Parametric Analysis of Critical Buckling in Composite Laminate Structures under Mechanical and Thermal Loads: A Finite Element and Machine Learning Approach.

This research focuses on investigating the buckling strength of thin-walled composite structures featuring various shapes of holes, laminates, and composite materials. A parametric study is conducted to optimize and identify the most suitable combination of material and structural parameters, ensuring the resilience of structure under both mechanical and thermal loads. Initially, a numerical approach employing the finite element method is used to design the C-section thin-walled composite structure. Later, various structural and material parameters like spacing ratio, opening ratio, hole shape, fiber orientation, and laminate sequence are systematically varied. Subsequently, simulation data from numerous cases are utilized to identify the best parameter combination using machine learning algorithms. Various ML techniques such as linear regression, lasso regression, decision tree, random forest, and gradient boosting are employed to assess their accuracy in comparison with finite element results. As a result, the simulation model showcases the variation in critical buckling load when altering the structural and material properties. Additionally, the machine learning models successfully predict the optimal critical buckling load under mechanical and thermal loading conditions. In summary, this paper delves into the study of the stability of C-section thin-walled composite structures with holes under mechanical and thermal loading conditions using finite element analysis and machine learning studies.

Imperfection-Enabled Strengthening of Ultra-Lightweight Lattice Materials.

Lattice materials are an emerging family of advanced engineering materials with unique advantages for lightweight applications. However, the mechanical behaviors of lattice materials at ultra-low relative densities are still not well understood, and this severely limits their lightweighting potential. Here, a high-precision micro-laser powder bed fusion technique is dveloped that enables the fabrication of metallic lattices with a relative density range much wider than existing studies. This technique allows to confirm that cubic lattices in compression undergo a yielding-to-buckling failure mode transition at low relative densities, and this transition fundamentally changes the usual strength ranking from plate > shell > truss at high relative densities to shell > plate > truss or shell > truss > plate at low relative densities. More importantly, it is shown that increasing bending energy ratio in the lattice through imperfections such as slightly-corrugated geometries can significantly enhance the stability and strength of lattice materials at ultra-low relative densities. This counterintuitive result suggests a new way for designing ultra-lightweight lattice materials at ultra-low relative densities.

Thermal buckling analysis of reinforced composite conical shells in acidic environments: Numerical and experimental investigation on the effects of nanoparticles.

This study investigates the effects of acid penetration and temperature on the buckling behavior of conical composite shells, to enhance structural integrity and longevity in corrosive environments. The study explores the impact of acid exposure on thermal properties and examines the efficacy of incorporating nano-silica and nano-clay in preventing buckling. Additionally, it analyzes the influence of nanoparticles on the thermal, moisture, and mechanical properties of the composite material. Experimental assessments are conducted to measure material properties during exposure to a sulfuric acid solution, providing a comprehensive understanding of the material's behavior under extreme conditions. However, due to the complexity of investigating the combined effects of temperature, acid, and nanoparticles on composite shell buckling, a combined numerical and experimental approach is adopted to predict the critical buckling load. To this end, equations of conical shells under hygrothermal loading are derived, and the critical buckling load is determined through pre-buckling analysis. The Generalized Differential Quadrature (GDQ) method is employed to solve the hygrothermal buckling of the composite shell using experimentally obtained material properties. Comparative results are presented for different nanoparticles, shell geometries, and exposure times in acidic environments. The experiments reveal that adding nanoparticles enhances mechanical properties and reduces thermal and moisture expansion coefficients. Conversely, the acidic conditions deteriorate these properties. Numerical analysis demonstrates that incorporating nanoparticles significantly increases the critical buckling temperature, with nano-silica and nano-clay particles resulting in an 11.5 % and 34.2 % increase, respectively. However, acidic environments decrease the critical buckling temperature, with reductions of 32 % for unreinforced, 29 % for nano-silica reinforced, and 46 % for nano-clay reinforced composites after three months of exposure.

Self-locking and stiffening deployable tubular structures.

