Liquid-crystalline elastomers (LCEs) exhibit anomalously high mechanical damping in the nematic phase, arising from coupling between elastic deformation and orientational relaxation. However, their use in impact protection is limited by the low restoring force associated with soft-elastic deformation and by the poor structural stability of bulk soft elastomers under severe loading. Here we investigate hybrid LCE metamaterials in which a thermoplastic polyurethane scaffold provides mechanical reinforcement while the LCE phase remains the primary dissipative medium. Two LCE compositions, differing in crosslink density, were incorporated into thin 2D honeycomb and thicker 3D diamond scaffold architectures. Tensile and compression tests show that scaffolding strongly increases mechanical stability without eliminating large-strain deformability. Impulse-calibrated drop-impact measurements show that both scaffolded architectures retain the broad, attenuated force pulses characteristic of nematic LCE damping, despite their higher stiffness. This preservation of damping is lost when the LCE is heated into the isotropic phase, confirming the essential role of nematic orientational dissipation. Under high-energy impact, 3D diamond LCE metamaterials remain mechanically coherent, whereas isotropic elastomeric controls fail catastrophically. These results show that internal scaffolding can stabilise and reinforce LCEs without suppressing their anomalous impact-damping response, providing a design route to soft metamaterials that combine load-bearing integrity with molecularly enabled energy dissipation.
Adhesive detachment of a flat punch is a fundamental problem in contact and adhesion mechanics and is crucial to soft interfacial systems in fields including robotics and wearables. Classical energy balance method, derived from purely elastic systems, predicts that the pull-off point coincides with crack initiation, so the maximum adhesive force is commonly determined from the crack initiation criterion. However, most soft materials are viscoelastic and dissipative, making the validity of this criterion questionable. Here, we propose a theoretical model based on the Maugis-Dugdale adhesive model to investigate the delayed detachment of a flat punch from a viscoelastic substrate across a broad velocity range. We show that the crack initiation and the pull-off point coincide only at very small or very large retraction velocities, while pronounced deviation appears at intermediate velocities. The delay originates from the low resistance to crack initiation and the stable expansion of the cohesive zone during crack propagation. We further investigate the effects of retraction velocity, adhesion parameters, and modulus ratio on the delay and present an analytical estimate of the critical velocity corresponding to the maximum delay, as well as the pull-off force below this velocity. Experimental results are broadly consistent with the model, while also revealing the limitations of the model in describing real systems for further research. This study clarifies the applicability of the crack initiation criterion for pull-off prediction in viscoelastic adhesive systems and provides a simple practical approximation for pull-off force when this criterion no longer holds.
The desire to make tough and damage tolerant ceramics has long been a challenge in structural materials. Although significant progress has been made in developing ceramic matrix composites (CMCs) as the most common solution, challenges associated with manufacturing net-shaped components have restricted their broader application. Non-equilibrium synthesis of elemental powders provides new opportunities for near net shape processing of tough monolithic ceramics that comprise binary carbides and ternary MAX phases. This study presents a detailed numerical study of the stiffness-toughness trade-off in such a binary-ternary system. Specifically, we investigate the influence of the ternary phase clusters’ volume fraction, shape, and shear strength. The key finding of this study is that decreasing the strength of the ternary phase precipitates can increase the toughness without significant loss of stiffness. Increasing the aspect ratio of the ternary precipitates also increases toughness, but at the cost of reduced stiffness. Increasing the ternary volume fraction will also increase toughness, albeit at the cost of reduced stiffness. Our results are expected to serve as a design tool to help vector the processing of binary-ternary ceramics for specific applications.
