Pneumatically controlled lattices with tunable mechanical behavior

Abstract

Buckling is a common failure mode in lattice structures, limiting their use in some applications. The tendency of a strut to buckle is related to the local nodal connectivity. In this work, we introduce a pneumatic actuation strategy to actively tune the mechanical behavior of lattice structures by locally reconfiguring their effective nodal connectivity. By selectively inflating pneumatic actuators embedded in the lattice into spatial patterns with varying levels of connectivity, we demonstrate a method to modulate mechanical properties, including stiffness and buckling response. The most reinforced pattern can lead to 121.6% improvement in buckling strength relative to the regular lattice itself. Additionally, the post-buckling behavior of pneumatically controlled lattices can be programmably tuned by varying the input air pressure signals. The pneumatically controlled lattices reduced the peak acceleration by 50.9%, demonstrating enhanced impact mitigation capability. These results show that pneumatic actuation provides a versatile approach to enhancing structural performance under both static and dynamic loading. Since this strategy does not rely on multi-material interfaces or specific cell topologies, it can be broadly applied to optimize a wide range of lattice architectures.

Lattice structures enable programmable mechanics but often require complex manufacturing or electronic systems. Xiaoheng Zhu, Yucong Hua and colleagues present a pneumatic control method that is easily reconfigurable and suitable for diverse structural applications

Introduction

Periodic lattices have long been used in engineering for their combination of desirable properties, including high stiffness, high strength, and low mass. The relationship between topology and the mechanical response has been studied^1–3, leading to reliable models that have enabled such lattices to be widely incorporated in applications in civil engineering, aerospace, and more.

The topology of the cellular architecture plays a significant role in determining the deformation mode and, consequently, the buckling resistance of lattices^4–6. For example, increasing the nodal connectivity can shift the deformation mode from bending-dominated to stretching-dominated (e.g., going from a hexagonal to a triangular lattice), the latter of which exhibits superior buckling resistance⁴. Recent work has explored creative topologies and how these can result in superior mechanical properties. Examples include Neovius lattices⁷, sea sponge-inspired lattices⁸, and inverse-designed truss lattices⁶.

However, in all of the above cases, the topology is fixed at the time of manufacturing, resulting in a specific set of mechanical properties. Many engineering applications could benefit from structures that behave differently (i.e., exhibit a different stress–strain response) in different circumstances. This has led to increasing interest in developing more adaptive lattices with tunable mechanical properties. Examples of such lattices include strain-rate-dependent metamaterials⁹, liquid-induced transformable cellular solids¹⁰, tunable multi-material lattices¹¹, shape memory metamaterials¹², and reprogrammable chiral lattices¹³. Other related strategies include jamming-enhanced adaptive lattices for impact protection¹⁴, electromagnetic connectivity control¹⁵, mechanically confined metamaterials¹⁶, and pneumatically actuated pattern-transforming systems¹⁷. However, most of these tunable lattice designs^10–12 are constrained to specific structural configurations and lack generality, making them difficult to adapt for broader engineering applications that require versatile and scalable tunability. As a result, identifying a generalizable, rapid, and precise control strategy to modify the nodal connectivity and thereby accurately regulate the buckling of the struts could enable new capabilities in tunable structures. Interestingly, recent developments in soft robotics also demand similar control strategies that are rapid^18,19 and generalizable^20–22. Therefore, solutions commonly employed in soft robotics, such as pneumatic actuators, provide a promising control strategy.

In this work, we introduce a pneumatic actuation strategy to actively tune the mechanical behavior of lattice structures by locally reconfiguring their effective nodal connectivity (Fig. 1). Pneumatic actuators, typically deformable sealed chambers, convert the energy of compressed air or gas into shape transformations or mechanical motion. Pneumatic actuators have been developed with various materials^23,24, shapes^25–27, and mechanisms²⁸, enabling functions such as adaptive locomotion^29–31, real-time shape reconfiguration³², and active control of mechanical properties^33,34. These versatile pneumatic actuators offer new possibilities for precise control of strut buckling. By introducing different actuation patterns, regular bending-dominated lattices can be made to behave more like stretching-dominated lattices. This strategy can be used to control both the buckling strength and post-buckling behavior of pneumatically controlled lattices under different loading conditions, including uniaxial compression, impact loading, and point loading. The pneumatic strategy proposed in this work is tunable, reconfigurable, and employable in a wide range of existing lattice structures made from different engineering materials^35,36. It enables real-time modulation of mechanical behavior, thereby expanding the applicability of lattice structures to more demanding and dynamic environments.

