Carlos M. Portela

Abstract Shape memory behavior in engineered systems is traditionally achieved through material-level phase transformations or polymer network rearrangements. While effective, these approaches tightly couple functionality to chemistry, limiting scalability, material choice, and manufacturing flexibility. An alternative paradigm is to embed recoverability within structural architecture itself, decoupling actuation from intrinsic material phase changes. We present a feather-inspired phase-transforming cellular material–spring system (F-PXCM) that achieves shape recovery through structural interactions rather than active phases. PXCMs, designed with bistable sinusoidal geometries, mimic the hydration-induced softening of the feather matrix, while temperature-invariant springs replicate keratinous fibers. Finite element simulations show that thermal softening of PXCMs, combined with spring restitution, enables complete recovery, while additive-manufactured prototypes confirm the computational results. Exploratory microscale fabrication with two-photon polymerization highlights key challenges and pathways forward.

Granular materials dissipate energy efficiently through intergranular interactions, yet their disordered, dense nature precludes precise control and integration into lightweight systems. Architected materials offer tunable mechanical responses at low densities but tend to localize stress, limiting dissipation efficiency. Here, we introduce hierarchical granular metamaterials that reconcile these trade-offs through three levels of design: lightweight architected grains engineered with hollow elliptical inclusions, crystal-inspired grain packings, and functional gradients and defects within grain tessellations. These metamaterials exhibit simultaneous increases in impact energy absorption per unit mass and reductions in transmitted peak force at low densities, outperforming conventional architected materials. In situ nanomechanical experiments and nonlinear computational models reveal that enhanced lateral grain expansion drives recruitment of neighboring grains, amplifying plastic and frictional dissipation. Multiscale impact experiments confirm that these mechanisms persist across length scales, constituent materials, and dimensionalities. Beyond mechanical performance, we demonstrate that spatially programmable inter-grain contact networks enable deterministic routing of deformation, which extends to electrical transport pathways independently of packing geometry. By combining granular principles with architected material design, this work establishes a paradigm for multifunctional metamaterials whose contact topology, mechanical response, and transport properties can be programmed independently.

Granular materials dissipate energy efficiently through intergranular interactions, yet their disordered, dense nature precludes precise control and integration into lightweight systems. Architected materials offer tunable mechanical responses at low densities but tend to localize stress, limiting dissipation efficiency. Here, we introduce hierarchical granular metamaterials that reconcile these trade-offs through three levels of design: lightweight architected grains engineered with hollow elliptical inclusions, crystal-inspired grain packings, and functional gradients and defects within grain tessellations. These metamaterials exhibit simultaneous increases in impact energy absorption per unit mass and reductions in transmitted peak force at low densities, outperforming conventional architected materials. In situ nanomechanical experiments and nonlinear computational models reveal that enhanced lateral grain expansion drives recruitment of neighboring grains, amplifying plastic and frictional dissipation. Multiscale impact experiments confirm that these mechanisms persist across length scales, constituent materials, and dimensionalities. Beyond mechanical performance, we demonstrate that spatially programmable inter-grain contact networks enable deterministic routing of deformation, which extends to electrical transport pathways independently of packing geometry. By combining granular principles with architected material design, this work establishes a paradigm for multifunctional metamaterials whose contact topology, mechanical response, and transport properties can be programmed independently.

Filamentous entanglements such as textiles achieve resilience and toughness through topology rather than material composition alone. Yet architected materials rarely exploit dense interlooping and sliding contacts to achieve extraordinary physical behavior. While research across mechanics, architecture, and design has linked stitch structure to physical behavior, a predictive quantitative framework has remained elusive. Here we show that knitting can be reinterpreted as a general strategy for designing three-dimensional entangled solids with programmable mechanics. Using a geometrically exact description of each stitch and multimaterial 3D printing-a topology-agnostic fabrication approach-we create planar and volumetric knits whose loop parameters directly control stiffness, strength, and energy dissipation. The printed fabrics faithfully reproduce the nonlinear, anisotropic, and hysteretic responses of conventional machine-knitted textiles. We identify a simple normalization that collapses stress-strain curves across stitch geometries, yarn architectures, constituent materials, and length scales, unifying the behavior of traditional and 3D-printed knits on a single master curve. Extending the topology into the "Z" or stacking direction yields volumetric knits whose stiffness and dissipation can be tuned by imposed prestrain. Finally, we realize the same architecture from centimeters down to micrometers, culminating in, to our knowledge, the smallest knitted structure ever fabricated. By demonstrating that 3D-printed knits can be interpreted both as a traditional fabric composed of a single yarn and as an architected material with defined periodicity, this work establishes entangled filaments as a foundation for a class of material architectures whose mechanics are encoded in their topology.