Mechanical characterization remains one of the principal efficiency-limiting steps in the materials development and deployment pipeline. The traditional paradigm, based on standardized tests using geometrically simple specimens followed by calibration and validation of pre-assumed constitutive laws, has proven remarkably effective for ensuring reproducibility and inter-laboratory comparability. However, it was not conceived for the combinatorial design spaces emerging from modern materials discovery frameworks. Each conventional test probes only a limited region of the admissible stress–strain space, whereas characterizing complex or anisotropic materials requires multiple specimens and loading configurations, increasing inter-specimen variability and compounding time and resource costs. Consequently, existing workflows remain structurally incompatible with the throughput, adaptability, and autonomy demanded by modern manufacturing and digital design systems. Recent advances in experimental and computational mechanics are reshaping what is achievable. Full-field measurement techniques now provide high-resolution full-field kinematic information per experiment, while developments in scientific computing and machine learning enable data-driven constitutive model discovery and strategies for autonomous systems. Despite progress, these components remain largely fragmented, and coherent frameworks linking experimental design, data integration, model discovery, and validation remain underdeveloped. This review identifies four interdependent pillars enabling autonomous mechanics-based materials characterization: informative experimental design using heterogeneous specimen geometries; multi-fidelity data integration for denoising, sparse reconstruction, and dimensionality reduction of full-field measurements; physics-informed constitutive model discovery enforcing thermodynamic admissibility; and closed-loop validation with adaptive feedback driven by residual model uncertainty. We outline a path toward autonomous characterization systems operating at the pace and scale required for materials engineering.
As a physics-based free-form design methodology, topology optimization has long served as an inverse design tool for creating materials and structures with targeted linear mechanical properties. In the past decade, its extension to nonlinear and potentially multi-physics mechanical behaviors has grown rapidly, enabling the development of wide-ranging new materials and structures with highly complex mechanical responses. This review paper discusses recent advances in this dynamic and fast-evolving field, highlighting key achievements, existing challenges, and potential future directions. The focus is on nonlinear mechanical behaviors, complex responses, and various functions enabled by topology optimization. We explore several categories of nonlinear mechanical phenomena arising from various sources, including material nonlinearity, large deformations, contact mechanics, and multi-physics interactions. As detailed in the paper, the field still faces substantial and multifaceted challenges ranging from accurate modeling and efficient computation to advanced fabrication techniques and experimental validation. Meanwhile, there is considerable room for innovation both in advancing technical methods and in exploring new nonlinear mechanical responses and functions, particularly through inverse design. This paper aims to serve as a guide and reference for topology optimization of nonlinear mechanics for programmable materials and structures.
Machine knitting provides a scalable platform for manufacturing multifunctional textiles in which geometry, mechanics, and embedded functionality can be programmed at the stitch level. However, predictive design tools capable of linking knit architecture to large-deformation mechanical response remain limited. Here, we develop a reduced-order spring-network model that captures the relaxation, unfolding, and deformation of knitted fabrics composed of checkerboard arrangements of rib and garter patches. The model accurately predicts the corrugated relaxed configuration of the knits and the evolution of local deformations under tensile loading using only linear extensional and torsional springs. Combining simulations with experiments, we show that the programmed unfolding of the corrugations generates tunable auxetic behavior, with both the magnitude of the negative Poisson's ratio and the strain at which it occurs governed by the unit-cell geometry. We further integrate capacitive strain sensing directly during fabrication through partial plating of conductive yarns, eliminating post-processing. The resulting knitted capacitors exhibit programmable tradeoffs between strain sensitivity and sensing range, enabling either highly sensitive sensors over narrow deformation windows or lower-sensitivity sensors capable of measuring larger strains. Together, our modeling framework and fabrication strategy provide a route toward the rational design of mechanically programmable, sensorized knits with tailored shape-morphing and sensing functionalities.
In a previous paper (Itskov, 2026) we presented a hyperelastic isotropic material model whose stress-strain response is nonlinear even at infinitesimal deformations and cannot thus be linearized. As a result values of Poisson's ratio greater than one half were obtained. In this contribution, we further propose an isotropic strain energy function which is always positive-definite and depending on material constants predicts arbitrary values of Poisson's ratio (except of-1) in agreement with the laws of thermodynamics. The model response appears plausible in various strain states and stable within a wide range of deformations.
