Vibration responses from nonlinear mechanical systems exhibit rich dynamical structure that can be utilized for information encoding and processing. We demonstrate that such structures can be used to encode and manipulate information in a manner analogous to multi-qubit systems. By using a coupled mass and conical spring oscillator, we reveal that distinct harmonic segments of the nonlinear response can be projected onto modal eigenstates to form two-level elastic-bit subsystems, which are analogous to qubits. These bits arise from measurable amplitudes and phase relationships across the Fourier spectrum and evolve deterministically under steady-state excitation. By combining multiple spectral segments within a single oscillator, we achieve two-bit and three-bit states that occupy four- and eight-dimensional Hilbert spaces, respectively. The time dependence of the complex modal coefficients yields intrinsic transformations that act as phase and rotation type gates. The temporal evolution of the complex modal coefficients results in phase accumulation and a rotation-like evolution within this state space. To characterize how the system moves between experimentally observed logical states at different times, we derive a Householder reflection that yields the exact Hermitian and unitary operator connecting these states. This unitary transformation is subsequently decomposed into sequences of analogous quantum gates, providing a representation of the observed modal evolution in terms of familiar multi-qubit logic primitives. This spectral-encoding approach enables scalable state construction within a single mechanical platform, establishing a pathway toward room-temperature mechanical computation based on deterministic nonlinear dynamics.
In this study, we provide a comprehensive analytical framework that examines the undrained electromechanical behavior of porous piezoelectric (PP) cones when bending and torsional moments are applied at the apex. By integrating Biot's theory of poroelasticity with a coupled electroelastic formulation for transversely isotropic materials, this study presents a unified continuum model that accurately captures the interaction between solid and fluid phases. The governing field equations are systematically derived through the potential function method, leading to exact closed-form solutions for the displacements, stresses, and electric potential. The model's accuracy is verified against classical electroelastic benchmark solutions and corresponding finite element method (FEM) simulations. Parametric studies reveal that porosity, apex angle, and electromechanical coupling coefficients, and anisotropy tests significantly influence stress localization, electric displacement, and field attenuation. The results show that field singularities are more pronounced near the apex (e.g., exhibiting a high-order dependency on the radius) and gradually decrease in the far-field region. In addition, when the apex angle approaches pi/2 , the solutions reduce to the corresponding semi-infinite body (half-space) problem. The developed formulation provides a strong theoretical foundation for understanding and designing advanced porous piezoelectric sensors, actuators, and energy harvesting devices, particularly in environments with complex electromechanical loading conditions.
Full-field three-dimensional (3D) deformation measurement of flexible structures undergoing large reconfigurable deformation remains a significant challenge in experimental solid mechanics, particularly when pronounced surface curvature and large out-of-plane displacements exceed the depth-of-field limitations. Local defocusing leads to incomplete displacement fields and deteriorated measurement accuracy in stereo digital image correlation (DIC). To address the challenge, this article presents a single-camera stereo DIC system integrated with an electrically tunable lens (ETL) to enable large-depth-of-field 3D deformation measurement. High-quality speckle pattern imaging is achieved by dynamically adjusting the focal state. To address the intrinsic inconsistency of geometric parameters induced by ETL-driven focal variation, a cross-current calibration and coordinate-unification framework is developed, allowing 3D reconstructions obtained under different focal states to be accurately mapped into a unified physical coordinate system. A periodic calibration target and a defocus-robust frequency-domain feature extraction strategy are employed to ensure reliable reference-point localization under defocused conditions. The performance of the proposed system is validated through experiments, including repeatability assessment under repeated focal switching, large-range axial translation measurement over 200 mm, and full-field deformation measurement of a flexible multistable thin-shell structure undergoing configuration transitions. The results demonstrate that the proposed approach achieves continuous and physically consistent 3D displacement fields across an extended depth range, with high repeatability and low measurement error. The developed method provides an effective experimental tool for investigating large deformation and reconfiguration behaviors of flexible structures.
