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Instabilities and phase transitions in architected metamaterials: a gradient-enhanced continuum approach

Architected metamaterials such as foams and lattices exhibit a wide range of properties governed by microstructural instabilities and emerging phase transitions. Their macroscopic response–including energy dissipation during impact, large recoverable deformations, morphing between configurations, and auxetic behavior–remains difficult to capture with conventional continuum models, which often rely on discrete approaches that limit scalability. In this work, we propose a nonlocal continuum formulation that captures both stable and unstable responses of elastic architected metamaterials. The framework extends anisotropic hyperelasticity by introducing nonlocal variables and internal length scales reflective of microstructural features. Local polyconvex free-energy models are systematically augmented with two families of non-(poly)convex energies, enabling both metastable and bistable responses. Implementation in a finite element framework enables solution using a hybrid monolithic–staggered strategy. Simulations capture densification fronts, forward and reverse transitions, hysteresis loops, imperfection sensitivity, and globally coordinated auxetic modes. Overall, this framework provides a robust foundation for accelerated modeling of instability-driven phenomena in architected metamaterials, while enabling extensions to anisotropic, dissipative, and active systems as well as integration with data-driven and machine learning approaches.

42 ENGINEERING

Tailored ultrasound propagation in microscale metamaterials via inertia design

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.

42 ENGINEERING

A review of fluids under nanoconfinement: Reactivity, geomechanics, phase transitions, and flow

Due to its many industrial applications, the physics associated with the nanoconfinement of fluids has garnered great attention from the scientific community in roughly the last fifteen years. One pioneer of that research has been the Multi-Scale Fluid-Solid Interactions in Architected and Natural Materials (MUSE) Energy Frontier Research Center, which produced more than 50 journal articles from 2018 to 2023. We structure the findings of MUSE into four categories and contextualize the work with the broader literature. Here, the four categories are (1) the dependence of chemical reactions on the degree of confinement, which given the lower freedom of motion of molecules yet improved availability of reaction sites generally lead to enhancement from bulk reactions; (2) the mechanical properties of the porous matrix, which are dependent on the heterogeneity of the system in terms of both composition and structure; (3) the phase transitions under nanoconfinement, which are influenced by the pore size and morphology, surface chemistry, and substrate composition; and (4) the physical controls of slip flow, which demonstrate the importance of several factors, such as wettability. These aspects of nanoconfinement are becoming clearer, but there are other elements such as mathematical theory that are still being developed.

58 GEOSCIENCES

Probing Carbon Mineralization Mechanisms in Pore and Bulk Fluids by Harnessing Architected Calcium Silicates

The ability to synthesize materials with well-controlled pore structures gives us unprecedented control over probing fluid interactions with reactive interfaces and advancing calibrated insights into coupled chemo-morphological interactions. One of the primary challenges in developing crystalline silicate materials lies in achieving ordered pore structures. Existing approaches of producing amorphous mesoporous metal silicates via sol–gel methods and heat-treatment of these materials to produce crystalline phases cause the pore structures in the amorphous phases to collapse. To overcome this challenge, carbon coating of amorphous mesoporous calcium silicate particles is carried out to retain the pore structure, while the material is heated to produce crystalline calcium silicate with calcium sulfate inclusions. The pore diameter in these materials is about 3.9 nm, with a surface area and a pore volume of 28.75 m 2 /g and 0.092 cm 2 /g, respectively. The mechanisms of carbon mineralization are investigated by reacting architected calcium silicate with 1 M Na 2 CO 3 and monitoring the evolution in the structural phases using operando wide-angle X-ray scattering (WAXS) measurements. Formation of stable calcium carbonate polymorph or calcite and metastable calcium carbonate polymorph or vaterite in pore and bulk fluids, respectively, resulting from the reaction between Na 2 CO 3 and CaSiO 3 , are noted. The mechanisms associated with carbon mineralization are delineated using ReaxFF molecular dynamics (MD) simulations. The surface dissolution reaction is initiated by 2H + ions that replace a Ca 2+ ion in the Ca–silicate matrix. Ca 2+ ions in the solution initially react with water to form calcium hydroxide and eventually form calcium (bi)carbonate. A slow and gradual increase in the formation of sodium silicate in the solution resulting from the reactions of silicic acid or the silicon dioxide reaction with sodium hydroxide is noted. When carbon mineralization occurs in environments bearing interfacial fluids, calcite is the dominant calcium carbonate polymorph, as determined using experiments with pore fluids and molecular-scale simulations. In conclusion, these studies provide fundamental insights into the mechanisms underlying the carbon mineralization of calcium silicate informed by experiments and molecular-scale simulations.