Materials designed by nature commonly exhibit functional grading and laminated structures, particularly when intended for enhanced impact protection. Synthetic materials have also found success in exploiting this concept with fully dense but spatially varying architectures, as is the case with advanced fiber-based composites. In the lightweight materials space, porous architected materials have shown benefits for extreme impact mitigation, proving to be advantageous in dissipating large amounts of energy per unit mass, but rarely harness the benefits of layering or functional grading in designs. Here, a design paradigm for lightweight multilayered materials towards high impact-mitigation efficacy is demonstrated, showing that the use of alternating monolithic and beam-based architectures leads to enhanced and predictable responses under extreme conditions. These layered, mass-equivalent `heterostructures' with different ordering and proportions of octet and monolithic layers outperform single-architecture lattices on a mass-normalized energy dissipation basis by >50% when subjected to supersonic microparticle impact. Through analysis that combines wave-propagation analysis, nonlinear finite element simulations, and post-impact crater reconstruction, layer-by-layer mechanical properties are mapped to crater formation and energy dissipation behaviors. This heterostructure design framework offers a simple approach towards tuning failure and impact resistance of materials for protective applications from Whipple shields to sports equipment.

Materials designed by nature commonly exhibit functional grading and laminated structures, particularly when intended for enhanced impact protection. Synthetic materials have also found success in exploiting this concept with fully dense but spatially varying architectures, as is the case with advanced fiber-based composites. In the lightweight materials space, porous architected materials have shown benefits for extreme impact mitigation, proving to be advantageous in dissipating large amounts of energy per unit mass, but rarely harness the benefits of layering or functional grading in designs. Here, a design paradigm for lightweight multilayered materials towards high impact-mitigation efficacy is demonstrated, showing that the use of alternating monolithic and beam-based architectures leads to enhanced and predictable responses under extreme conditions. These layered, mass-equivalent `heterostructures' with different ordering and proportions of octet and monolithic layers outperform single-architecture lattices on a mass-normalized energy dissipation basis by >50% when subjected to supersonic microparticle impact. Through analysis that combines wave-propagation analysis, nonlinear finite element simulations, and post-impact crater reconstruction, layer-by-layer mechanical properties are mapped to crater formation and energy dissipation behaviors. This heterostructure design framework offers a simple approach towards tuning failure and impact resistance of materials for protective applications from Whipple shields to sports equipment.

Microneedle (MN) devices provide a platform for development of products that can facilitate intra-and trans-dermal delivery and sampling of active pharmaceutical ingredient (APIs) and biomarkers that would otherwise be restricted by the skin barrier. Despite significant progress in the development of laboratory-based prototypes, no Microneedle Array Patch (MAP) drug delivery products have been approved for commercial use by the relevant national regulatory authorities. This discrepancy reflects the technical, commercial, and regulatory challenges to their clinical translation. This review presents some of the pertinent challenges facing MN development, discusses potential approaches to them, and provides a future outlook. MN design is discussed, including their intrinsically conflicting requirement of being slender enough for skin penetration and voluminous enough to accommodate clinically relevant doses of APIs. The anatomy and constitutive behavior of skin tissue, and the related insertion mechanics of MNs with distinct morphologies are also considered, enabling understanding of how MNs achieve the mechanical strength to withstand handling and use. The fabrication methods for these materials are compared, including their amenability to large-scale manufacturing based on factors such as high throughput, cost efficiency, and process capability. Biocompatibility and dissolution behaviors in the dermal compartment are also considered. MN applicator designs are summarized, with a focus on their different mechanisms of application and impact energies. Key elements of the regulatory science of MAPs are also discussed. This review highlights challenges in the development of MN-based drug delivery systems compatible with applicators for on-demand, self-applied patient-specific intra- and trans-dermal therapy.