In this article, the thermodynamic configurational force and velocity associated with a reaction-diffusion moving interface are studied to derive both the Cauchy stress, its Eshelbian form, and their Piola transformations to the reference configuration. The driving force on the interface is mathematically connected to mechanical, thermal, and chemical fields both in the bulk and on the interface, including anisotropic and inhomogeneous interface stress. Systematically applying a general interface transport theorem, we derive the balance laws, the thermodynamic principles, and the consequent thermodynamic restrictions on the interface stress under the driving forces. These forms are shown to mirror their bulk versions. Next, the velocity-force Eshelbian forms of momentum balance in the bulk are reviewed, followed by the derivation of Eshelbian forms for the analogous interface momentum balance equations. However, the interface momentum balance includes an additional curvature term that only vanishes on a planar surface. We illustrate the derived Eshelbian forms and the interface configurational force through three examples. In the first example, we show that the Griffith criterion of fracture mechanics naturally results from the second-law condition on a crack in two-dimensional plane. In the second and third examples, we calculate the configurational force on a planar interface as well as an interface at a constant radius of curvature. We show that when the curvature is constant, the interface configurational force in the current configuration vanishes but does not in the reference configuration. This indicates that all the inhomogeneities of the material are expressed through the bulk configurational force alone in the current configuration when curvature is constant.
Geometric imperfections are the primary cause of the pronounced reduction in the buckling load of cylindrical shells subjected to axial compression. Localized defects, which are commonly introduced during manufacturing, are particularly prevalent. This study investigates how interactions between such localized defects affect the critical buckling load of cylindrical shells through high-fidelity finite element simulations. We first quantify the influence of defect amplitude on the knockdown factor for cylinders with various radius-to-thickness ratios containing a single defect. The results show that the knockdown factor decreases with increasing defect amplitude and gradually approaches a threshold value. We then examine the buckling behavior of shells containing two identical defects. The results reveal that the knockdown factor varies nonmonotonically with increasing spacing between the defects. To identify the relative location beyond which defect interaction vanishes, we introduce a new definition of defect spacing such that the minimum threshold spacing for noninteracting defects is independent of the defect width. The simulations further demonstrate how the relative orientation of the defects, measured by the inclination angle, affects the threshold spacing. Finally, we consider shells containing two defects of different amplitudes. It is shown that the qualitative behavior of the relationship between the knockdown factor and defect spacing is strongly affected by the ratio of defect amplitudes. When the defects are sufficiently far apart, the buckling load of the shell is determined entirely by the defect with the larger amplitude.
A design methodology is proposed for architected microstructures that exhibit highly anisotropic and tunable stiffness, achieved solely through geometric configuration without modification of the material composition. Systematic variation of key geometric parameters yields stiffness anisotropy exceeding three orders of magnitude, thereby enabling independent control of axial and shear moduli. Such decoupled stiffness tailoring provides substantial flexibility for optimizing mechanical performance across diverse engineering applications. The dynamic characteristics of the proposed microstructures are comprehensively investigated, revealing pronounced wave anisotropy, directional energy transmission, and frequency-dependent phenomena, including directional bandgaps, single-mode propagation, and wave mode conversion. In particular, mode conversion enables elastic waves to be redirected by 90 deg, while the adoption of an oblique lattice enhances conversion efficiency and broadens the directional bandgap, thereby improving waveguiding performance. The concept is further extended to an annular metastructure, which exhibits efficient wave trapping and azimuthal energy confinement, in sharp contrast to the omnidirectional propagation observed in isotropic counterparts. These findings establish a rigorous framework for the design of anisotropic architected materials with finely tunable wave control, offering significant potential for applications in vibration isolation, acoustic steering, and energy localization.