Deployable tubular structures, designed for functional expansion, serve a wide range of applications, from flexible pipes to stiff structural elements. These structures, which transform from compact states, are crucial for creating adaptive solutions across engineering and scientific fields. A significant barrier to advancing their performance is balancing expandability with stiffness. Using compliant materials, these structures achieve more flexible transformations than those possible with rigid mechanisms. However, they typically exhibit reduced stiffness when subjected to external pressures (e.g., tube wall loading). Here, we utilize origami-inspired techniques and internal stiffeners to meet conflicting performance requirements. A self-locking mechanism is proposed, which combines the folding behavior observed in curved-crease origami and elastic shell buckling. This mechanism employs simple shell components, including internal diaphragms that undergo pseudofolding in a confined boundary condition to enable a snap-through transition. We reveal that the deployed tube is self-locked through geometrical interference, creating a braced tubular arrangement. This arrangement gives a direction-dependent structural performance, ranging from elastic response to crushing, thereby offering the potential for programmable structures. We demonstrate that our approach can advance existing deployment mechanisms (e.g., coiled and inflatable systems) and create diverse structural designs (e.g., metamaterials, adaptive structures, cantilevers, and lightweight panels).Weanticipate our design to be a starting point to drive technological advancement in real-world deployable tubular structures.

Calibration and Modeling of the Semmes-Weinstein Monofilament for Diabetic Foot Management.

Diabetic foot is a serious complication that poses significant risks for diabetic patients. The resulting reduction in protective sensitivity in the plantar region requires early detection to prevent ulceration and ultimately amputation. The primary method employed for evaluating this sensitivity loss is the 10 gf Semmes-Weinstein monofilament test, commonly used as a first-line procedure. However, the lack of calibration in existing devices often introduces decision errors due to unreliable feedback. In this article, the mechanical behavior of a monofilament was analytically modeled, seeking to promote awareness of the impact of different factors on clinical decisions. Furthermore, a new device for the automation of the metrological evaluation of the monofilament is described. Specific testing methodologies, used for the proposed equipment, are also described, creating a solid base for the establishment of future calibration guidelines. The obtained results showed that the tested monofilaments had a very high error compared to the 10 gf declared by the manufacturers. To improve the precision and reliability of assessing the sensitivity loss, the frequent metrological calibration of the monofilament is crucial. The integration of automated verification, simulation capabilities, and precise measurements shows great promise for diabetic patients, reducing the likelihood of adverse outcomes.

Improvement of Posterior Cruciate Ligament Buckling and Anterior Tibial Subluxation by Anterior Scar Removal of the Posterior Cruciate Ligament: A Case Report.

Posterior cruciate ligament (PCL) buckling and anterior tibial subluxation are observed in patients with insufficient anterior cruciate ligament (ACL). Here, we report the case of a patient after ACL reconstruction in whom these symptoms were improved by anterior scar resection of buckled PCL. The patient was a 46-year-old man. Six years ago, he underwent ACL reconstruction; however, his condition was not satisfactory. Magnetic resonance imaging (MRI) showed intercondylar impingement of the graft, anterior tibial subluxation, and PCL buckling. Intercondylar notchplasty and resection of the anterior scar of PCL were performed arthroscopically. Postoperative MRI showed improvement in PCL buckling and anterior tibial subluxation. His symptoms improved, and he was able to jog one year after surgery.  Anterior scar resection of PCL may improve PCL buckling and anterior tibial subluxation after ACL reconstruction.

Microstructure-Reconfigured Graphene Oxide Aerogel Metamaterials for Ultrarobust Directional Sensing at Human-Machine Interfaces.

Graphene aerogels hold huge promise for the development of high-performance pressure sensors for future human-machine interfaces due to their ordered microstructure and conductive network. However, their application is hindered by the limited strain sensing range caused by the intrinsic stiffness of the porous microstructure. Herein, an anisotropic cross-linked chitosan and reduced graphene oxide (CCS-rGO) aerogel metamaterial is realized by reconfiguring the microstructure from a honeycomb to a buckling structure at the dedicated cross-section plane. The reconfigured CCS-rGO aerogel shows directional hyperelasticity with extraordinary durability (no obvious structural damage after 20 000 cycles at a directional compressive strain of ≤0.7). The CCS-rGO aerogel pressure sensor exhibits an ultrahigh sensitivity of 121.45 kPa-1, an unprecedented sensing range, and robust mechanical and electrical performance. The aerogel sensors are demonstrated to monitor human motions, control robotic hands, and even integrate into a flexible keyboard to play music, which opens a wide application potential in future human-machine interfaces.

Low-Cycle Fatigue Properties of Bimetallic Steel Bar with Buckling: Energy-Based Numerical and Experimental Investigations.