Fig. 1. Overview of the pneumatically controlled lattices.

Pneumatic actuators are embedded into regular lattices, with inflation actively regulated by air pressure. By inflating different spatial patterns, tunable mechanical properties can be achieved. Potential application scenarios include static loading, impact mitigation, and adaptive structures.

Results

Design and characterization of pneumatic actuators

In this work, we use pneumatic actuators to control the buckling of struts. The hollow cylindrical pneumatic actuators are inserted into the interstices of the lattices. Since the inflation of the actuators must influence the buckling of the struts in the lattice, there are limits on how different the moduli of the actuator material and lattice material can be. We chose a thermoplastic polyurethane (TPU) for the lattice and a silicone rubber (Dragon Skin 10) for the actuators. Mechanical characterization of the TPU and silicone rubber materials is detailed in the Supplementary Information (Figs. S1 and S2). The uninflated diameter of the pneumatic actuators precisely matches the lattice dimensions.

When not inflated, they do not influence the behavior of the lattice. However, when inflated, the actuators resist the buckling of adjacent struts. Inflating different patterns of actuators leads to different buckling behaviors (Fig. 1). Details of the actuators and lattices can be found in the “Methods” section and the Supplementary Information.

To understand the fundamental response of the actuators themselves before integrating them into the lattice, we first characterized the inflation behavior of a single actuator. As the internal air pressure increases from 0 to 15 psi, the actuators exhibit a nonlinear increase in volume, with a sharp increase observed beyond 9 psi (Fig. 2A). To evaluate actuator hysteresis, we also conducted 50 consecutive inflation-deflation cycles on individual actuators and recorded their pressure–volume behavior at cycles 1, 10, and 50. As shown in Fig. S3, the hysteresis effects remained minimal across cycles. All tests were performed on three randomly picked actuators, and the results were statistically analyzed. To quantify the possible force exerted by an actuator on the lattice structure, we placed force sensors on the surface of the actuators and inflated the actuators with increasing air pressure from 3 to 12 psi. We found that the force output increased with pressure from approximately 1 N at 3 psi to 10 N at 12 psi (Fig. 2B). To balance sufficient actuation with actuator integrity and pump limitations, we selected an actuation pressure of 9 psi for all subsequent experiments.

Fig. 2. Mechanical characterization of lattices with pneumatically controlled buckling strength.

A Volume change of actuators as a function of pressure, normalized by initial volume V₀. Error bars represent the standard deviation across five actuators. B Force output of actuators under increasing pressure. C Stress–strain curves comparing unfilled and filled lattices. Orange and green correspond to 1 × 3 lattices and single cells, respectively; solid and dashed lines represent unfilled and filled states. D Stress–strain curves for square lattices with 12 actuators in filled and unfilled conditions.

Next, we investigated how the presence of inflated actuators influences the buckling behavior of struts (Fig. 2C). We studied the effect of actuators on individual cells (i.e., a single square unit cell and 1 × 3 lattice). Please note, these lattices have the same unit cell size as the 6 × 6 lattice used in the later part. We first obtained the loading curves of these lattices under uniaxial compression. Then, we tested the mechanical behavior of these lattices with inflated actuators. For a single unit cell, the actuator causes the adjacent struts to buckle outward during compression. As a result, a single actuator does not significantly improve the buckling strength, which only increases slightly from 466.5 to 487.9 kPa. However, the buckling strain increases from 0.06 to 0.09. This confirms that the inflated actuator can be used to control the buckling of the lattice. For the 1 × 3 lattice, the inflated actuators result in substantial improvement to buckling strength (providing an increase of 39.3%, from 229.1 to 319.3 kPa) and buckling strain (providing an increase from 0.05 to 0.09). These results indicate that actuator–actuator interactions across multiple cells can more effectively stabilize the structure under compressive loading.