Developing underwater acoustic devices with flexibility in both shape and functionality is critical for applications in sonar, tracking, and communication, where adaptation to complex environments is required. Among such devices, acoustic metasurfaces have attracted significant attention for their exceptional ability to manipulate acoustic wave propagation. However, most existing metasurfaces are predesigned for specific flat or curved geometries and lack the flexibility to adapt to diverse shapes. Moreover, the strong coupling between acoustic and elastic waves in solid-water systems tightly links device functionality to its shape and deformation, posing major challenges for reconfigurability. Here, we present a design strategy for flexible waterborne acoustic metasurfaces that combine conformability with tunable acoustic-path control. The metasurface comprises Helmholtz resonant unit cells interconnected by soft hydrogel materials. The low stiffness of the hydrogel allows the metasurface to deform freely without inducing mechanical strains in the resonant unit cells. In addition, the hydrogel's low shear modulus suppresses nonlocal acoustic-solid coupling, enabling a discrete analytical design approach. By exploiting local acoustic-solid interactions, each unit cell achieves dual control of phase and amplitude across a broad frequency range. Furthermore, introducing symmetric sliders into the unit cells imparts tunable acoustic functions. The resulting flexible metasurface supports multiple functionalities-including acoustic illusion, wideband diffuse reflection, conversion of propagating waves into surface waves, and acoustic cloaking-demonstrated through simulations and experiments. Our work provides a new design strategy for multifunctional underwater acoustic manipulation by integrating mechanical flexibility with controlled acoustic-solid coupling.
Wave invisibility has great values in aerospace and military fields. In this work, a flexural wave metamaterial cloak is proposed for multiple arbitrary targets in elastic thick plate. The fuzzy proportional-integral-derivative (PID) active control is applied. The scattering field of flexural wave in thick plate is considered. Based on the wave function expansion method and Mindlin thick plate theory, the wave equation for infinite and arbitrary hole targets with their enveloping cloaks is derived. Both structure and material parameters are considered to discuss about the dynamic stress concentration, scattering amplitude, and scattering cross section (SCS) of the multiple targets. In addition, the cloaking device is designed to locate around every hole target, in which multiple layers with regularly arranged piezoelectric (PZT) patches are included. Every PZT patch is connected to the external active circuit with fuzzy PID control function. The theoretical and experimental results indicate that the present flexural cloak meets invisible requirements. Dynamic stress concentration, scattering amplitude, and scattering cross section of multiple targets are reduced by the cloaking configuration. Compared to the original structure without fuzzy PID active control, the invisible performance with the active cloak can be effectively enhanced.
Subsurface penetration by compliant actuators is limited by the competing requirements of force generation and elastic stability. This work investigates the mechanics of granular penetration using thermally actuated liquid crystal elastomer (LCE) structures, focusing on buckling-limited force output and structural design. Reversible shape programming enabled by liquid crystal alignment and Poisson-effect-induced transverse strain produces controlled axial extension and torsional deformation under thermal actuation. Experiments and numerical simulations show that single-pillar LCE actuators are limited by global buckling. To overcome this limitation, multi-pillar architectures are introduced to increase effective bending stiffness while preserving soft actuation. Specifically, a tri-pillar configuration increases the buckling-limited force capacity by more than an order of magnitude compared to a single pillar. Finite element simulations and buckling analyses quantify the dependence of critical load on elastic modulus, pillar geometry, and pillar number, identifying the governing instability modes under laterally constrained conditions. Sequential penetration cycles are enabled through the integration of shape memory polymer supports that mechanically reset actuator geometry, achieving cumulative penetration depths of up to 24 mm. Measurements of granular resistance further demonstrate that imposed tip rotation substantially reduces external loading and delays buckling. Integration of a flexible temperature sensor into the actuator tip shows the feasibility of in situ subsurface measurement during penetration. These results provide mechanics-based design guidelines for compliant actuators operating under compressive loading in granular environments, including the ocean floor.