A bimetallic steel bar (BSB) consisting of stainless-steel cladding and carbon steel substrate exhibits excellent corrosion resistance and good mechanical properties. The bimetallic structure of BSBs may affect their low-cycle fatigue performance, and current investigations on the above issue are limited. In this study, the low-cycle fatigue properties of bimetallic steel bars (BSBs) with inelastic buckling were investigated. Experiments and numerical studies were conducted to investigate the low-cycle fatigue capacity for BSBs, considering buckling. The buckling mode of BSBs is discussed. The hysteretic loops and energy properties of BSBs with various slenderness ratios (L/D) and fatigue strain amplitudes (εa) are investigated. With increases in the L/D and εa, the original symmetry for hysteresis loops disappears gradually, which is caused by the buckling. A predictive equation revealing the relation between the εa and fatigue life is suggested, which considers the effects of the L/D. A numerical modelling method is suggested to predict the hysteretic curves of BSBs. The effect of buckling on the stress and energy properties of BSBs is discussed through the numerical analysis of 44 models including the effects of the L/D, εa, and cladding ratios. The numerical analysis results illustrate that the hysteresis loops of BSBs with various εa values exhibit similar shapes. The increase in the cladding ratio reduces the peak stress and the dissipated energy properties of BSBs. The hysteresis loop energy density decreases by about 3% with an increase of 0.1 in the cladding ratio. It is recommended that the proportion of stainless steel inBSBs should be minimized once the corrosion resistance requirements are met.

Posterior Cruciate Buckling Angle Variations Are Associated with Different Patterns of Medial Meniscus Tears in Anterior-Cruciate-Deficient Knees: Results of a Prospective Comparative Magnetic Imaging Resonance Study.

BACKGROUND: The diagnosis of anterior cruciate ligament (ACL) tear relies on clinical evaluation and magnetic resonance imaging (MRI). Direct and indirect signs of ACL tear have been described with MRI evaluation. Posterior cruciate ligament (PCL) buckling has been described as an indirect radiographic sign of an ACL tear. PURPOSE: The aim of the present study was to assess the variations in PCL buckling angles in patients with ACL tears and in patients with isolated lesions in the posterior horn of the medial meniscus. In addition, the influence of different patterns of medial meniscus tears in ACL-deficient knees was investigated. Finally, the influences of risk factors such as tibial slope, delay from injury to surgery, absence of medial meniscus tear, degree of Lachman and pivot shift testing were also assessed. STUDY DESIGN: This was a cohort study. METHODS: A total of 154 patients (78 in the group with ACL tear and 76 in the control group) were assessed with MRI and lateral weight-bearing X-ray to assess PCL buckling angle and tibial slope by two independent observers. The presence of a medial meniscus bucket handle or ramp lesion of the medial meniscus was assessed and recorded at the time of surgery. RESULTS: PCL buckling angle measurement was highly reliable, with an ICC of 0.866 and 0.894, respectively, in the study group and the control group for interobserver reliability. The intrarater reliability was found to be high in PCL buckling angle for the study group [ICC = 0.955] and the control group [ICC = 0.943]. The mean angle in patients with ACL tear was 110.7 ± 15.2° and 115.3 ± 16.2° (for the two examiners) and 111.4 ± 12° and 114 ± 14.5° (for the two examiners) in patients with an intact, healthy ACL. An association emerged between bucket handle tears of the medial meniscus (p = 0.010) and a decreased PCL buckling angle and between ramp lesions of the medial meniscus and increased PCL buckling angle both (p = 0.024). CONCLUSIONS: Good inter- and intraobserver reliability for the measurement of the PCL buckling angle was observed. Increased PCL buckling angle values were observed in patients with concomitant ACL and bucket handle tears of the medial meniscus, while decreased angle values were observed in those who had ACL tear and ramp lesion of the medial meniscus. No statistically significant difference in the PCL buckling angle emerged between patients with ACL tears and those who had a healthy, intact ACL.

Nonlinear static and dynamic response of a metastructure exhibiting quasi-zero-stiffness characteristics for vibration control: an experimental validation.

This work introduces a novel metastructure designed for quasi-zero-stiffness (QZS) properties based on the High Static and Low Dynamic Stiffness mechanism. The metastructure consists of four-unit cells arranged in parallel, each incorporating inclined beams and semicircular arches. Under vertical compression, the inclined beams exhibit buckling and snap-through behavior, contributing negative stiffness, while the semicircular arches provide positive stiffness through bending-dominated behavior. The design procedure to achieve QZS is established and validated through finite element analysis and experimental investigations. The static analysis confirms a QZS region for specific displacement. Dynamic behavior is analyzed using a nonlinear dynamic equation solved using the Harmonic Balance Method, validated experimentally with transmissibility curves showing sudden jump down with effective vibration isolation. Parametric studies with varied payload masses and excitation amplitudes further verify the ability to of metastructure to attenuate vibrations effectively in low-frequency ranges.