After understanding the benefits of inflated actuators on individual cells, we further studied their effect on larger 6 × 6 square lattices. We first confirmed that the presence of uninflated actuators (i.e., air pressure of 0 psi) does not appreciably affect the constitutive behavior of a lattice under compression (Fig. S4 in SI). We then explored a localized inflation pattern where 12 actuators were placed along both diagonals of the lattice (Fig. 2D). When inflated, these actuators led to a significant improvement in both buckling strength and buckling strain. Specifically, the buckling stress increases from approximately 60 to 155 kPa, and the buckling strain increases from 0.012 to 0.03. This confirms that inflating a localized set of pneumatic actuators can effectively tune the global buckling behavior of the lattice.

Lattices controlled by pneumatic actuators

The lattices in this study can achieve a wide range of mechanical properties by tuning two design parameters: (1) the actuator inflation pattern and (2) the number of inflated actuators. We first systematically studied how different actuator inflation patterns can affect the structural response of a bending-dominated 6 × 6 square lattice.

Bending-dominated lattices are more susceptible to buckling, relative to stretching-dominated lattices⁴. For 2D and 3D lattices, the minimum nodal connectivities for stretching-dominated lattices are Z = 6 and Z = 12, respectively. By inflating (or deflating) interstitial pneumatic actuators, we can increase (or decrease) the effective local nodal connectivity of the cell. By triggering different local-stiffening strategies, the global buckling behavior of the lattice can be tuned. Here, we introduce three inflation patterns with different effective local cell nodal connectivity, denoted as strong, medium, and weak. In the 6 × 6 square lattice, a minimum of 6 actuators is required to fully populate either a diagonal (corresponding to the strong pattern) or a single column (corresponding to the medium pattern). Therefore, we began with 6 actuators.

To provide a theoretical framework for interpreting the influence of different inflation patterns, we introduce the concept of nodal connectivity as a qualitative design principle. In our definition, a node’s connectivity includes both the original structural connections inherent to the lattice geometry and any additional connections introduced by actuator inflation. A connection is considered present when a node is either directly linked to a neighboring strut (by design) or when an inflated actuator is placed adjacent to the midpoint of a wall segment shared by two struts, effectively coupling their ends. This is referred to as actuator-induced connections. For example, in a regular 2 × 2 unit cell, the center node typically has four connections due to the linkage between neighboring struts. If an actuator is inflated within the adjacent 1 × 1 cell, it adds one more effective link at that node, increasing its connectivity from four to five. Specifically, we define two metrics: (1) maximum nodal connectivity, referring to the highest number of actuator-induced connections associated with any node of a 2 × 2 unit cell and (2) total nodal connectivity within the unit cell, which counts the total number of such actuator-induced connections across all nodes of the 2 × 2 unit cell. Across different inflation patterns, a higher maximum or total nodal connectivity within a unit cell correlates with enhanced local resistance to buckling. Consequently, this local reinforcement influences the global mechanical performance of the lattice. This framework allows us to qualitatively evaluate the effectiveness of various inflation strategies in modifying lattice behavior.