High-throughput characterization of architected materials across a wide range of length scales enables rapid screening of topologies for engineering applications. Scaled-down specimens manufactured and evaluated in laboratory environments enable this iteration, but application scenarios may involve differing length scales and loading conditions that complicate direct comparisons. Here, we use a spinodal architected morphology to determine the interplay among the constituent material's strain-rate sensitivity, the topological length scale, and the imposed deformation rates. We report characterization spanning strain rates from $10^{-3}$ s$^{-1}$ to $10^{4}$ s$^{-1}$ on spinodal architected specimens with length scales of 100 $μ$m (microscale) and 30 mm (macroscale). The experiments show that while microscale specimens exhibit moderate increase in strength at high strain rates, macroscale specimens exhibit a nearly tenfold increase in strength at equivalent strain rates. Finite element calculations reveal that this increase is linked to a transition from a response governed by constituent material strain-rate sensitivity to inertia-dominated behavior in macroscale specimens, a transition not observed in microscale specimens at the strain rates investigated here. Using extensive finite element calculations, we develop maps to establish the parameters governing the regimes of behavior, illustrating that the transition from behavior governed by constituent material rate sensitivity to inertia-dominated behavior has analogies to fluids in that it depends on a structural length scale. Our findings provide insights into the physical parameters that govern responses across length and time scales, towards the development and design of new laboratory experiments that extract relevant dynamic properties for structural applications.

High-throughput characterization of architected materials across a wide range of length scales enables rapid screening of topologies for engineering applications. Scaled-down specimens manufactured and evaluated in laboratory environments enable this iteration, but application scenarios may involve differing length scales and loading conditions that complicate direct comparisons. Here, we use a spinodal architected morphology to determine the interplay among the constituent material's strain-rate sensitivity, the topological length scale, and the imposed deformation rates. We report characterization spanning strain rates from $10^{-3}$ s$^{-1}$ to $10^{4}$ s$^{-1}$ on spinodal architected specimens with length scales of 100 $μ$m (microscale) and 30 mm (macroscale). The experiments show that while microscale specimens exhibit moderate increase in strength at high strain rates, macroscale specimens exhibit a nearly tenfold increase in strength at equivalent strain rates. Finite element calculations reveal that this increase is linked to a transition from a response governed by constituent material strain-rate sensitivity to inertia-dominated behavior in macroscale specimens, a transition not observed in microscale specimens at the strain rates investigated here. Using extensive finite element calculations, we develop maps to establish the parameters governing the regimes of behavior, illustrating that the transition from behavior governed by constituent material rate sensitivity to inertia-dominated behavior has analogies to fluids in that it depends on a structural length scale. Our findings provide insights into the physical parameters that govern responses across length and time scales, towards the development and design of new laboratory experiments that extract relevant dynamic properties for structural applications.

Magnetic remote actuation of soft materials is attractive for applications such as transforming materials and medical robots. However, due to manufacturing limitations, microscale magnetoactive devices are scarce -- light-based additive manufacturing methods, despite achieving microscale resolution, struggle with particle-induced light scattering. Moreover, large hard-magnetic microparticles restrict ultimate feature sizes, and deformation of soft-magnetic nanoparticle composites requires impractically high loading and field gradients. Among successfully fabricated microscale soft-magnetic composites, limited control over particle loading, distribution, and matrix-phase stiffness has hindered their functionality. Here, we combine two-photon polymerization with iron oxide nanoparticle coprecipitation to fabricate 3D-printed microscale nanocomposites with spatially tunable nanoparticle distribution. We control nanoparticle content by locally modulating the two-photon dose, imbuing parts with varied magnetic functionality and achieving millimeter-scale elastic deformations, demonstrated by a soft robotic gripper and a bistable bit register and sensor. Our approach enables precise control of mechanical and magnetic properties towards microscale metamaterial and robotics applications.