Calcium

Overcoming the Critical Shortage of STEM - Prepared Secondary Students Through Modeling and Simulation

In developing understanding of technological systems - modeling and simulation tools aid significantly in the learning and visualization processes. In design courses we sketch , extrude, shape, refine and animate with virtual tools in 3D. Final designs are built using a 3D printer. Aspiring architects create spaces with realistic materials and lighting schemes rendered on model surfaces to create breathtaking walk-throughs of virtual spaces. Digital Electronics students design systems that address real-world needs. Designs are simulated in virtual circuits to provide proof of concept before physical construction. This vastly increases students' ability to design and build complex systems. We find students using modeling and simulation in the learning process, assimilate information at a much faster pace and engage more deeply in learning. As Pre-Engineering educators within the Career and Technical Education program at our school division's Technology Academy our task is to help learners in their quest to develop deep understanding of complex technological systems in a variety of engineering disciplines. Today's young learners have vast opportunities to learn with tools that many of us only dreamed about a decade or so ago when we were engaged in engineering and other technical studies. Today's learner paints with a virtual brush - scenes that can aid significantly in the learning and visualization processes. Modeling and simulation systems have become the new standard tool set in the technical classroom [1-5]. Modeling and simulation systems are now applied as feedback loops in the learning environment. Much of the study of behavior change through the use of feedback loops can be attributed to Stanford Psychologist Alfred Bandura. "Drawing on several education experiments involving children, Bandura observed that giving individuals a clear goal and a means to evaluate their progress toward that goal greatly increased the likelihood that they would achieve it."

Spencer, Thomas

Electrochemical Solutions for Advanced Life Support

The Oxygen Generating Assembly (OGA) on-board the International Space Station (ISS) employs a polymer electrolyte membrane (PEM) water electrolysis cell stack to electrochemically dissociate water into its two components – oxygen and hydrogen. Oxygen is provided to the cabin atmosphere for crew respiration while the hydrogen is delivered to a carbon dioxide reduction system to recover oxygen as water. The design of the OGA evolved over a number of years to arrive at the system solution that is currently operational on ISS. Future manned missions to space will require advanced technologies that eliminate the need for resupply from earth and feature in-situ resource utilization to sustain crew life and to provide useful materials to the crew. The architects planning such missions should consider all potential solutions at their disposal to arrive at an optimal vehicle solution that minimizes crew maintenance time, launch weight, installed volume and energy consumption demands. Skyre is developing new technologies through funding from NASA, the Department of Energy, and internal investment based on PEM technology that could become an integral part of these new vehicle solutions. At varying stages of Technology Readiness Level (TRL) are: an oxygen concentrator and compressor that can separate oxygen from an air stream and provide an enriched oxygen resource for crew medical use and space suit recharge without any moving parts in the pure oxygen stream; a regenerative carbon dioxide removal system featuring a PEM-based sorbent regenerator; a carbon dioxide reduction system that electrochemically produces organic compounds that could serve as fuels or as a useful intermediary to more beneficial compounds; and an electrochemical hydrogen separator and compressor for hydrogen recycle. The technical maturity of these projects is presented along with pertinent performance test data that could be beneficial in future study efforts.

Roy, Robert J.

Color Choice is Everything - Impacts Color makes to the Lighting Environment

When contracts are let out to design multiple systems in a vehicle, it is a challenge to maintain integration between system leads. Designers on niche systems, like lighting and control panel design, often get caught up in the challenge of designing the light source or visual interface and fail to include time in their schedule to work with system architects on how their lighting system will be integrated. Additionally, behavioral scientists, industrial designers, and materials engineers get caught up with the materials and look of the system, but often fail to consider how the selection of their materials could affect the certification or performance of electronic devices like lighting systems. Additionally, computer modeling of the system architecture often assumes a perfect environment without the clutter of actual human use (dirt, stowage, crowding). As a result, lighting systems, and backlit displays run the risk of being overdesigned or under designed. Engineers making the assumption that because they have no input or there is no requirement on work surface reflectance, make the assumption that they can t count on good material choices and thus may install more lighting than is necessary. While having more lights may seem better, for a vehicle that is trying to conserve power, more lights may not be a good option. On the other hand, designers who made the opposite assumption and designed a lighting system that only produced just enough light, often wind up with a system that did conserve power, but didn t produce enough light. These situations are exasperated when the system starts to be used and the models are not perfect anymore. The lack of coordination and iterative design not only can impact lighting levels within an environment, but also can affect color perception. This is because, if materials do not represent a gradation of white or black, the material unevenly absorbs and reflects light at different wavelengths of the visual spectrum. The lighting designer may have built a light that meets light spectra requirements, but the eventual light reaching the human user may not be the spectra of light architects intended, if materials near the light source change the spectrum just by how much color is absorbed or reflected. With the recent findings concerning Circadian rhythm, where the spectra of light is extremely important for addressing crew sleep and wake cycles, system architects should pay considerable attention on the impact material choices have in changing the light spectrum in an environment. This presentation will show examples of how material choices impact the resulting illuminance, color spectrum, and power usage of an illuminated space. Its goal is to encourage system designers and planners to use more care in development of requirements and the verification of systems intended for the human visual interface.