As shown in Fig. 3A, in the strong pattern, the actuators are placed diagonally along the 6 × 6 square lattice. Due to the symmetry of the lattice, placing actuators along the opposite diagonal line results in an equivalent configuration. Within a representative 2 × 2 local cell, the maximum nodal connectivity is 6, and the total nodal connectivity across the cell is 28. In the medium pattern, the six actuators are aligned vertically in a single column (here, the third column), resulting in vertical adjacency between actuators. Placing them in the fourth column would yield an equivalent layout. For a corresponding 2 × 2 local cell, the maximum nodal connectivity is 5, and the total nodal connectivity remains 28. In the weak pattern, actuators are spaced to avoid direct adjacency. This layout also yields a maximum nodal connectivity of 5, but the total nodal connectivity of the 2 × 2 region is reduced from 28 to 26. The weak and medium patterns preserve the bending-dominated characteristics of the square lattice, as their local nodal connectivity remains at Z = 5, while the strong pattern increases the local nodal connectivity to Z = 6, enabling a transition from a bending-dominated to a stretching-dominated configuration. Comparing the weak and medium patterns, although both of them have the same maximum nodal connectivity, the medium pattern has a higher total nodal connectivity in the 2 × 2 local cell. We then conducted uniaxial compression tests, as shown on the left side of Fig. 3A, to test the mechanical responses of each actuation pattern. In these experiments, we used a square lattice with a relative density of 0.245, in which all 36 interstitial sites were filled with pneumatic actuators. Then, a pattern of actuators (weak/medium/strong) was inflated. The buckling strength of the weak pattern is 103.5 kPa, whereas that of the strong pattern is 134.4 kPa. The medium pattern outperformed the weak pattern as well.

Fig. 3. Mechanical response of lattices under different pneumatic inflation patterns.

A Left: Photographs of lattice deformation at 0, 0.2, and 0.4 strain under different inflation patterns. Inflated actuators appear black, uninflated ones white. Right: Schematic infill patterns with nodal connectivity annotations. B Buckling strength map for all tested lattices. Black dots represent regular lattices with varying relative densities; the dashed line shows scaling behavior. Orange dots show lattices with fixed relative density (ρ = 0.245) and varying numbers of inflated actuators. Dot outlines denote the inflation pattern.

Another parameter that influences the buckling strength of the lattice is the number of inflated actuators. Since increasing the number of actuated elements introduces more local stiffening areas, we can expect that higher levels of actuation will result in improved buckling resistance. In this work, we gradually increased the inflated actuator number from 6. However, beyond 12 actuators, the scattered inflation configuration used in the weak pattern becomes geometrically constrained and ineffective (i.e., it is no longer possible to allocate isolated actuators without neighboring actuators). Because of that constraint, our analysis of inflation strategies is limited to configurations containing 6–12 actuators.

Compared to the six-actuator cases, increasing the number of actuators to 12 led to a significant improvement in buckling strength (Fig. 3B). Specifically, the strong pattern exhibited a 22.8% increase in buckling strength, rising from 134.4 to 165.1 kPa. Similarly, the weak pattern showed a 24.5% increase, from 103.5 to 128.9 kPa.

In traditional lattice design, improving buckling resistance typically requires increasing beam thickness and relative density, following a scaling law between strength and density³⁷. To benchmark this conventional strategy, we fabricated passive square lattices with relative densities ranging from 0.245 to 0.395 and measured their buckling strengths (black data points in Fig. 3B), which increased from 74.5 to 130.6 kPa accordingly. In contrast, our pneumatic strategy modifies mechanical response without altering the base lattice geometry. All actuator-related data points (orange markers) correspond to lattices with a fixed relative density of ρ = 0.245, and the x-axis in Fig. 3B reflects the number of inflated actuators rather than a change in density. This representation allows us to isolate the effect of actuator inflation while keeping geometric parameters constant. This comparison illustrates that selective pneumatic actuation can enhance the buckling strength of low-density lattices beyond that of denser passive structures. For instance, inflating 12 actuators in the strong pattern within a ρ = 0.245 lattice (same configuration as in Fig. 2D) achieved a 121.6% increase in buckling strength over the non-inflated case. Even the six-actuator strong pattern surpassed the performance of a geometrically reinforced lattice with ρ = 0.395. These results suggest that our strategy provides an efficient alternative to strut thickening for enhancing buckling resistance and tuning mechanical behavior. Finally, we note that this pneumatic control strategy is also compatible with stretching-dominated lattices. For example, Fig. S5 in the SI demonstrates its effectiveness when applied to triangular architectures. To further evaluate the generalizability of our approach, we performed finite element simulations applying the same control strategy to lattices composed of stiffer materials. As illustrated in Fig. S6, the inflation-induced modulation of buckling behavior remains effective even in high-stiffness systems, provided that the actuator and lattice materials are appropriately matched in their mechanical properties.