ABSTRACT Nanoarchitected metamaterials exhibit exceptional specific strength and energy absorption under quasi‐static conditions, but their performance scaling toward high strain rates is critical for their adoption in dynamic loading applications. Using energy absorptive carbon nanoarchitectures of Tubulanes and Schwarzites, we demonstrate their mechanical resilience for strain rates spanning twelve orders of magnitude from = 10 −3 to 10 8 s −1 . Quasi‐static testing reveals specific strengths approaching the Suquet limit for Tubulane architectures with failure strain exceeding ε = 26%, the combination of which produces the highest quasi‐static specific energy absorption of any architected material at Ω/ρ = 321 ± 38 J g −1 . Distinct from bulk ceramics, these carbon nanoarchitectures show strain rate‐independent mechanical properties under uniaxial compression from = 10 −3 to 10 2 s −1 . Molecular dynamics simulations of complete unit cells highlight atomic reconfiguration to enable high failure strain and energy absorption. Micro‐ballistics testing at impact velocities up to 900 m s −1 demonstrate exceptional resilience to impact with shielding up to 687 m s −1 for 12 µm thick Tubulanes and ultrahigh specific inelastic energy absorption of 865 J g −1 at = 10 8 s −1 . Collectively, this study highlights the marked promise of pyrolytic carbon and its nanoarchitecture for translation beyond quasi‐static conditions toward supersonic mechanical resilience with pressing impacts in ballistics defence, protective equipment, and micro‐asteroid shielding.

Mechanical metamaterials have continued to offer unprecedented tunability in mechanical properties, but most designs to date have prioritized attaining high stiffness and strength while sacrificing deformability. The emergence of woven lattices—three-dimensional networks of entangled fibers—has introduced a pathway to the largely overlooked compliant and stretchable regime of metamaterials. However, the design and implementation of these complex architectures has remained a primarily manual process, restricting identification and validation of their full achievable design and property space. Here, we present a geometric design framework that encodes woven topology using a graph structure, enabling the creation of woven lattices with tunable architectures, functional gradients, and arbitrary heterogeneity. Through use of microscale in situ tension experiments and computational mechanics models, we reveal highly tunable anisotropic stiffness (varying by over an order of magnitude) and extreme stretchability (up to a stretch of four) within the design space produced by the framework. Moreover, we demonstrate the ability of woven metamaterials to exhibit programmable failure patterns by leveraging tunability in the design process. This framework provides a design and modeling toolbox to access this previously unattainable high-compliance regime of mechanical metamaterials, enabling programmable large-deformation, nonlinear responses. Woven lattices offer a pathway to highly compliant and tunable mechanical metamaterials. Here, authors present a geometric design framework for woven lattices that encodes topology and compliance, allowing for arbitrary complexity and enabling programmable large-deformation and failure responses.

Segmented elastomers, such as polyurea, dissipate energy through various mechanisms. Although dynamic stiffening of soft domains is often cited, growing evidence highlights the dominant role of hydrogen-bond breaking and reformation. To clarify the specific role of hard domains, we synthesized polyurea, polyurethane, and polyurethane-urea with systematically varied hard-domain order, while maintaining comparable soft-domain dynamics at a target strain rate. Microballistic impact experiments revealed two distinct dissipation regimes, with ordered polyurea performing best. FTIR spectroscopy and strain-rate-dependent cyclic tension experiments confirmed an order–disorder transition coinciding with maximum energy dissipation. These findings emphasize the role of ordered hard domains in elastomer design.

Abstract Historical and recent advances in the field of nanomechanics, ranging from the early development of nanoindentation to recent advances in artificial intelligence- and machine learning-based characterization and modeling are covered in this article. Early advances were motivated by thin-film mechanics challenges driven by the microelectronics industry. In the ensuing years, different methodologies for probing mechanical properties at length scales relevant to a myriad of applications and materials systems have been developed, coupled with a variety of in situ testing methods that shed insights into new mechanisms. Built upon the knowledge base from nanomechanics, new mechanical metamaterials with otherwise unachievable material properties have been discovered, and new methods in testing and analyzing properties for extreme conditions have been recently reported. This article discusses the journey that the nanomechanics community has gone through over the past 50 years and shares the scale-bridging mechanistic insights through the looking glass. Graphical Abstract