Clark, Toni A.

Hierarchical Composites Patterned via 3D Printed Cellular Fluidics

Additive manufacturing of freeform structures containing multiple materials with deterministic spatial arrangement and interactions remains a challenge for most 3D printing processes, due to complex fabrication tool requirements and limitations in printability of some material classes. Here, in this paper, a versatile method is reported to produce architected composites using the concept of cellular fluidics, in which lattices of unit cells are used as templating scaffolds to guide flowable infill materials in a programmed spatial pattern, upon which they are cured in place to produce a deterministically ordered multimaterial solid. The lattice design relies on the unit cell size, type, strut diameter, surface wetting, and distribution of cellular structures to control liquid flow and retention. Individual unit cells are tuned to achieve reliable infilling and combined into higher-order architectures to achieve multiscale composite materials with disparate mechanical properties, including those considered non-printable. Lattice design considerations for leveraging capillary phenomena and demonstrate several methods of patterning polymers in 3D-printed cellular fluidic structures are presented. The concept of tuning the compressive response of an architected composite using a flexible-elastomer as the lattice and a stiff-epoxy as the infill material is illustrated.

36 MATERIALS SCIENCE

Laboratory on the Moon: Equipping and Testing of a Habitat Laboratory for the Scientific Exploration of the Moon by Humans

A human habitat on the Moon is predestined to house a laboratory, especially if it is built for scientific missions on the Moon. This laboratory could be used for (1) conducting experiments utilizing the lunar gravity and prepare experiments to be placed outside the laboratory in the lunar environment, (2) conducting analyses of lunar rock and regolith in high volume, and (3) performing preliminary analyses and screening of samples to be sent to Earth for more detailed, specialized analysis. In the past, spaceflight missions have often been implemented by adding scientific instruments after most of the engineering work is already finished, limiting scientific studies to relatively scattered, insular topics. However, if prepared appropriately, a research laboratory on the Moon can help address scientific questions thoroughly and at a fundamental level. Moreover, the challenge of creating a viable habitat is not only an engineering one, but one that requires input from architects, designers, and psychologists. After all, the crew not only works inside the habitat laboratory, but they spend (close to) their entire time on the Moon inside the habitat and under the isolation and confinement that comes with it. We combine science, engineering, and architecture to create a habitat laboratory that meets their conflicting requirements: The laboratory of the Moon and Mars Base Analog (MaMBA) has been designed with inputs from (1) scientists of selected disciplines, particularly geology, materials science, chemistry, biology, and medicine, (2) space architects specializing on extraterrestrial bases, and (3) engineers for the constraints imposed by the lunar environment. The MaMBA laboratory was built in 2019 into the mock-up of the first MaMBA module (out of six). Subsequently, the laboratory was tested by volunteer scientists for its usability. The scientists used the laboratory for work deemed representative of lunar scientific analyses; the complete test runs lasted one week each, with one test run in June 2019 and the second test run in late September 2019 following some modifications suggested by the scientists. Here, we will present an overview of the scientific topics that we think should be addressed on the Moon, together with a suggestion of scientific instrumentation that would be helpful for such investigations. Moreover, we present the MaMBA laboratory, equipped with the proposed instrumentation, and the outcomes of the test runs with a particular focus on the lessons learned regarding the equipping of the laboratory.