Impact mitigation

Next, we considered the behavior of these lattices subjected to impact loading. In this set of experiments, we compared three different actuator infill patterns. The first pattern included no pneumatic actuators and served as a control group, referred to as the “no infill” case. The second and third patterns both included 12 actuators, but with different spatial arrangements. In the medium pattern, actuators were placed linearly along the third and fifth columns of a 6 × 6 lattice (which is symmetric to placing them in the second and fourth columns), resulting in a maximum nodal connectivity of Z = 5. This configuration provided moderate resistance to buckling. In the strong pattern, actuators were placed along both diagonals of the lattice, resulting in a nodal connectivity of 6 and a correspondingly higher resistance to buckling. Here, we characterized the ability of these lattices to provide protection during impact by dropping the samples from a given height, h, while recording the acceleration with a piezoelectric accelerometer attached to their top surfaces. As shown in Fig. 4A, we attached the lattice to a plate and then released the plate to initiate free-fall.

Fig. 4. Impact mitigation performance of pneumatically controlled lattices.

A Schematic illustration of the drop test setup. B Measured acceleration of the lattice during impact events. C and D First and second peak accelerations under different inflation pressures. Gray bars correspond to 3 psi, and orange bars to 9 psi. The inset in D shows the tested inflation patterns.

The resulting acceleration data (Fig. 4B) includes both positive peaks and negative peaks. Positive peaks result from the initial impact, while the negative peaks result from the lattice bouncing after the impact. Here, we measured two negative peaks to characterize the impact mitigation effect brought by our pneumatic system. We examined the impact mitigation capability of our pneumatically controlled lattices with two inflation pressures: 3 and 9 psi. Figure 4C shows the first peak acceleration. With the inflation pressure at 3 psi, the medium inflation pattern can reduce the peak acceleration from 612.1 to 483.2 cm/s². The strong pattern can further reduce the peak acceleration to 452.8 cm/s². For the medium inflation pattern, increasing the inflation pressure from 3 to 9 psi reduces the first peak acceleration from 483.2 to 404.9 cm/s². Increasing the inflation pressure reduces the first peak acceleration of the strong pattern from 452.8 to 300.5 cm/s². The second peak acceleration shows the same trend as the first peak acceleration (Fig. 4D). The high-pressure strong pattern (inflation pressure P = 9 psi) can reduce 79.8% of the second peak loading (reduced from 252.0 to 50.7 cm/s²). Similar to the static buckling resistance tests discussed earlier, the stretching-dominated “strong” pattern also has superior impact properties relative to the bending-dominated “medium” pattern, according to the metrics used here. Overall, by inflating different patterns of actuators, a lattice can be converted between bending-dominated and stretching-dominated. This could enable a wide range of tunability for both static and impulsive loading. We acknowledge that the enhanced impact mitigation observed in our experiments may arise not only from increased structural stiffness but also from internal damping mechanisms. Specifically, air flow within the actuators and friction at the actuator–lattice interfaces could introduce additional energy dissipation, which our current measurements do not explicitly separate from stiffness-related effects. Nonetheless, the tests provide some information about the relative performance of different inflation patterns in mitigating the impact.

Tunable, reconfigurable post-buckling behavior

Structural buckling strength is an important parameter, representing the maximum loading of the structure without losing stability. However, the behavior after buckling is also important for manipulating loading characteristics such as energy absorption.