Triply periodic minimal surfaces (TPMS) are a class of metamaterials with a variety of applications and well-known primitive morphologies. We present a new method for discovering novel microscale TPMS structures with exceptional energy-dissipation capabilities, achieving double the energy absorption of the best existing TPMS primitive structure. Our approach employs a parametric representation, allowing seamless interpolation between structures and representing a rich TPMS design space. As simulations are intractable for efficiently optimizing microscale hyperelastic structures, we propose a sample-efficient computational strategy for rapid discovery with limited empirical data from 3D-printed and tested samples that ensures high-fidelity results. We achieve this by leveraging a predictive uncertainty-aware Deep Ensembles model to identify which structures to fabricate and test next. We iteratively refine our model through batch Bayesian optimization, selecting structures for fabrication that maximize exploration of the performance space and exploitation of our energy-dissipation objective. Using our method, we produce the first open-source dataset of hyperelastic microscale TPMS structures, including a set of novel structures that demonstrate extreme energy dissipation capabilities, and show several potential applications of these structures.

Additively manufactured (AM) architected materials have enabled unprecedented control over mechanical properties of engineered materials. While lattice architectures have played a key role in these advances, they suffer from stress concentrations at sharp joints and bending-dominated behavior at high relative densities, limiting their mechanical efficiency. Additionally, high-resolution AM techniques often result in low-throughput or costly fabrication, restricting manufacturing scalability of these materials. Aperiodic spinodal architected materials offer a promising alternative by leveraging low-curvature architectures that can be fabricated through techniques beyond AM. Enabled by phase separation processes, these architectures exhibit tunable mechanical properties and enhanced defect tolerance by tailoring their curvature distributions. However, the relation between curvature and their anisotropic mechanical behavior remains poorly understood. In this work, we develop a theoretical framework to quantify the role of curvature in governing the anisotropic stiffness and strength of shell-based spinodal architected materials. We introduce geometric metrics that predict the distribution of stretching and bending energies under different loading conditions, bridging the gap between curvature in doubly curved shell-based morphologies and their mechanical anisotropy. We validate our framework through finite element simulations and microscale experiments, demonstrating its utility in designing mechanically robust spinodal architectures. This study provides fundamental insights into curvature-driven mechanics, guiding the optimization of next-generation architected materials for engineering applications.

Mechanical metamaterials with nanoscale features exhibit exceptional properties, including high specific strength, modulus, energy absorption, and recoverability. The ability to fabricate these metamaterials out of complex nanocomposites could further boost their mechanical properties. Recently, two-photon lithography (TPL) has been used to fabricate architected microlattices out of high-performance polymer nanocomposites that contain metallic nanoclusters. However, the mechanism that leads to unique mechanical properties of the nanocomposites, such as high strain hardening, remains unclear. Here, TPL is used to fabricate nanocluster-based polymer nanocomposite micropillars and investigate how nanocluster content and chemical bonding with the polymer matrix impact their mechanical properties. The nanocomposites are tested in compression at strain rates of 10 –3 to 10 2 s –1, and after heat treatment up to 550 °C. Findings show that nanoclusters establish hydrogen bonds and exhibit strong interfacial bonding with the polymer, restricting polymer chain movement and significantly enhancing mechanical strength compared to unfilled polymers.

Mechanical metamaterials can achieve high stiffness and strength at low densities, but often at the expense of low ductility and stretchability—a persistent trade-off in materials. In contrast, double-network hydrogels feature interpenetrating compliant and stiff polymer networks, and exhibit unprecedented combinations of high stiffness and stretchability, resulting in exceptional toughness. Here we present double-network-inspired metamaterials by integrating monolithic truss (stiff) and woven (compliant) components into a metamaterial architecture, which achieves a tenfold increase in stiffness and stretchability compared to its pure counterparts. Nonlinear computational mechanics models elucidate that enhanced energy dissipation in these double-network-inspired metamaterials stems from increased frictional dissipation due to entanglements between networks. Through introduction of internal defects, which typically degrade mechanical properties, we demonstrate a threefold increase in energy dissipation for these metamaterials via failure delocalization. This work opens avenues for developing metamaterials in a high-compliance regime inspired by polymer network topologies. Inspired by the entangled structure of double-network hydrogels, the authors integrate stiff truss and compliant woven components into metamaterial architectures to realize simultaneous high stiffness and high stretchability.