A Simplified Analytical Model for Strip Buckling in the Pressure-Assisted Milling Process.

A simplified column-buckling model is developed to understand the buckling mechanism of thin-walled strips restrained by uniform lateral pressure in the milling process. The strip is simplified as two rigid columns connected by a rotation spring, resting on a smooth surface, restrained by a uniform pressure and loaded by an axial force. Two loading cases are considered, i.e., the dead load and the follower load. Analytical solutions for the post-buckling responses of the two cases are derived based on the energy method. The minimum buckling force, Maxwell force and stability conditions for the two cases are established. It is demonstrated that the application of higher uniform pressure increases the minimum buckling force for the column and thus makes the column less likely to buckle. For the same pressure level, the dead load is found to be more effective than the follower load in suppressing the buckling of the system. The effect of initial geometric imperfection is also investigated, and the imperfection amplitude and critical restraining pressure that prevent buckling are found to be linearly related. The analytical results are validated by finite element simulations. This analytical model reveals the buckling mechanism of strips under lateral pressure restraint, which cannot be explained by the conventional bifurcation buckling theory, and provides a theoretical foundation for buckling-prevention strategies during the milling process of thin-walled strips, plates and shells commonly encountered in aerospace or automotive industries.

Some Unfamiliar Structural Stability Aspects of Unsymmetric Laminated Composite Plates.

It is widely recognized that certain structures, when subjected to static compression, may exhibit a bifurcation point, leading to the potential occurrence of a secondary equilibrium path. Also, there is a tendency of deflection increment without a bifurcation point to occur for imperfect structures. In this paper, some relatively unknown phenomena are investigated. First, it is demonstrated that in some conditions, the linear buckling mode shape may differ from the result of geometrically nonlinear analysis. Second, a mode jumping phenomenon is described as a transition from a secondary equilibrium path to an obscure one as a tertiary equilibrium path or a second bifurcation point. In this regard, some non-square plates with unsymmetric layer arrangements (in the presence of extension-bending coupling) are subjected to a uniaxial in-plane compression. By considering the geometrically linear and nonlinear problems, the bucking modes and post-buckling behaviors, e.g., the out-of-plane displacement of the plate versus the load, are obtained by ANSYS 2023 R1 software. Through a parametric analysis, the possibility of these phenomena is investigated in detail.

Neural Network-Based Surrogate Modeling for Buckling Performance Optimization of Lightweight-Composite Collapsible Tubular Masts.

The collapsible tubular mast (CTM) can be compactly folded for transport and deployed in orbit to serve as a key structural element. Once deployed, the CTM is vulnerable to buckling under axial load and bending moments, compromising its load-bearing capacity. The intricate relationship between the CTM's cross-section and its buckling behavior poses a significant challenge for designers. This is due to the ultra-thin nature of the CTM, which gives rise to highly localized buckling modes rather than global ones. To overcome this challenge, we developed surrogate models using a neural network (NN) trained with data from finite element analysis (FEA). These NN-based surrogate models provide high computational accuracy in predicting nonlinear buckling loads under axial force and bending moments around the two principal axes of the CTM's cross-section, achieving R2 values of 0.9906, 0.9987, and 0.9628, respectively. These models also significantly improve computational efficiency, reducing prediction time to a fraction of a second compared to several minutes with FEA. Furthermore, the NN-based surrogate models enable the usage of the non-dominated sorting genetic algorithm (NSGA-II) for multi-objective optimization (MOO) of the CTMs. These models can be integrated in the NSGA-II algorithm to evaluate the objective function of existing and new individuals until a set of 1000 non-dominated solutions, i.e., cross-sectional configurations optimizing buckling performance, is identified. The proposed approach enables the design of ultra-thin CTMs with optimized stability and structural integrity by promoting design decisions based on the quantitative information provided by the NN-based surrogate models.

Comparison of Chandelier-Assisted versus Standard Scleral Buckling for the Treatment of Primary Rhegmatogenous Retinal Detachment: A Systematic Review and Meta-Analysis.