Here, we describe how the pneumatic actuators can be used to influence the post-buckling response. We inflated all 36 actuators in a 6 × 6 lattice with time-varying air pressure inputs to demonstrate reprogrammable post-buckling behavior of the pneumatically controlled lattice (Fig. 5A). We used three types of time-varying air pressure signals: (1) Square wave, (2) Sine wave, (3) Linear increase, i.e.,

$$P\left(t\right)=\frac{p_{\max }}{2}\times \left(1+\text{sgn}\left(\sin \left(\omega t\right)+D\right)\right)$$ 1a

$$P\left(t\right)=p_{\max }\times \sin \left(\omega t\right)+C$$ 1b

$$P\left(t\right)=k\times t$$ 1c

where P is the pressure as a function of time t, p_max is the maximum pressure, ω is the frequency, k is the slope. Figure 5B and C shows the loading curves with square function pressure inputs. Here we set p_max to be 9 psi, following the previous experiments. We started varying the input air pressure after the buckling strain was reached (ε = 0.02). By increasing the frequency of the pressure oscillation, more peaks appeared on the loading curve within a given loading strain. It is also noticeable that although we input a square wave, the oscillations of the loading curve are not perfect squares. A pattern of a gentle increase in stress followed by a sudden drop in stress was observed in experiments. Figure 5D and E shows the pressure–time input for sine waves of two different frequencies. The corresponding stress–strain plots are shown to the right of these.

Fig. 5. Post-buckling behavior of pneumatically controlled lattices under time-varying pressure inputs.

A Schematic illustration of the test setup. Inflation begins after the buckling strain is reached (ε = 0.02), and a time-dependent pressure input P(t) is applied to all actuators. B, C Square-wave pressure inputs of different frequencies and the corresponding stress–strain responses. D, E Sine-wave pressure inputs of different frequencies and their associated stress–strain curves. F, G Post-buckling responses generated using monotonic pressure inputs, including continuously increasing and decreasing pressure profiles.

A monotonic increase or decrease in air pressure might be more practical, as shown in Fig. 5F and G. For example, by continuously increasing the air pressure, the lattice post-buckling response can be flattened (Fig. 5F). This is often desirable in the design of energy-absorbing protective materials, where a flat post-buckling response maximizes the amount of energy absorbed without exceeding a defined critical load. Of course, other post-buckling responses can be achieved, if desired, by choosing other monotonic pressure inputs (e.g., Fig. 5G).

Behavior of 2D pneumatically controlled lattices under 3D complex loading

Next, we consider how the assembled lattice structures respond to asymmetric point loads. We assembled five 2D square lattices together to form a 3D pentagonal structure. We applied a localized point load near one corner of the pentagon (instead of at the centroid of the pentagon), as shown in Fig. S7, which can create an asymmetric stress distribution across the five lattices, resulting in observable tilting of the top surface (Fig. 6A).

Fig. 6. Performance of pneumatically controlled lattices under non-uniform point loading.

A Schematic and time-lapse images showing deformation of the lattice stabilizer under increasing vertical point load. B Inflation patterns used in the experiments. C Schematics of different stabilization strategies applied to the same loading point. D Bending angle of the top surface versus vertical displacement of the loading rod, indicating stabilization effectiveness across inflation patterns.

To mitigate this deformation, we explored three inflation strategies using the actuator patterns introduced earlier (Fig. 6B): (1) No inflation, in which all actuators remain uninflated; (2) Uniform inflation, in which all five lattices follow the same strong pattern; (3) Adaptive inflation, in which actuator patterns are selected based on proximity to the load: the strong pattern is applied to lattices near the loading rod to provide enhanced local resistance, the medium pattern is used in the central lattices, and no actuators are inflated in the lattice farthest from the load (Fig. 6C). This adaptive strategy introduces spatially programmed asymmetry in stiffness, enabling better redistribution of load and improved overall structural resilience under non-uniform loading.

Figure 6D shows the relation between the bending angle and the loading rod displacement for the three stabilization strategies. Compared to the no-inflation case, the uniform inflation strategy reduced the final tilting angle (at δ = 12 mm displacement) from 8.17° to 7.01°. The adaptive inflation strategy further reduced the angle to 5.71°, demonstrating the benefit of localized, programmable reinforcement. These results highlight the potential of tunable, reprogrammable lattices for adaptive structural applications under complex loading conditions.