Bayesian Optimization of Carbon Nanolattices Machine Learning designs new nanolattice geometries with the strength of carbon steel, but the density of Styrofoam, offering record strength-to-weight of lightweight materials. By implementing multi-objective Bayesian optimization in combination with two-photon polymerization and pyrolysis, these ultrahigh specific strength carbon nanolattices more than double the performance of benchmark materials. More details can be found in article number 2410651 by Peter Serles, Tobin Filleter, Seunghwa Ryu, and co-workers.

Abstract Nanoarchitected materials are at the frontier of metamaterial design and have set the benchmark for mechanical performance in several contemporary applications. However, traditional nanoarchitected designs with conventional topologies exhibit poor stress distributions and induce premature nodal failure. Here, using multi‐objective Bayesian optimization and two‐photon polymerization, optimized carbon nanolattices with an exceptional specific strength of 2.03 MPa m 3 kg −1 at low densities <215 kg m −3 are created. Generative design optimization provides experimental improvements in strength and Young's modulus by as much as 118% and 68%, respectively, at equivalent densities with entirely different lattice failure responses. Additionally, the reduction of nanolattice strut diameters to 300 nm produces a unique high‐strength carbon with a pyrolysis‐induced atomic gradient of 94% sp 2 aromatic carbon and low oxygen impurities. Using multi‐focus multi‐photon polymerization, a millimeter‐scalable metamaterial consisting of 18.75 million lattice cells with nanometer dimensions is demonstrated. Combining Bayesian optimized designs and nanoarchitected pyrolyzed carbon, the optimal nanostructures exhibit the strength of carbon steel at the density of Styrofoam offering unparalleled capabilities in light‐weighting, fuel reduction, and contemporary design applications.

Spinodal metamaterials , with architectures inspired by natural phase-separation processes, have presented a significant alternative to periodic and symmetric morphologies when designing mechanical metamaterials with extreme performance. While their elastic mechanical properties have been systematically determined, their large-deformation, nonlinear responses have been challenging to predict and design, in part due to limited data sets and the need for complex nonlinear simulations. This work presents a novel physics-enhanced machine learning (ML) and optimization framework tailored to address the challenges of designing intricate spinodal metamaterials with customized mechanical properties in large-deformation scenarios where computational modeling is restrictive and experimental data is sparse. By utilizing large-deformation experimental data directly, this approach facilitates the inverse design of spinodal structures with precise finite-strain mechanical responses. The framework sheds light on instability-induced pattern formation in spinodal metamaterials—observed experimentally and in selected nonlinear simulations—leveraging physics-based inductive biases in the form of nonconvex energetic potentials. Altogether, this combined ML, experimental, and computational effort provides a route for efficient and accurate design of complex spinodal metamaterials for large-deformation scenarios where energy absorption and prediction of nonlinear failure mechanisms is essential.

Metamaterials with functional responses can exhibit varying properties under different conditions (e.g., wave‐based responses or deformation‐induced property variation). This work addresses rapid inverse design of such metamaterials to meet target qualitative functional behaviors, a challenge due to its intractability and nonunique solutions. Unlike data‐intensive and noninterpretable deep‐learning‐based methods, this work proposes the random‐forest‐based interpretable generative inverse design (RIGID), a single‐shot inverse design method for fast generation of metamaterials with on‐demand functional behaviors. RIGID leverages the interpretability of a random forest‐based “design → response” forward model, eliminating the need for a more complex “response → design” inverse model. Based on the likelihood of target satisfaction derived from the trained random forest, one can sample a desired number of design solutions using Markov chain Monte Carlo methods. RIGID is validated on acoustic and optical metamaterial design problems, each with fewer than 250 training samples. Compared to the genetic algorithm‐based design generation approach, RIGID generates satisfactory solutions that cover a broader range of the design space, allowing for better consideration of additional figures of merit beyond target satisfaction. This work offers a new perspective on solving on‐demand inverse design problems, showcasing the potential for incorporating interpretable machine learning into generative design under small data constraints.

