Deformation mechanisms and prediction of laser butt-welded thin-walled laminated cooling plates with equivalent section-modulus modeling and experimental verification

Fracture in flexoelectric and strain-gradient elastic solids is governed by higher-order electromechanical interactions that strongly alter the near tip behavior of cracks at the nanoscale. Yet most prior studies are restricted to the simplest crack modes or treat only selected aspects, yielding an incomplete picture. This work develops and verifies a higher-order fracture electromechanics framework that consistently incorporates strain gradient elasticity and flexoelectricity within an electric field based formulation. Analytical asymptotics are first established for Modes I-III, highlighting the role of true stress measures in capturing higher-order singularities. A mixed finite element scheme is then employed to resolve all strain-gradient components and to provide accurate post-processing of electrical and mechanical crack-tip fields. Numerical investigations address (i) a Mode I edge-cracked panel, and (ii) a mixed-mode cracked truncated pyramid. Results show that SGE introduces an r − 3 / 2 singularity near the crack tip and shifts the transition zone between higher-order and classical r − 1 / 2 regimes. Flexoelectric coefficients induce nonlinear variations of the crack-tip electric potential, while the material length scale governs the extent and shape of the crack-tip opening profile. In a truncated pyramid, surface cracks significantly bias electromechanical fields and may influence the experimental back calculation of flexoelectric parameters. The study provides a comprehensive framework for higher-order electromechanical fracture mechanics, with implications for the design and reliability of nano- and microelectromechanical systems. • A unified higher-order fracture framework combining strain-gradient elasticity and flexoelectricity. • Analytical asymptotics for Modes I-III showing r-3/2 true-stress singularities. • A mixed finite-element formulation resolving complete strain gradient tensors. • Nonlinear size-dependent crack-tip fields governed by material length scale l and flexoelectric coefficients are found. • Mixed-mode surface-crack effects on electromechanical fields in truncated pyramid specimens are demonstrated.

Nonlocal and strain gradient methods for analysis of vibration characteristics of a spherical nanoparticle submerged in Maxwell fluid

Strain gradient crystal plasticity model with strengthening and kinematic hardening due to plastic slip gradient

Study on the differences in response of GNDs in gradient heterogeneous structures and heterogeneous deformation-induced (HDI) strengthening

How bending causes distal radius fracture: Evidence from 6dof load measurement and digital image correlation.

Flexoelectricity is an electromechanical coupling phenomenon in which strain gradients induce electric polarization in solids, which have promising applications in flexible electronics, photovoltaic devices, and self-powered sensing systems. However, many flexoelectric materials suffer from poor thermal stability. High-entropy ceramics are materials characterized by multiple elements occupying lattice sites in near-equimolar ratios. The high configurational entropy is believed to stabilize phase structures and enhance the material's overall properties, especially temperature stability. This work employs the compositionally engineered high-entropy perovskite ceramics (Bi0.2X0.2Ba0.2Sr0.2Pb0.2) TiO3 (X = Li, Na, K) to elucidate the mechanisms governing the flexoelectric coefficients and their temperature stability via defect engineering and local strain modulation. Among these compositions, (Bi0.2Na0.2Ba0.2Sr0.2Pb0.2) TiO3 (HEC-Na) exhibits a well-defined perovskite structure and superior mechanical robustness, together with an optimized defect concentration and pinning landscape, as well as a reduced polarization barrier and weakened A–O bond strength. These synergistic factors collectively enhance flexoelectric performance and thermal stability in the HEC-Na system. This study provides a design strategy for next-generation high-sensitivity, thermally stable flexible mechatronic devices based on high-entropy perovskite ceramics.

Size-dependent resonance and transient dynamics of functionally graded nanoplates via modified nonlocal strain gradient theory

Abstract High-throughput graded tensile samples were used to measure the response of Incoloy 800H to annealing after cold work. Macroscale strain gradients between $$\sim 0\%-27\%$$ ∼ 0 % - 27 % von Mises strain were tested. For these strains, full recrystallization did not occur for annealing at 1050°C or 1075°C for times up to 2 h, while full recrystallization was observed after 1 h at 1100°C. Strain–time–temperature relationships for initiation and completion of recrystallization were obtained from EBSD and hardness characterization. Special boundary fractions were analyzed for each thermomechanical condition, showing the potential of gradient samples to accelerate grain-boundary engineering studies. Extensive M 23 C 6 precipitation was observed in samples annealed at 1050°C and 1075°C, and appeared to retard recrystallization. Dissolution of M 23 C 6 was observed at 1100°C, contributing to rapid recrystallization. Relationships for recrystallized hardness and grain diameter were also developed. Prior to this study, little data on the response of Incoloy 800H to heat treatment after cold work has been published, despite it being a workhorse alloy in many industries. It is hoped that manufacturers in these industries can use this work as a guide to select optimal thermomechanical conditions for their cold-worked components.

The realization of complex, high-order topological textures in ferroelectrics typically relies on demanding epitaxial growth under substrate clamping. Here, we report hierarchical polar bubbles in the van der Waals ferroelectric CuInP2S6, enabled by a facile wrinkle-induced strain-engineering strategy. Vector piezoresponse force microscopy reveals that localized wrinkled bulges generate large strain gradients, which activate a flexoelectric-assisted polarization reversal and form a macroscopic polar envelope. This macro-bubble encapsulates pre-existing intrinsic ferroelectric nanodomains, resulting in a distinctive nested bubble-in-a-bubble hierarchical architecture. Statistical analysis indicates that the formation probability decreases with increasing flake thickness, providing strong evidence for a strain-gradient-dominated flexoelectric origin. Real-time in situ manipulation demonstrates the mechanical recoverability of these hierarchical states under external loading. This work introduces a novel form of ferroelectric topology and establishes a mechanical pathway for designing resilient functional elements for next-generation straintronic devices.

