly dependent on the employed printing parameters. In particular, the mechanical features of elastomeric polymers, such as IP-PDMS, are important for cell culture studies as they can influence cell mechanobiological responses. Herein, we employed optical-interferometer-based nanoindentation to characterise two-photon-polymerised structures manufactured with varying laser powers, scan speeds, slicing distances, and hatching distances. The minimum reported effective Young’s modulus (YM) was 350 kPa, while the maximum one was 17.8 MPa. In addition, we showed that, on average, immersion in water lowered the YM by 5.4%, a very important point as in the context of cell biology applications, the material must be employed within an aqueous environment. We also developed a printing strategy and performed a scanning electron microscopy morphological characterisation to find the smallest achievable feature size and the maximum length of a double-clamped freestanding beam. The maximum reported length of a printed beam was 70 µm with a minimum width of 1.46 ± 0.11 µm and a thickness of 4.49 ± 0.05 µm. The minimum beam width of 1.03 ± 0.02 µm was achieved for a beam length of 50 µm with a height of 3.00 ± 0.06 µm. In conclusion, the reported investigation of micron-scale two-photon-polymerized 3D IP-PDMS structures featuring tuneable mechanical properties paves the way for the use of this material in several cell biology applications, ranging from fundamental mechanobiology to in vitro disease modelling to tissue engineering.@en

A major obstacle in glioma research is the lack of in vitro models that can retain cellular features of glioma cells in vivo. To overcome this limitation, a 3D-engineered scaffold, fabricated by two-photon polymerization, is developed as a cell culture model system to study patient-derived glioma cells. Scanning electron microscopy, (live cell) confocal microscopy, and immunohistochemistry are employed to assess the 3D model with respect to scaffold colonization, cellular morphology, and epidermal growth factor receptor localization. Both glioma patient-derived cells and established cell lines successfully colonize the scaffolds. Compared to conventional 2D cell cultures, the 3D-engineered scaffolds more closely resemble in vivo glioma cellular features and allow better monitoring of individual cells, cellular protrusions, and intracellular trafficking. Furthermore, less random cell motility and increased stability of cellular networks is observed for cells cultured on the scaffolds. The 3D-engineered glioma scaffolds therefore represent a promising tool for studying brain cancer mechanobiology as well as for drug screening studies.

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One of the essential requirements to create nanoparticle (NP)-based applications and functions is the ability to control their deposition in specific locations. Many methods have been proposed, with wet direct writing (DW) techniques such as inkjet printing being the most employed. These methods generally depend on off-line and solvent-based NP synthesis leading to contamination and impurity in the final NP film as well as inhomogeneity in the deposition caused by solution-substrate interactions. This paper introduces a dry aerosol direct writing (dADW) method, which combines spark ablation-based and solvent-free NP synthesis with spatially selective deposition using aerodynamic focusing in a vacuum chamber. The challenge is to print high-resolution lines and spots of nanoparticles with a diameter < 100 nm. We study two aerodynamic nozzle concepts, a converging nozzle (CN) and a sheath gas nozzle (SGN), and investigate numerically how their design, as well as operating parameters, relate to the deposition process performance. This is quantified by three criteria: contraction factor, focusing ratio, and collection efficiency. We also compared our numerical results to experimental assays by manufacturing two SGNs and three CNs and evaluating the performance of each nozzle in terms of resolution, sharpness and thickness of the line. Using one of the SGN designs with an outlet diameter of 248 µm and an aerosol to total flow rate ratio of 0.17, we achieved a high-resolution line with a width of 67 µm, i.e., equal to 27% of the nozzle diameter, when printing < 100 nm Au NPs. The presented additive manufacturing method enables, therefore, the creation of high-resolution and sharp patterns of metallic nanoparticles, which can be employed in a wide range of applications, ranging from interconnects to optical and gas sensors.

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Microglia are the resident macrophages of the central nervous system and contribute to maintaining brain’s homeostasis. Current 2D “petri-dish” in vitro cell culturing platforms employed for microglia, are unrepresentative of the softness or topography of native brain tissue. This often contributes to changes in microglial morphology, exhibiting an amoeboid phenotype that considerably differs from the homeostatic ramified phenotype in healthy brain tissue. To overcome this problem, multi-scale engineered polymeric microenvironments are developed and tested for the first time with primary microglia derived from adult rhesus macaques. In particular, biomimetic 2.5D micro- and nano-pillar arrays (diameters = 0.29–1.06 µm), featuring low effective shear moduli (0.25–14.63 MPa), and 3D micro-cages (volume = 24 × 24 × 24 to 49 × 49 × 49 μm3) with and without micro- and nano-pillar decorations (pillar diameters = 0.24–1 µm) were fabricated using two-photon polymerization (2PP). Compared to microglia cultured on flat substrates, cells growing on the pillar arrays exhibit an increased expression of the ramified phenotype and a higher number of primary branches per ramified cell. The interaction between the cells and the micro-pillar-decorated cages enables a more homogenous 3D cell colonization compared to the undecorated ones. The results pave the way for the development of improved primary microglia in vitro models to study these cells in both healthy and diseased conditions.@en