Leveraging the ability to customize dispersion characteristics in phononic crystals (PnCs) enables the arbitrary control of elastic or acoustic wave propagation. However, the whole dispersion involves complex profuseness eigenstates from low frequencies to high ones, while the wave vectors should cover the small wave vectors to the large ones. Here, a physics-informed framework is introduced for forward prediction and inverse design of PnCs with customized dispersion relations. By integrating the elastic wave equation and elastic wave field information into the learning process, the proposed approach ensures both high computational efficiency and enhanced interpretability, enabling customized dispersion engineering of PnCs and thereby achieving arbitrary required whole dispersion relations covering the total frequency range and wave vectors. Furthermore, the method effectively handles diverse kinds of dispersion curves in PnCs, including the dispersion curves with Bragg scattering, local resonance, prescribed group velocities, and modal degeneracy. Numerical results show that the present physics-informed design methodology has an obvious advantage of purely data-driven approach in the aspect of design accuracy and data efficiency, constructing the meticulous elastic/acoustic wave propagation in PnCs or periodic structures.
A finite strain, multi-field model for hydrogen embrittlement in porous ductile metals is presented, based on a geometric phase-field approach applied on the Gurson-Tvergaard-Needleman model. The hydrogen-enhanced decohesion mechanism is incorporated by augmenting the damage-driving force with a Rankine-type, hydrogen-dependent term governed by the maximum principal stress. This allows the model to capture both ductile and brittle fracture modes, as well as the transition between them. The phase-field formulation introduces an intrinsic length scale that regularizes the solution and eliminates mesh dependency. To address volumetric locking, a mixed finite element formulation with pressure variation is employed. The model successfully captures key experimental observations, including the strain-rate dependence of tensile failure, the transition from internal to surface fracture with increasing deformation rate, and the significant reduction in fracture toughness under hydrogen exposure.
The homogenization approach is widely used in lattice structure design to simplify modeling of complex geometries by representing them as simple solid elements in finite element analysis (FEA). Homogenized material properties are obtained through microscale analysis of a representative volume element (RVE). Several methods exist to compute effective properties, including beam theory, asymptotic homogenization, and the finite element method. FEA is commonly used for its ability to model arbitrary lattice geometries accurately. However, for complex structures, conventional FEA is computationally expensive, requiring extensive preprocessing and producing large stiffness matrices, which reduces efficiency in multiscale analysis and optimization. This study introduces an image-based machine learning framework for efficient microscale modeling of arbitrarily shaped lattice structures. Unlike traditional surrogate modeling approaches that rely solely on machine learning, the novelty of this method lies in maintaining consistency between physical modeling and machine learning representations. Specifically, the binary matrix obtained via image processing is used to generate the finite element model for asymptotic homogenization (AH)-based microscale analyses, whose outputs train a convolutional neural network (CNN). This eliminates the need for conventional mesh generation and ensures the network learns from physically consistent data. The CNN framework enables rapid and accurate prediction of effective material properties from image-based RVE representations. The developed CNN models predict the homogenized elastic properties with normalized mean absolute error below 2% and normalized mean squared error on the order of 10(-4), while requiring only a fraction of the computational time associated with conventional finite element-based homogenization analyses.
Twin boundaries play a central role in the functional behavior of martensitic materials; yet, the mechanisms governing the initiation of their motion remain poorly understood for twins lying along irrational crystallographic directions. Here, we present an atomistic investigation of the onset of motion of both rational and irrational twin interfaces in a two-dimensional model lattice with rectangular unit cells. Using quasistatic shear loading and full linear stability analysis, we show that the initiation of twin boundary motion is signaled by a nonlocal linear instability, marked by the vanishing of the lowest eigenvalue of the Hessian; the corresponding eigenmode predicts the atomic displacements that initiate motion. We find that irrational twin boundaries have significantly lower critical shear stress to initiate motion compared to rational twin boundaries. Furthermore, we find that they display unusual mechanisms to initiate motion such as the formation of microtwins in directions orthogonal to the overall twin boundary. Finally, we compare various local measures against the nonlocal stability analysis and find that the former do not capture that irrational twin boundaries initiate their motion at lower stresses compared to rational boundaries.