The quasi-static properties of micro-architected (meta)materials have been extensively studied over the past decade, but their dynamic responses, especially in acoustic metamaterials with engineered wave propagation behavior, represent a new frontier. However, challenges in miniaturizing and characterizing acoustic metamaterials in high-frequency (megahertz) regimes have hindered progress toward experimentally implementing ultrasonic-wave control. Here, we present an inertia design framework based on positioning microspheres to tune responses of 3D microscale metamaterials. We demonstrate tunable quasi-static stiffness by up to 75% and dynamic longitudinal-wave velocities by up to 25% while maintaining identical material density. Using noncontact laser-based dynamic experiments of tunable elastodynamic properties and numerical demonstrations of spatio-temporal ultrasound wave propagation, we explore the tunable static and elastodynamic property relation. This design framework expands the quasi-static and dynamic metamaterial property space through simple geometric changes, enabling facile design and fabrication of metamaterials for applications in medical ultrasound and analog computing.

Mechanical metamaterials are renowned for their ability to achieve high stiffness and strength at low densities, often at the expense of low ductility and stretchability-a persistent trade-off in materials. In contrast, materials such as double-network hydrogels feature interpenetrating compliant and stiff polymer networks, and exhibit unprecedented combinations of high stiffness and stretchability, resulting in exceptional toughness. Here, we present double-network-inspired (DNI) metamaterials by integrating monolithic truss (stiff) and woven (compliant) components into a metamaterial architecture, which achieve a tenfold increase in stiffness and stretchability compared to their pure woven and truss counterparts, respectively. Nonlinear computational mechanics models elucidate that enhanced energy dissipation in these DNI metamaterials stems from increased frictional dissipation due to entanglements between the two networks. Through introduction of internal defects, which typically degrade mechanical properties, we demonstrate an opposite effect of a threefold increase in energy dissipation for these metamaterials via failure delocalization. This work opens avenues for developing new classes of metamaterials in a high-compliance regime inspired by polymer network topologies.

Triply periodic minimal surfaces (TPMS) are a class of metamaterials with a variety of applications and well-known primitive morphologies. We present a new method for discovering novel microscale TPMS structures with exceptional energy-dissipation capabilities, achieving double the energy absorption of the best existing TPMS primitive structure. Our approach employs a parametric representation, allowing seamless interpolation between structures and representing a rich TPMS design space. As simulations are intractable for efficiently optimizing microscale hyperelastic structures, we propose a sample-efficient computational strategy for rapid discovery with limited empirical data from 3D-printed and tested samples that ensures high-fidelity results. We achieve this by leveraging a predictive uncertainty-aware Deep Ensembles model to identify which structures to fabricate and test next. We iteratively refine our model through batch Bayesian optimization, selecting structures for fabrication that maximize exploration of the performance space and exploitation of our energy-dissipation objective. Using our method, we produce the first open-source dataset of hyperelastic microscale TPMS structures, including a set of novel structures that demonstrate extreme energy dissipation capabilities, and show several potential applications of these structures.

Ultralight architected materials enabled by advanced manufacturing processes have achieved density-normalized strength and stiffness properties that are inaccessible to bulk materials. However, the majority of this work has focused on static loading and elastic-wave propagation. Fundamental understanding of the mechanical behavior of architected materials under large-deformation dynamic conditions remains limited, due to the complexity of mechanical responses and shortcomings of characterization methods. Here, we present a microscale suspended-plate impact testing framework for three-dimensional micro-architected materials, where supersonic microparticles to velocities of up to 850 m/s are accelerated against a substrate-decoupled architected material to quantify its energy dissipation characteristics. Using ultra-high-speed imaging, we perform in situ quantification of the impact energetics on two types of architected materials as well as their constituent nonarchitected monolithic polymer, indicating a 47% or greater increase in mass-normalized energy dissipation under a given impact condition through use of architecture. Post-mortem characterization, supported by a series of quasi-static experiments and high-fidelity simulations, shed light on two coupled mechanisms of energy dissipation: material compaction and particle-induced fracture. Together, experiments and simulations indicate that architecture-specific resistance to compaction and fracture can explain a difference in dynamic impact response across architectures. We complement our experimental and numerical efforts with dimensional analysis which provides a predictive framework for kinetic-energy absorption as a function of material parameters and impact conditions. We envision that enhanced understanding of energy dissipation mechanisms in architected materials will serve to define design considerations toward the creation of lightweight impact-mitigating materials for protective applications.