Discussion and conclusion

We have designed pneumatic actuators to improve and tune the buckling behavior of lattices. By inflating different patterns of actuators (strong, medium, and weak), different bending-dominated or stretching-dominated behaviors can be achieved within the same structure. Under static loading and impact loading, the pneumatically controlled lattices can be tuned to achieve superior mechanical properties relative to the lattices without pneumatic actuation. Further, we realized versatile post-buckling behavior, including flattening the post-buckling plateau to maximize energy absorption without exceeding a critical load. Finally, we used the inflation patterns described above in 3D assemblies of the lattices to control the deformation of the structure in response to non-uniform point loading. By combining different inflation patterns with different buckling resistances, the adaptive inflation strategy can mitigate the tilting angle that results from non-uniform loading. The pneumatic control strategy proposed in this work does not rely on specific lattice sizes or topologies. As demonstrated in Fig. S5, the approach is effective for triangular lattices, and as shown in Fig. S8, it is readily scalable to square lattices of varying sizes with appropriately matched pneumatic actuators. This strategy could, in principle, be used to realize a wide range of tunability in existing engineering structures.

Our study demonstrates that nodal connectivity serves as a useful qualitative framework to interpret and guide the design of pneumatic actuation strategies. While this approach provides intuitive insights into how local actuator placement can influence global mechanical behavior, it does involve key assumptions and simplifications that need further discussion. First, our actuators interact with the midpoints of unit cell walls rather than true lattice nodes. Therefore, the term “nodal connectivity" is used as a conceptual extension of traditional nodal connectivity. It captures actuator-induced coupling between structural elements, but does not reflect a topological change in the lattice’s underlying node connectivity. Second, we emphasize that this framework is currently qualitative. Although it offers an effective design heuristic, it does not provide quantitative predictions of global mechanical performance. A more rigorous theoretical model that links actuator inflation states, local structural modifications, and overall mechanical response would be a useful direction for future work.

Beyond the specific patterns explored in this study, the design space for connectivity modulation is broad and highly configurable. By selectively actuating different interstitial sites, a wide range of spatial patterns, such as gradient, asymmetric, or hierarchical configurations, could potentially be implemented to achieve diverse mechanical responses, including multistability, localized buckling, or anisotropic stiffness tuning. Our current work presents three representative strategies (weak, medium, strong) as illustrative examples, chosen for their clarity and feasibility in experimental realization. These examples serve to demonstrate how varying nodal connectivity influences global behavior, but do not exhaust the possibilities enabled by this approach. More broadly, the actuator-lattice system can be viewed as a programmable architecture in which connectivity, stiffness pathways, and deformation modes can be reassigned on demand, suggesting a much larger design space than what is experimentally sampled here. Future work may explore more complex or application-specific patterns to fully harness the programmability of the system.

Compared to prior uses of pneumatic actuators in metamaterials and soft robotics, our approach offers a key advantage in its ability to achieve localized, reconfigurable, and reversible mechanical tuning. Rather than actuating the entire structure or relying on global pressure changes, our method targets specific unit cells, enabling spatially selective modulation of mechanical behavior without altering the base lattice geometry. This capability is critical for creating adaptive materials that respond dynamically to changing environments or loading conditions.

One limitation of the current work is the lack of autonomous control over the pneumatic system. In this study, actuator inflation patterns were manually controlled. A promising future direction would be to enable each actuator to independently sense its local environment and make inflation decisions accordingly (e.g., using microelectronics or nontraditional approaches, such as mechanical valves capable of responding to environmental stimuli like mechanical forces, light, moisture, etc.³⁸). Integrating such responsive control with logic gating and lattice buckling may enable new structural functionalities. In addition, as this work focuses on demonstrating the overall control strategy, we employed simple cylindrical silicone rubber actuators. While our experimental demonstrations focus on small-scale lattices with uniform pneumatic control, we recognize that scaling to larger structures presents practical challenges, such as managing complex pneumatic networks and enabling independent control across numerous actuators in larger or stiffer systems. One possible solution is to adopt hydraulic actuation, which offers higher energy density and more efficient routing in densely packed environments. Alternatively, embedded microfluidic logic or self-regulating valves could enable decentralized control in future implementations. Importantly, our core concept of modulating mechanical behavior by altering the effective nodal connectivity of unit cells remains broadly applicable. This principle is not restricted to pneumatic systems and could be extended to a range of actuation mechanisms and structural platforms.