Stretchable inorganic electronics have emerged as a promising technology for integrating electronic devices into complex, deformable surfaces, offering advantages in applications such as wearable electronics, health monitoring, and soft robotics. Porous elastomer substrates combine high permeability with a low effective modulus, enabling large elastic stretchability and improved breathability and wearing comfort. However, unavoidable pore inhomogeneity and interconnect misregistration introduced during the fabrication process can significantly affect the elastic stretchability and the consistency of this stretchability. In this work, we perform systematic finite element analyses of serpentine interconnect on porous elastomer substrates to quantify the effects of stochastic pore inhomogeneity and interconnect misregistration on both elastic stretchability and its consistency. The results reveal a significant trade-off between maximum stretchability and robustness: low-pore-density designs offer enhanced stretchability under ideal fabrication conditions but are highly sensitive to pore irregularities and transfer-printing misregistration, leading to large performance scatter and poor consistency. In contrast, high-pore-density designs, though inherently less stretchable, are far less sensitive to manufacturing deviations, thus maintaining small performance scatter and good predictability even when multiple deviations are present. Further analysis shows that the influence of various geometric perturbations can be rationalized by their impact on the effective suspended area of the serpentine interconnect. These findings provide quantitative guidelines for structural optimization and process-tolerance design of stretchable inorganic electronics based on porous elastomer substrates.
Lattice materials offer extraordinary opportunities for lightweight structural design, yet their practical application is often compromised by their propensity for brittle fracture originating from inherent defects. This study introduces a novel design strategy to overcome this limitation by incorporating nonlocal interactions into the lattice architecture. We investigate the fracture mechanics of two-dimensional lattice materials with and without nonlocal connections through a combination of finite element analysis and a node-based homogenization method. Our theoretical model accurately predicts the crack-tip displacement field, revealing significant deviations from classical continuum mechanics. The results strikingly demonstrate that nonlocal lattices exhibit superior stiffness, strength, and fracture toughness compared to their local counterparts. An energy-based analysis unveils the core toughening mechanism: nonlocal interactions effectively redistribute stress at the crack tip, leading to the formation of a larger plastic zone. This enhanced plasticity not only delays crack initiation by increasing the required energy for fracture but also elevates crack growth resistance by dissipating more energy during propagation. This work elucidates the fundamental role of nonlocality in enhancing fracture performance and provides a robust framework for designing tough, defect-tolerant lattice materials for high-performance applications.
Materials exhibiting near-zero transverse deformation under tension, a property known as an ultralow Poisson's ratio (UPR), are highly sought for precision applications. However, UPR materials are conventionally limited to soft matters, hindering their use in extreme load-bearing environments. Here, we overturn this paradigm by discovering robust UPR and even negative Poisson's ratio behaviors in diamond and cubic boron nitride (c-BN)-two of the known hardest crystals-across finite strains. Combining finite-strain elasticity theory with first-principles calculations, we uncover highly anisotropic elastic responses hidden within their simple cubic structures. Most interestingly, Poisson's ratio of diamond and c-BN for loading along the [101] direction with transverse deformation measured along the [-101] direction (nu([101], [-101])) is ultralow (|nu| < 0.02) across a wide range of strain from -10% to +10%. These results are further supported by direct first-principles tensile simulations and analyses of in situ experimental data. The underlying mechanism is an atomic-scale cancellation of competing transverse deformation generated by bond and angle deformations. This work offers fresh insights into the nearly strain-invariant lateral dimensions in the known hardest crystals, and provides a roadmap for discovering and designing materials that combine extreme mechanical robustness with transverse dimensional stability.