Driven by the development of advanced miniaturized devices, the pursuit of higher precision in ultra-precision cutting increasingly demands smaller cutting scales, and critically, surfaces with superior atomistic integrity. Consistently, understanding of cutting mechanisms has evolved from macroscopic to diverse nanoscale phenomena. However, the fundamental cutting mechanisms at atomic and close-to-atomic scales, where defect activity is severely constrained, remain elusive. Using molecular dynamics simulations, we show that atomic-scale cutting enables defect-suppressed machining for the model single-crystal copper system considered here. Specifically, at close-to-atomic cutting depths, the limited defect nucleation volume compels the material to be removed via elastic strain-induced amorphous transformation. This unique mechanism contrasts sharply with shear band-mediated grain boundary sliding during nanometric cutting. Crucially, under the simulated conditions, this amorphization-driven removal introduces no additional crystalline defects, yielding exceptionally high-quality surfaces. Our simulations suggest the potential importance of atomic-scale cutting for future advanced manufacturing and offer mechanistic insights into material removal at these extreme scales.
Mechanical logic systems offer a promising pathway for creating autonomous materials and “electronics-free” soft robotics, yet achieving post-reprogrammability and scalable integration remains a critical bottleneck. Here, we report a universal mechanical computing platform based on a Kinematic-Energy Decoupled (KED) architecture. By isolating the kinematic trajectory (defined by a rigid four-bar linkage) from the energy storage mechanism (governed by modular elastic constraints), we create a “mechanical bit” with a highly tunable double-well potential energy landscape. We demonstrate that fundamental logic gates (AND, OR, XOR) can be precisely “programmed” into identical physical layouts simply by modulating elastic parameters and geometric boundaries, rather than altering the structural topology. Leveraging the unit’s inherent biaxial symmetry, we successfully scale these units into complex combinational modules, including a mechanical half-adder and a 2-to-1 multiplexer. Furthermore, we implement non-volatile sequential logic (SR Latch) by exploiting path-dependent, non-Abelian energy transitions. This energy-centric design strategy provides a robust, scalable, and functionally complete foundation for the next generation of intelligent mechanical metamaterials and autonomous structural controllers.
First-principles-accurate predictions of single-crystals strength are widely used to build materials databases and accelerate the design of new materials. However, accurate strength prediction requires accounting for cooperative atomic motion in large systems, whereas typical first-principles energy calculations are limited by computational resources to only several hundred atoms. We combine the atomic finite element method (AFEM) with density functional theory (DFT) to obtain the first-principles-accurate atomic stiffness (Hessian) matrix for large single crystals from calculating energies on small atomic subsystems. A fast method is then developed to compute the strength of large single crystals under arbitrary uniform loading with first-principles accuracy, enabling the strength calculation of a 14,000-atom system in 20 min on 256 cores. The computational cost is reduced by 4 orders of magnitude compared with existing methods. We further propose a normalized minimum eigenvalue convergence indicator to determine the minimum system size required for accurate ideal-strength simulations. With this indicator, a 3D atomic system is found to require about 8000 atoms to achieve ideal-strength convergence. The converged values are closer to experimental results and may help accelerate the search for new and better materials.
Polymeric foams are widely used architected materials, owing to their great versatility exploited in a broad spectrum of applications. However, the lack of control over their morphology has led to the emergence of a new field of investigation, referred to as liquid foam templating, which aims at controlling finely the architectures of solid foams by controlling those of their liquid precursors. Here we focus specifically on the liquid/solid transition of monodisperse polyurethane foams, where the solidification is externally triggered via UV irradiation for a precise control of the foam morphology. We show that it is possible to take advantage of the mechanics of drainage of the matrix of the foam to quantify the efficiency of the external stimulus. To do so, monodisperse foams are prepared via millifluidics, and their morphology is analyzed via X-ray tomography as a function of the delay between generation and irradiation of the foam. The mechanism of solidification triggered by UV exposure includes here thermal effects, but the protocol developed to follow the influence of the external stimulus could be applied to a wide range of stimuli to assess-and exploit-the solidification of foams in a non-destructive manner.