Methods

Fabrication of samples

We constructed the lattices from thermoplastic polyurethane (TPU) and the actuators from silicone rubber (Dragon Skin 10). Detailed characterization of these materials is provided in the Supplementary Information. The TPU lattices were fabricated using a Bambu P1S fused deposition modeling (FDM) 3D printer (Bambu Lab). Overture TPU 95A Orange filaments were used. The printing speed was 25 mm/s, and the nozzle temperature was set to 220 °C. The solid infill pattern was set as monotonic with an infill percentage of 100%. The pneumatic actuators were molded using Dragon Skin 10 silicone rubber (Smooth-On, Inc.) in 3D-printed PLA molds. These molds were also printed with the Bambu P1S FDM printer. Parts of the actuators were glued using Sil-Poxy (Smooth-On, Inc.). The pneumatic actuators were subsequently connected to the pneumatic control system using tubes and tube fittings purchased from McMaster-Carr. Figure S9 shows the schematics of the mold components and actuator assembly. Actuator dimensions are also provided in the Supplementary Information.

Pneumatic control system

The air pressure within the pneumatic actuators was controlled by a custom-built multi-channel pneumatic control system consisting of an air pump, solenoid valves, MOSFETs, and air pressure sensors. The output pressures were regulated using the pulse width modulation (PWM) algorithm, and the stability of the air pressure output was ensured by the proportional integral derivative (PID) control algorithm. The air pressure output modes were controlled automatically using a programmed Arduino Mega 2560 board. To assess the energy consumption of our pneumatic setup, we report the power requirements of the key components. The system uses a Parker D737-23-01 miniature diaphragm pump (nominal efficiency of 1.0 L/min per Watt), which requires ~6 W when operating at our experimental flow rates (6 L/min). The system maintains stable pressure through an SMC VQ110L-5M solenoid valve operating at a PWM frequency of 50 Hz, with a continuous holding power of ~1 W. Since only a single valve controls all actuators in this study, the total electrical power draw of the pneumatic system remains on the order of 7 W during operation.

Mechanical testing

Uni-axial compression testing was performed under displacement control with a loading rate of 1 mm/s using an Instron-65SC at room temperature. In the drop tests, the acceleration was measured with a piezoelectric accelerometer (PCB Piezotronics, Inc., Model No. 352C23). The point loading test was performed using a custom loading rod with a loading rate of 1  mm/s using an Instron-65SC at room temperature.

Bending angle test of the stabilizer

The tilt angle of the stabilizer platform was measured using two calibrated MPU6050 gyro sensors. As shown in Fig. S7, these sensors were placed in parallel on the stabilizer platform and located on opposite sides of the loading rod. The sensors were positioned on either side of the axis where the loading rod was located, enabling the cancellation of the gyro in the X and Y directions. As a result, the average Z-direction gyro value was the bending angle of the platform. The data from the sensors was collected by an Arduino Mega 2560 at a frequency of 2 Hz.

Author contributions

Xiaoheng Zhu: Conceptualization, methodology, investigation, visualization, writing—original draft, writing—review and editing. Yucong Hua: Conceptualization, methodology, investigation, visualization, writing—original draft, writing—review and editing. Dengge Jin: Investigation, visualization, writing—original draft. Jordan R. Raney: Conceptualization, supervision, funding acquisition, writing—review and editing.

Peer review

Peer review information

Communications Engineering thanks the anonymous reviewers for their contribution to the peer review of this work. Primary Handling Editors: [Philip Coatsworth].

Data availability

All data for this work are available in the main text and/or the supplementary information.

Competing interests

Jordan R. Raney is an Editorial Board Member for Communications Engineering, but was not involved in the editorial review of, nor the decision to publish this article. The remaining authors declare no other competing interests.

Supplementary information

The online version contains supplementary material available at 10.1038/s44172-025-00570-8.