The biomechanical properties of the brain microenvironment, which is composed of different neural cell types, the extracellular matrix, and blood vessels, are critical for normal brain development and neural functioning. Stiffness, viscoelasticity and spatial organization of brain tissue modulate proliferation, migration, differentiation, and cell function. However, the mechanical aspects of the neural microenvironment are largely ignored in current cell culture systems. Considering the high promises of human induced pluripotent stem cell- (iPSC-) based models for disease modelling and new treatment development, and in light of the physiological relevance of neuromechanobiological features, applications of in vitro engineered neuronal microenvironments should be explored thoroughly to develop more representative in vitro brain models. In this context, recently developed biomaterials in combination with micro- and nanofabrication techniques 1) allow investigating how mechanical properties affect neural cell development and functioning; 2) enable optimal cell microenvironment engineering strategies to advance neural cell models; and 3) provide a quantitative tool to assess changes in the neuromechanobiological properties of the brain microenvironment induced by pathology. In this review, we discuss the biological and engineering aspects involved in studying neuromechanobiology within scaffold-free and scaffold-based 2D and 3D iPSC-based brain models and approaches employing primary lineages (neural/glial), cell lines and other stem cells. Finally, we discuss future experimental directions of engineered microenvironments in neuroscience.@en

Glioblastoma (GBM) is a devastating cancer of the brain with an extremely poor prognosis. For this reason, besides clinical and preclinical studies, novel in vitro models for the assessment of cancer response to drugs and radiation are being developed. In such context, three-dimensional (3D)-engineered cellular microenvironments, compared to unrealistic two-dimensional (2D) monolayer cell culture, provide a model closer to the in vivo configuration. Concerning cancer treatment, while X-ray radiotherapy and chemotherapy remain the current standard, proton beam therapy is an appealing alternative as protons can be efficiently targeted to destroy cancer cells while sparing the surrounding healthy tissue. However, despite the treatment's compelling biological and medical rationale, little is known about the effects of protons on GBM at the cellular level. In this work, we designed novel 3D-engineered scaffolds inspired by the geometry of brain blood vessels, which cover a vital role in the colonization mechanisms of GBM cells. The architectures were fabricated by two-photon polymerization (2PP), cultured with U-251 GBM cells and integrated for the first time in the context of proton radiation experiments to assess their response to treatment. We employed Gamma H2A.X as a fluorescent biomarker to identify the DNA damage induced in the cells by proton beams. The results show a higher DNA double-strand breakage in 2D cell monolayers as compared to cells cultured in 3D. The discrepancy in terms of proton radiation response could indicate a difference in the radioresistance of the GBM cells or in the rate of repair kinetics between 2D cell monolayers and 3D cell networks. Thus, these biomimetic-engineered 3D scaffolds pave the way for the realization of a benchmark tool that can be used to routinely assess the effects of proton therapy on 3D GBM cell networks and other types of cancer cells.

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Biomimicking biological niches of healthy tissues or tumors can be achieved by means of artificial microenvironments, where structural and mechanical properties are crucial parameters to promote tissue formation and recreate natural conditions. In this work, three-dimensional (3D) scaffolds based on woodpile structures were fabricated by two-photon polymerization (2PP) of different photosensitive polymers (IP-S and SZ2080) and hydrogels (PEGDA 700) using two different 2PP setups, a commercial one and a customized one. The structures' properties were tuned to study the effect of scaffold dimensions (gap size) and their mechanical properties on the adhesion and proliferation of bone marrow mesenchymal stem cells (BM-MSCs), which can serve as a model for leukemic diseases, among other hematological applications. The woodpile structures feature gap sizes of 25, 50, and 100 μm and a fixed beam diameter of 25 μm, to systematically study the optimal cell colonization that promotes healthy cell growth and potential tissue formation. The characterization of the scaffolds involved scanning electron microscopy and mechanical nanoindenting, while their suitability for supporting cell growth was evaluated with live/dead cell assays and multistaining 3D confocal imaging. In the mechanical assays of the hydrogel material, we observed two different stiffness ranges depending on the indentation depth. Larger gap woodpile structures coated with fibronectin were identified as the most promising scaffolds for 3D BM-MSC cellular models, showing higher proliferation rates. The results indicate that both the design and the employed materials are suitable for further assays, where retaining the BM-MSC stemness and original features is crucial, including studies focused on BM disorders such as leukemia and others. Moreover, the combination of 3D scaffold geometry and materials holds great potential for the investigation of cellular behaviors in a co-culture setting, for example, mesenchymal and hematopoietic stem cells, to be further applied in medical research and pharmacological studies.

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The design of advanced functional devices often requires the use of intrinsically curved geometries that belong to the realm of non-Euclidean geometry and remain a challenge for traditional engineering approaches. Here, it is shown how the simple deflection of thick meta-plates based on hexagonal cellular mesostructures can be used to achieve a wide range of intrinsic (i.e., Gaussian) curvatures, including dome-like and saddle-like shapes. Depending on the unit cell structure, non-auxetic (i.e., positive Poisson ratio) or auxetic (i.e., negative Poisson ratio) plates can be obtained, leading to a negative or positive value of the Gaussian curvature upon bending, respectively. It is found that bending such meta-plates along their longitudinal direction induces a curvature along their transverse direction. Experimentally and numerically, it is shown how the amplitude of this induced curvature is related to the longitudinal bending and the geometry of the meta-plate. The approach proposed here constitutes a general route for the rational design of advanced functional devices with intrinsically curved geometries. To demonstrate the merits of this approach, a scaling relationship is presented, and its validity is demonstrated by applying it to 3D-printed microscale meta-plates. Several applications for adaptive optical devices with adjustable focal length and soft wearable robotics are presented.

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