INTRODUCTION: Compare the anatomical and functional outcomes, operation duration, and complication rates between standard scleral buckling (SSB) and chandelier-assisted scleral buckling (CSB) for phakic eyes with rhegmatogenous retinal detachment (RRD). METHODS: PubMed, Embase, and Cochrane Library databases were searched from inception to June 2024. The primary endpoint will be set as a final success. The secondary endpoint will be primary success, operation time, and final BCVA. RESULTS: Our meta-analysis showed that there is no statistical difference between CSB and SSB for the final success rate (RR = 1.00, 95% CI = 0.97-1.03). For the primary success rate, there is no statistical difference between CSB and SSB (RR = 1.00, 95% CI = 0.94-1.06). For operation time, our meta-analysis showed that the CSB group is less than the SSB group (pooled MD = -15.8, 95% CI = -22.60 to -9.00). For postoperative complications, our study shows that the CSB group presented with lower pooled risk than the SSB group (RR = 0.59, 95% CI = 0.41-0.89). There is a trend that the ERM formation risk is higher in the CSB group if there is no routine suture for the sclerotomy (p = 0.08). CONCLUSION: CSB showcases a significantly reduced operation duration and less postoperative complication in contrast to the SSB group, maintaining comparable primary and ultimate anatomical success rates as well as final BCVA.

Efficacy and visual outcomes of the foldable capsular buckle scleral buckling in rhegmatogenous retinal detachment.

Objective: To investigate the difference in the effectiveness and refraction of the foldable capsular buckle (FCB) in rhegmatogenous retinal detachment (RRD). Methods: Six patients with simple RRD were treated for FCB scleral buckling at Xiamen Eye Center of Xiamen University from October 2023 to February 2024. The parameters assessed included demographic data, clinical data such as preoperative ocular axis, corneal endothelial count, macular foveal thickness, operative time, preoperative and final follow-up intro ocular pressure (IOP), retinal attachment status, and postoperative complications. Refractive change before and after surgery, including sphere, cylinder degree, spherical equivalent, and absolute spherical equivalent difference were compared. Results: All six patients with sound retinal reattachment after FCB scleral buckling, including two men and four women, mean age 41.33 ± 12.40 years old, duration before surgery onset to 7.17 ± 7.16 days, FCB mean operation time 36.67 ± 13.07 min, Preoperative IOP mean 13.35 ± 2.64 mmHg and mean 21.12 ± 8.09 mmHg of final follow-up IOP; there was no significant difference between preoperative IOP and follow-up IOP (p = 0.050). The preoperative sphere range was -6.25 to +2.50 D, and the cylinder range was -2.50 to +1.00 D; the absolute spherical equivalent difference before and after was 1.60 ± 1.69 degrees. Conclusion: FCB can achieve retinal reattachment and restore visual function in cases of RRD. The shorter duration of external scleral buckle compression with FCB suggests that FCB scleral buckling holds greater promise in the clinical treatment of RRD caused by retinal tears.

Vitrectomy versus scleral buckle for retinal detachment without posterior vitreous detachment.

To compare the effectiveness and safety of scleral buckling and pars plana vitrectomy in treating retinal detachment without posterior vitreous detachment. A total of 88 eyes of 83 patients with retinal detachment without prior posterior vitreous detachment were investigated retrospectively. Group A comprised patients who underwent scleral buckling (n = 47) and Group B (n = 36) patients who were treated with pars plana vitrectomy. Anatomical success, postoperative visual acuity, and ocular adverse events were evaluated. The primary and final anatomical success rate showed a nonsignificant difference (p = 0.465 and p = 0.37 respectively). No significant difference was observed in the reoperation rate or development of epiretinal membrane between the groups (p = 0.254 and p = 0.254 respectively). However, scleral buckling resulted in significantly better visual acuity at the last follow-up (0.12 ± 0.23) compared to pars plana vitrectomy (0.37 ± 0.46, p = 0.001). The incidence of cataract progression was also significantly higher in the pars plana vitrectomy group (46%) compared to the scleral buckling group (10%, p < 0.001). Scleral buckling and pars plana vitrectomy show similar success rates in treating retinal detachment without vitreous detachment. However, due to less cataract progression and better visual acuity outcomes, scleral buckling is recommended for these cases. Determining vitreous status before surgery is crucial for optimal outcomes.

Advancements in Myopic Macular Foveoschisis Research.