Christiane Heinicke

Viability of Additively Manufactured Electrodes for Lithium-Ion Batteries

As the global economy becomes increasingly electrified, the demand for batteries and energy storage is expected to rise significantly, particularly in the transportation and electricity sectors. Lithium-ion batteries (LIBs) are currently the most advanced and widely used technology in this field. Traditionally, LIBs are manufactured using simple 2D planar geometries to maximize production efficiency and minimize costs. However, this approach limits energy density due to the restricted design flexibility of the electrodes. Additive manufacturing (AM) offers a promising solution to enhance the energy density and efficiency of LIBs by enabling the design of architectures that reduce diffusive losses and allow for a greater amount of active material to be incorporated within the same device footprint, thereby minimizing the use of inactive materials. Different AM techniques come with their own set of limitations, including printing speed, material compatibility, and scale, which must be considered when designing electrodes. Scalable and cost-effective methods are particularly important for electric vehicle batteries, while achieving higher energy densities in microbatteries is crucial for the miniaturization of wearable electronics and medical devices. Here, in this study, we simulate various 3D porous electrode designs for LIBs using graphite and nickel manganese cobalt oxide (NMC) electrodes. These designs are selected to represent structures that could be produced using different AM techniques, such as direct ink writing, fused deposition modeling, and stereolithography. Our results indicate that at higher charging rates and increased areal mass loading, 3D structures can outperform traditional 2D electrodes, although the benefits may diminish with more complex designs that are harder to manufacture. The observed gains in energy density are attributed to improved electrode utilization and reduced diffusive energy losses. This comprehensive analysis of structure–performance relationships will provide valuable insights to guide future research on 3D designs, material selection, and AM techniques for additively manufactured battery electrodes.

25 ENERGY STORAGE

Optimizing acoustical treatment

A mathematical linear programming model is presented for optimizing acoustical treatment and interior decoration of concert and other public halls. This method provides the designer with a range of acoustically correct solutions at increased economical efficiency. The mathematical model uses geometrical data about the room, recommended reverberation time values, the architect's choice of given sound absorbing structures and finishing materials. The model permits inclusion of aesthetical considerations about conditioning, proportioning, or, on the contrary, reciprocal exclusion of any classes of material and/or sound absorbing structure.

Beuran, N.

Print-and-Plate Architected Electrodes for Electrochemical Transformations Under Flow

Flow cell electrodes are typically composed of porous carbon materials, such as papers, felts, and cloths. However, their random architecture hinders the fundamental characterization of electrode structure-performance relationships during in situ operation of porous electrochemical flow systems. This work describes a “print-and-plate” method that combines direct ink writing of micro-periodic lattices with a two-step metal plating process that converts them into highly conductive (sheet resistance 40 mΩ sq -1 ) electrodes. Their operando performance is assessed in an anthraquinone disulfonic acid half-cell using widefield electrochemical fluorescence microscopy, where output current and fluorescence intensity are in excellent agreement. The pressure drop associated with flow through three electrode designs is determined via simulations from which the most efficient design is identified and manufactured via print-and-plate. Confocal fluorescence microscopy is then used to create a 3D map of the state of charge (SOC) inside this print-and-plate electrode. The experimental state of the charge map is in good agreement with computational predictions. The rapid design, simulation, and fabrication of print-and-plate electrodes enable fundamental investigations of how architected porosity affects electrochemical performance under flow.

3D-printing

Investigating property-porosity relationships for micro-architected lattice structures

Micro-architected structures are increasingly valued for their light weight and tunable mechanical properties; this class of material includes sheet structures like the Schöen gyroid and beam lattices like the octet. For design purposes, it is critical to understand how to tune the relative density (RD) to obtain desired mechanical properties. This study investigates the mechanical response of Ti-6Al-4V gyroid structures, spanning a broad range of RDs (0.03–0.90), unit cell sizes (1–4 cm), and sheet thicknesses (0.2–7.8 mm). Results demonstrate that the classical Gibson-Ashby power law scaling between RD and modulus and yield stress does not adequately capture the response over a wide range of RDs, nor does it extrapolate correctly to the fully dense solid. Analytical models, in concert with experimental results and high-fidelity finite element calculations, show that the deviation from Gibson-Ashby reflects a transition from structure-dominated to material-dominated behavior. Distinctions are drawn between scaling relationships and property-porosity models, and an analytical model is proposed to better capture the evolution of mechanical properties with RD. These observations are mirrored in other architected topologies, like the octet, and highlight the importance of understanding the relationship between mechanical properties and geometry for design purposes.