This article presents a closed-form solution for the mixed-mode bending debond test configuration in sandwich composites. The solution is for the energy release rate and the mode partitioning. The finite-length sandwich specimen is considered to be a beam consisting of a debonded part (top face) and a substrate part (core and bottom face). A finite debond exists at the interface between the top face and the core. In the intact region, the two parts are considered to be joined through an elastic foundation, which is a uniform distribution of normal and shear springs. Based on the Euler-Bernoulli beam theory, the solution for a general asymmetric sandwich construction is derived. The energy release rate solution is derived via the J-integral and also from the energy of the broken springs in the elastic foundation. In this approach, the elastic foundation mode partitioning is defined based on the opening and shearing displacement at the tip of the elastic foundation (where the debond ends). The results are computed for a range of load configurations, core/face materials, core/face thicknesses, and debond lengths. The results are also compared with the ones from a finite element study and show good agreement, except for the very small debond lengths.
Poisson's ratio nu is defined by two orthogonal directions, one for longitudinal stretch and one for lateral strain. In elastic solids with cubic symmetry, there are only two stretch directions for which nu is independent of the strain direction. All other values of nu in cubic materials can be expressed in terms of these two, nu 001 and nu 111 , which are both restricted to the isotropic limits of - 1 and 1/ 2 . Extreme values of nu , which by definition lie outside the isotropic limits, occur in materials with nu 001 close to 1 /2 , with the most extreme values in materials with nu 111 far from 1/ 2 . Simple approximate but accurate expressions for the minimum and maximum values of nu are given in terms of nu 001 and nu 111 . Examples of materials with extreme Poisson's ratio are presented using more than 4,000 cubic materials from the Materials Project database.
Failure of rocks under complex loading and progression of damage is of great interest to various rock engineering problems. In this context, the Discrete Element Method (DEM) has proven particularly effective in capturing fracture processes in rocks. However, DEM model parameter calibrations in most studies remain scenario-specific, restricting their applicability under varying loading conditions. To address this limitation, this study develops a DEM framework for sandstone under multiple loading conditions, employing a bilinear elasto-softening contact constitutive model that incorporates tension, shear, mixed tension-shear, and compression damage variables to rigorously capture its cohesive-frictional fracture behavior. A single, scale-independent set of DEM model parameters is derived for uniaxial compressive strength (UCS), Brazilian tensile strength (BTS), and Mode I fracture toughness (SCB) simulations by validating macroscopic DEM predictions against in-house UCS and BTS experiments. The results indicate that the DEM framework accurately reproduces stress-strain responses, peak and post-peak behavior, and fracture evolution, including macro-crack initiation and propagation. Detailed insights into progressive deformation and fracture in sandstone (UCS, BTS, and SCB simulations) are obtained through damage progression indicators (tension and shear) and stress-damage contour plots. Furthermore, a parametric analysis of DEM model parameters is conducted, and the critical parameters governing each simulation are identified.
Wall shear stress (WSS) serves as a crucial link between the dynamics of blood flow and the biological mechanisms that underlie various cardiovascular diseases. This study investigates WSS fluctuations in a collapsible wavy channel using a two-dimensional (2D) fluid-structure interaction (FSI) model. A combination of immersed boundary-lattice Boltzmann and the generalized interpolation material point methods solves the nonlinear coupled equations. The effects of key parameters on WSS fluctuations, including Reynolds number, pulsatile flow period, and external pressures, are analyzed for two systems: one with a wall constraint and one without the constraint. The results show that decreasing the pulsatile flow period and increasing the external pressure increase local WSS fluctuations by destabilizing the system via a fluid symmetry-breaking mechanism. Across all investigated parameter domains, the unconstrained system demonstrates a significantly enhanced ability to minimize WSS fluctuations. Since the wavy channel represents a simplified model of a stented artery, the results from this study can guide and optimize stent design. The two-dimensional simulation is chosen for its low computational cost and its ability to capture key mechanisms. Future research can extend to three-dimensional models for a more comprehensive analysis.