BACKGROUND: Presently, the global prevalence of myopia and high myopia reaches approximately 1.95 billion and 277 million individuals, respectively. Projections suggest that by 2050, the number of people with myopia may rise to 4.758 billion and those with high myopia to 938 million. In highly myopic eyes, the occurrence of MF is reported to be as high as 8-33%. SUMMARY: This review comprehensively addresses the classification, pathogenesis, natural progression, concomitant pathologies, and therapeutic strategies for macular foveoschisis in highly myopic patients. KEY MESSAGES: In recent years, macular foveoschisis has emerged as a prevalent complication in individuals with high myopia, primarily resulting from the combination of inward traction by vitreoretinal adhesions and outward traction exerted by posterior scleral staphyloma on the retina. While some maintain partial visual stability over an extended period, others may progress to macular holes or even retinal detachment. For highly myopic patients with macular foveoschisis, the mainstay procedures are vitrectomy, macular buckle, and posterior scleral reinforcement. However, there is controversy about whether to perform inner limiting membrane peeling and gas filling.

Examination of Beam Theories for Buckling and Free Vibration of Functionally Graded Porous Beams.

This paper examines the accuracy and effectiveness of various beam theories in predicting the critical buckling loads and fundamental frequencies of functionally graded porous (FGP) beams whose material properties change continuously across the thickness. The beam theories considered are classical beam theory (CBT), first-order shear deformation beam theory (FSDBT), third-order shear deformation beam theory (TSDBT), and the broken-line hypothesis-based shear deformation beam theory (BSDBT). Governing equations for those beam theories are formulated by using the Hamilton's principle and are then solved by means of the generalised differential quadrature method. Finite element simulation solutions are provided as reference results to assess the predictions of those beam theories. Comprehensive numerical results are presented to evaluate the influences of the porosity distribution and coefficient, slenderness ratio, and boundary condition on the difference between theoretical predictions and simulation results. It is found that the differences significantly increase as the porosity coefficient rises, and this effect becomes more noticeable for the rigid beam with a smaller slenderness ratio. Nonetheless, the results produced by the BSDBT are always the closest to simulation ones. The findings in this paper will contribute to the establishment of more refined theories for the mechanical analysis of FGP structures.

Clinical features of retinal detachment treated with segmental scleral buckling.

PURPOSE: Our study aims to evaluate the surgical outcomes and clinical features of retinal detachment (RD) cases treated with segmental scleral buckling (SB), elucidating the role of segmental SB as a vital option in specific situations during the current era. METHODS: We retrospectively reviewed 128 eyes with primary rhegmatogenous RD that underwent segmental scleral buckling between November 2008 and December 2020. Clinical features and success rates were recorded and analyzed. RESULTS: A total of 128 eyes were included. The patient's ages ranged from 12 to 72 years, with a median age of 45. Most of the eyes were phakic (97%). Regarding the type of break, 47% were holes, and flap tears were found in 68 cases (53%). The break locations were superior-temporal (54%), inferior-temporal (31%), superior-nasal (9.5%), and inferior-nasal (5.5%). The length of the SB applied ranged from 3.5 to 8.0 clock hours, with a median of 6.0. Primary success was achieved in 121 eyes, and recurrence occurred in 7 eyes. All recurrent RD cases reattached after undergoing secondary VT. The causes of failure included 2 break reopens, 1 missed break, and 4 eyes with proliferative vitreoretinopathy. The single-surgery anatomic success (SSAS) rate for segmental SB was 94.5%. The final success rate was 100%. CONCLUSIONS: For phakic, low complexity retinal detachment in our study, segmental scleral buckling emerges as a surgical option with a high primary success rate and a lower incidence of complications.

Hard- and Soft-Coded Strain Stiffening in Metamaterials via Out-of-Plane Buckling Using Highly Entangled Active Hydrogel Elements.

Metamaterials show elaborate mechanical behavior such as strain stiffening, which stems from their unit cell design. However, the stiffening response is typically programmed in the design step and cannot be adapted postmanufacturing. Here, we show hydrogel metamaterials with highly programmable strain-stiffening responses by exploiting the out-of-plane buckling of integrated pH-switchable hydrogel actuators. The stiffening upon reaching a certain extension stems from the initially buckled active hydrogel beams. At low strain, the beams do not contribute to the mechanical response under tension until they straighten with a resulting step-function increase in stiffness. In the hydrogel actuator design, the acrylic acid concentration hard-codes the configuration of the metamaterial and range of possible stiffening onsets, while the pH soft-codes the exact stiffening onset point after fabrication. The utilization of out-of-plane buckling to realize subsequent stiffening without the need to deform the passive structure extends the application of hydrogel actuators in mechanical metamaterials. Our concept of out-of-plane buckled active elements that stiffen only under tension enables strain-stiffening metamaterials with high programmability before and after fabrication.