Spinodal metamaterials, with architectures inspired by natural phase-separation processes, have presented a significant alternative to periodic and symmetric morphologies when designing mechanical metamaterials with extreme performance. While their elastic mechanical properties have been systematically determined, their large-deformation, nonlinear responses have been challenging to predict and design, in part due to limited data sets and the need for complex nonlinear simulations. This work presents a novel physics-enhanced machine learning (ML) and optimization framework tailored to address the challenges of designing intricate spinodal metamaterials with customized mechanical properties in large-deformation scenarios where computational modeling is restrictive and experimental data is sparse. By utilizing large-deformation experimental data directly, this approach facilitates the inverse design of spinodal structures with precise finite-strain mechanical responses. The framework sheds light on instability-induced pattern formation in spinodal metamaterials -- observed experimentally and in selected nonlinear simulations -- leveraging physics-based inductive biases in the form of nonconvex energetic potentials. Altogether, this combined ML, experimental, and computational effort provides a route for efficient and accurate design of complex spinodal metamaterials for large-deformation scenarios where energy absorption and prediction of nonlinear failure mechanisms is essential.

Metamaterials with functional responses can exhibit varying properties under different conditions (e.g., wave-based responses or deformation-induced property variation). This work addresses the rapid inverse design of such metamaterials to meet target qualitative functional behaviors, a challenge due to its intractability and non-unique solutions. Unlike data-intensive and non-interpretable deep-learning-based methods, we propose the Random-forest-based Interpretable Generative Inverse Design (RIGID), a single-shot inverse design method for fast generation of metamaterial designs with on-demand functional behaviors. RIGID leverages the interpretability of a random forest-based "design$\rightarrow$response" forward model, eliminating the need for a more complex "response$\rightarrow$design" inverse model. Based on the likelihood of target satisfaction derived from the trained random forest, one can sample a desired number of design solutions using Markov chain Monte Carlo methods. We validate RIGID on acoustic and optical metamaterial design problems, each with fewer than 250 training samples. Compared to the genetic algorithm-based design generation approach, RIGID generates satisfactory solutions that cover a broader range of the design space, allowing for better consideration of additional figures of merit beyond target satisfaction. This work offers a new perspective on solving on-demand inverse design problems, showcasing the potential for incorporating interpretable machine learning into generative design under small data constraints.

Self-assembled nanoparticle superlattices (NPSLs) are an emergent class of self-architected nanocomposite materials that possess promising properties arising from precise nanoparticle ordering. Their multiple coupled properties make them desirable as functional components in devices where mechanical robustness is critical. However, questions remain about NPSL mechanical properties and how shaping them affects their mechanical response. Here, we perform in situ nanomechanical experiments that evidence up to an 11-fold increase in stiffness (∼1.49 to 16.9 GPa) and a 5-fold increase in strength (∼88 to 426 MPa) because of surface stiffening/strengthening from shaping these nanomaterials via focused-ion-beam milling. To predict the mechanical properties of shaped NPSLs, we present discrete element method (DEM) simulations and an analytical core–shell model that capture the FIB-induced stiffening response. This work presents a route for tunable mechanical responses of self-architected NPSLs and provides two frameworks to predict their mechanical response and guide the design of future NPSL-containing devices.

Although architected materials based on truss networks have been shown to possess advantageous or extreme mechanical properties, those can be highly affected by tolerances and uncertainties in the manufacturing process, which are usually neglected during the design phase. Deterministic computational tools typically design structures with the assumption of perfect, defect-free architectures, while experiments have confirmed the inevitable presence of imperfections and their possibly detrimental impact on the effective properties. Information about the nature and expected magnitude of geometric defects that emerge from the additive manufacturing processes would allow for new designs that aim to mitigate (or at least account for) the effects of defects and to reduce the uncertainty in the effective properties. To this end, we here investigate the effects of four most commonly found types of geometric imperfections in trusses, applied to eleven representative truss topologies in two and three dimensions. Through our study, we (i) quantify the impact of imperfections on the effective stiffness through computational homogenization, (ii) examine the sensitivity of the various truss topologies with respect to those imperfections, (iii) demonstrate the applicability of the model through experiments on 3D-printed trusses, and (iv) present a machine learning framework to predict the presence of defects in a given truss architecture based merely on its mechanical response.