Intermittent hypobaric hypoxia (IHH), a common exposure pattern in high-altitude occupational environments, can modulate arterial wall behavior and potentially affect pulsatile load buffering. In this study, we examined how acute and chronic IHH influence the passive elastic and viscoelastic properties of the descending thoracic aorta (DTA) in adult rats. Planar biaxial tensile tests under low strain-rate conditions and stress-relaxation protocols were combined with quantitative histology to assess both functional and structural adaptations. Most elastic parameters derived from the stress-stretch response remained unchanged across Control, acute IHH, and chronic IHH groups, indicating preservation of the overall passive biaxial mechanical response. Nevertheless, the chronic IHH group exhibited a significant reduction in the longitudinal high-stretch stiffness parameter (E2), suggesting subtle alterations in the arterial response under elevated loading conditions. Stress-relaxation experiments revealed trends toward increased stress decay and dissipated energy in the chronic IHH group, particularly in the circumferential direction, although these differences did not reach statistical significance. Histological analysis showed reduced cell nuclei density and modest elevations in elastin and collagen content in hypoxia-exposed groups, consistent with low-grade remodeling that does not translate into detectable changes in elastic behavior. Collectively, these findings indicate that IHH induces microstructural modifications and meaningful alterations in time-dependent mechanics while largely preserving the low strain-rate biaxial mechanical response of the aortic wall. This work provides an integrated biomechanical framework for evaluating arterial remodeling under hypoxic stress and supports the view that the DTA exhibits a robust passive mechanical phenotype under intermittent hypobaric exposure.
In this work, we develop a gradient-based design approach that exploits grayscale digital light processing (DLP) 3D printing for extremizing the nonlinear and linearized response of soft metamaterials — materials that harness engineered geometric instabilities to undergo large and programmable changes in configuration. Grayscale DLP approaches modulate local mechanical properties at the pixel scale by tuning the light intensity within a single grayscale image, unlocking an exceptionally large design space. To effectively navigate this space, we develop smooth mappings between local light intensity values and global quantities of interest that characterize the behavior of soft metamaterials. Enabling these smooth mappings are robust and differentiable nonlinear finite element simulations powered by a trust region solver. A PDE-constrained optimization problem is then solved to invert these mappings and produce light intensity distributions that endow the printed part with varying stiffness and flexibility in distinctive regions. It is shown that optimizing the distribution of soft and stiff phases throughout a metamaterial structure results in markedly different buckling and self-contact configurations to drive extremized nonlinear compression and linearized vibration responses. Optimized light intensity distributions are translated to grayscale images and directly used to print soft metamaterial samples, showing remarkable agreement between the buckling and self-contact response in simulated and measured deformed configurations.
Particle transport is traditionally described by the Stokes-Einstein relation, where diffusivity is primarily governed by particle size and medium viscosity, resulting in a relatively limited design flexibility for controlling transport behavior. Recent studies have shown that modulating the mechanical state of soft materials can dynamically regulate particle diffusion, a phenomenon referred to as mechano-diffusion, introducing a new design dimension for engineering transport in polymer networks. Such mechano-diffusion processes are particularly important in systems where the regulation of particle transport within soft media directly determines system performance, including controlled molecular delivery, selective transport across polymer networks, and particle transport in biological and environmental systems. In recent years, increasing attention has been devoted to mechanics-coupled particle transport in soft materials, motivating the need for a timely and comprehensive review. This review aims to provide a systematic overview of mechano-diffusion by (i) summarizing the fundamental mechanisms governing particle transport in polymer networks, (ii) introducing experimental platforms and computational tools to elucidate transport dynamics, and (iii) highlighting emerging strategies for engineering selective and controllable particle transport for future applications. Overall, this review establishes a unified perspective on mechano-diffusion that bridges polymer mechanics and particle transport, providing new insights for engineering responsive and selective transport processes in soft materials.