Materials science

Evaluating Fracture Behavior of Bioinspired Alumina-YSZ Composites through Static and Dynamic Mechanical Testing

Ceramic materials are known for their high hardness and strength but are limited by low toughness and sudden failure. Inspired by the microstructure of dental enamel, which features undulating rods that promote crack deflection and energy absorption, architected specimens were designed and manufactured. A bespoke ball-on-ring (BoR) testing apparatus measured the static biaxial rupture strength of these bioinspired materials. Additionally, impact testing with spherical steel projectiles assessed their behavior under dynamic conditions. Monolithic alumina specimens were compared to architected alumina reinforced with yttria-stabilized zirconia (YSZ) rods produced via direct ink write 3D printing. BoR tests revealed that monolithic alumina had a Weibull modulus of 10.53 and a characteristic strength of 372.3 MPa, while the composite specimens showed a Weibull modulus of 5.46 and a characteristic strength of 213.3 MPa. Although the composite failed at lower stresses and projectile velocities, it exhibited notable crack deflection and fracture resistance, with cracks being effectively interrupted by the rod inclusions. The composite specimens also resulted in fewer and larger fragments upon impact. Finite element simulations confirmed the effectiveness of the rod structures in enhancing fracture resistance.

Bioinspired materials

FAIR Data and Interpretable AI Framework for Architectured Metamaterials (Final Report)

This research program established a transformative framework for the discovery and design of mechanical metamaterials, which are architected structures engineered to control physical phenomena like sound and vibration in ways natural materials cannot. To overcome the traditional reliance on trial-and-error, the project developed an interpretable Artificial Intelligence (AI) framework that moves beyond "black box" models to reveal the specific geometric patterns—such as "unit-cell templates"—that govern a material’s performance. A major breakthrough was the development of a hierarchical design method, which allows a single material to block vibrations across multiple frequency ranges simultaneously by layering patterns at different scales without them interfering with one another. This was further expanded to include irregular, graph-based designs that use spanning tree algorithms to ensure structural connectivity while allowing for customized, direction-dependent properties like stiffness and acoustic impedance. Beyond design, the project addressed the practicalities of real-world production by developing uncertainty quantification techniques that account for manufacturing defects and material variability, reducing the need for expensive physical testing by orders of magnitude. To speed up the discovery process, the team implemented Gaussian Process Regression and other surrogate models that provide accurate performance predictions at a fraction of the traditional computational cost. The AI-generated designs were successfully validated through fabrication of physical samples and wave propagation experiments, confirming their ability to accurately guide or reflect waves as predicted. By contributing these tools and high-quality FAIR benchmark datasets to the wider scientific community, this work provides a scalable foundation for advancing technologies in aerospace vibration control, medical imaging, and noise reduction.

36 MATERIALS SCIENCE

Building Specifications

The building in the top photo is the new home of the National Permanent Savings Bank in Washington, D.C., designed by Hartman-Cox Architects. Its construction was based on a money-saving method of preparing building specifications which derived from NASA technology developed to obtain quality construction while holding down cost of launch facilities, test centers and other structures. Written technical specifications spell out materials and components to be used on construction projects and identify the quality tests each item must pass. Specifications can have major impact on construction costs. Poorly formulated specifications can lead to unacceptable construction which must be replaced, unnecessarily high materials costs, safety hazards, disputes and often additional costs due to delays and litigation. NASA's Langley Research Center developed a novel approach to providing accurate, uniform, cost-effective specifications which can be readily updated to incorporate new building technologies. Called SPECSINTACT, it is a computerized - system accessible to all NASA centers involved in construction programs. The system contains a comprehensive catalog of master specifications applicable to many types of construction. It enables designers of any structure to call out relevant sections from computer storage and modify them to fit the needs of the project at hand. Architects and engineers can save time by concentrating their efforts on needed modifications rather than developing all specifications from scratch. Successful use of SPECSINTACT has led to a number of spinoff systems. One of the first was MASTERSPEC, developed from NASA's experience by Production Systems for Architects and Engineers, Inc., an organization established by the American Institute of Architects. MASTERSPEC, used in construction of the bank building pictured, follows the same basic format as SPECSINTACT and can be used in either automated or manual modes. The striking appearance of the bank building shows that, while MASTERSPEC saves time and money, its use involves no sacrfice in architectural design freedom. The Naval Engineering Facilities Command employs an automated specifications system based on SPECSINTACT. The Public Buildings Service of the General Services Administration used SPECSINTACT as a starting point in a plan to make its guideline specifications available to architects and engineers on a nationwide computer network. Public Technology, Inc., a NASA Technology Application Team, is working with Production Systems for Architects and Engineers, Inc., to promote widespread use of the system by state and local governments for cost benefits to taxpayers.

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