Liquid crystal elastomer (LCE) is a soft active material capable of large, reversible actuation upon temperature changes, making it an ideal candidate for applications in smart structures, soft robotics, and sensors. Topology optimization of LCE can enable strategically distributed director patterns to fully exploit its multiphysics mechanism. However, existing approaches often miss to account for manufacturability. Aiming to produce fabricable optimized LCE structures and to further expand design space, this study proposes a general topology optimization framework for LCE under large deformations to simultaneously optimize free-form geometry and continuous LCE director distributions that are suitable for Direct Ink Writing (DIW). The framework is built upon a rigorous model to accurately capture LCE's large thermal deformation, with a novel continuation filtering technique to realign LCE directors smoothly, accounting for LCE's unique physical properties. With the proposed method, we present several optimization formulations to design various complex and intriguing LCE behaviors under temperature changes, including programmable complex shape morphing, inducing desired strains for biological tissues, and achieving non-monotonic thermal expansion-contraction under a monotonic temperature rise. The optimized LCE designs successfully achieve versatile desired functionalities while featuring a continuous director distribution suitable for DIW fabrication. Our findings will facilitate the discovery of arbitrarily manipulatable and physically realizable LCE responses, expanding the horizon for multi-physics active materials.
Auxetic lattices have demonstrated potential for impact mitigation thanks to their unique configurations. Building upon a prior theoretical framework, this study presents the experimental realization of a theoretically optimized, impact-mitigating bilayer auxetic metamaterial. However, physically realizing the idealized material parameters assumed in theoretical models remains a significant challenge. A central innovation of this work is the development of precise, custom digital polymer formulations, created by tuning the blending ratios of base 3D-printing photopolymers to realize theoretically optimal visco-elastic properties. To support this, we first characterized the broadband visco-elastic behavior of these candidate digital materials formed from a series of 3D-printable photopolymers using dynamic mechanical analysis (DMA). The data informed the development of a combined nonlinear visco-elastic constitutive model—integrating a multi-term Prony series with a neo-Hookean formulation—that accurately captures the intricate mechanical behaviors of real-world polymers. This model guided the selection of optimal digital formulations for fabricating an optimized bilayer metamaterial; its performance was then evaluated via drop-tower impact tests. The finite element predictions, using the nonlinear constitutive model, demonstrated excellent agreement with experiments, particularly throughout the critical loading phase across a wide range of impact severities. This validated our design's effectiveness in achieving simultaneous force and impulse reductions and highlighted a transition from a material-dominated to a hybrid deformation regime governed cooperatively by material and structural properties. By successfully bridging the gap between computational design and physical realization, this work demonstrates a reliable methodology for designing the next generation of high-performance protective metamaterials.
Scientific discovery is not only answer generation but revision of the representational regime in which evidence, artifacts, operations, and verifiers are typed. We develop a category-theoretic account of agentic discovery for materials science. In a fixed regime b with schema category S_b, the system state is a copresheaf I_t: S_b -> Set, and provenance is the category of elements ∫_S_b I_t. Fixed-regime operation is an update on such states, endofunctorial only when provenance-preserving refinements are specified and preserved. Discovery is instead a verified regime transition u: S_b -> S_b': old artifacts are preserved, transported by the left Kan extension Lan_u I_t, and compared with the post-transition state to identify residual content beyond functorial transport. This separates retrieval, search, and discovery without subjective novelty. We instantiate the framework in two systems. In Builder/Breaker, a protein-mechanics world model is revised under a Minimum Description Length gate; the accepted law expresses within-chain flexibility as all-mode elastic compliance conditioned by slow collective-mode participation, or mode-conditioned compliance. In CategoryScienceClaw, typed skills, artifacts, open needs, workflow mutation, gates, stress tests, and public discourse become a proof-carrying knowledge-computation graph. A fiber-network example records candidate models, rejected alternatives, an AIC gate, perturbation tests, and an accepted orientation-tensor anisotropic stiffness surrogate over an isotropic fiber-count descriptor. Together, the cases show how category theory can be both a mathematical language for discovery and an engineering specification for self-revising AI discovery systems.