This study investigates the nonlinear dynamic stability and internal resonance of osteon micro-beams under localized thermal gradients. Utilizing Nonlocal Strain Gradient Theory (NSGT), the size-dependent behavior of the Haversian system is modeled to bridge microscopic nuances and macroscopic thermal-mechanical responses. The governing equations are derived and solved via the Method of Multiple Scales (MMS) to determine nonlinear frequency-response characteristics. The results indicate that thermal gradients cause frequency reduction and convergence, while the nonlinear response retains a persistent hardening-type behavior at large amplitudes. A critical highlight is the identification of a 1:3 internal resonance threshold. At specific parametric configurations, the system exhibits sophisticated modal coupling, a ‘double-peak’ resonance profile, and the saturation phenomenon, indicating nonlinear energy transfer between the fundamental and second modes. Furthermore, 3D coupled parametric maps illustrate a ‘stability canyon’, highlighting osteon dynamic sensitivity under combined thermal and nonlocal influences. The obtained nonlinear vibration characteristics and internal resonance behavior may provide useful insight into how dynamic loading conditions influence stress redistribution and mechanical response at the osteon scale.

This study develops an eigenbuckling model for variable-thickness microplates based on the modified strain gradient theory (MSGT) and Kirchhoff–Love assumptions. The governing differential equations and corresponding boundary conditions are systematically derived for both in-plane and out-of-plane deformations of the microplates. Both uniformly and non-uniformly distributed in-plane loading cases are considered. Under constant-volume constraints, three longitudinal thickness variation profiles — linear, parabolic, and cubic — are investigated. Both [Formula: see text]-and [Formula: see text]-continuous nine-node differential quadrature finite elements (DQFEs) are applied to solve the developed eigenbuckling model. The accuracy and reliability of the derived formulations are established through a series of benchmark examples. Extensive parametric studies are conducted to show the effects of thickness variation, geometry, material length scale parameter (MLSP), in-plane loading pattern, and boundary condition on the eigenbuckling behavior of the microplates. Mode localization under various influencing factors is quantitatively assessed using the relative value of the direction cosine of the mode vector. The results demonstrate that both the taper ratio and dimensionless MLSP have a significant effect on the eigenbuckling loads and their associated mode contours. This influence is further enhanced in higher-order eigenbuckling modes, where the size effect is most evident. As the strain gradient effect intensifies, the eigenbuckling mode localization induced by the taper ratio is correspondingly mitigated. Moreover, mode transition phenomena are identified in symmetrically constrained microplates with uniform mass distribution under distributed in-plane compressive loading. These findings offer important insights for the design of tunable microscale structural systems.

The ability to control solid-state quantum emitters is fundamental to advancing quantum technologies. The performance of these systems is fundamentally governed by their spin-dependent photodynamics, yet conventional control methods using cavities offer limited access to key nonradiative processes. Here we demonstrate that anisotropic lattice strain serves as a powerful tool for manipulating spin dynamics in solid-state systems. Under high pressure, giant shear strain gradients trigger a complete reversal of the intrinsic spin polarization, redirecting ground-state population from |0⟩ to |±1⟩ manifold. We show that this reprogramming arises from strain-induced mixing of the NV center's excited states and dramatic alteration of intersystem crossing, which we quantify through a combination of optomagnetic spectroscopy and a theoretical model that disentangles symmetry-preserving and symmetry-breaking strain contributions. Furthermore, the polarization reversal is spatially mapped with a transition region below 120nm, illustrating sub-diffraction-limit control. Our Letter establishes strain engineering as a powerful tool for tailoring quantum emitter properties, opening avenues for programmable quantum light sources, high-density spin-based memory, and hybrid quantum photonic devices.

Tailoring at will polar textures in ferroelectrics is critical for the development of nanoscale electronics and functional oxide technologies. Freestanding ferroelectric membranes have enabled studies of strain-induced polarization responses, but the control over membrane shape and local polarization typically remains limited to spontaneous buckling or uniaxial mechanical deformations. In this work, we employ a versatile photosensitive-polymer patterning approach to impose programmable bending strain profiles in ferroelectric membranes. Using BaTiO3 as a model system, we demonstrate deterministic 90° polarization rotation driven by engineered in-plane strain, and 180° polarization reversal arising from flexoelectric coupling through a controlled strain gradient. These results establish this programmable bending as a powerful approach to investigate strain-dependent domain structures, leverage flexoelectric effects, and engineer custom ferroelectric landscapes across a wide range of oxide membranes.

Flexoelectricity, the modification of electric polarization induced by strain gradients, is ubiquitous in all materials and is typically a minor effect in bulk materials represented as a linear function of curvature. However, in 2D materials, the curvature can be dramatically large due to their flexibility, which naturally raises an intriguing question of whether flexoelectricity extends beyond the linear form. Here, we reveal a type of nonlinear flexoelectricity that depends on both the curvature and its gradients through first-principles calculations. This nonlinear flexoelectric effect only presents in certain materials such as monolayer CrI3, which is a consequence of the simultaneous breaking of the in-plane and out-of-plane mirror symmetries perpendicular to the curvature direction. In contrast, materials like graphene, h-BN, and 2H-WTe2 monolayers with no such symmetry breaking do not present such a nonlinear flexoelectric effect. Furthermore, a method to detect the nonlinear felexoelectricity is also proposed. Our research thus enriches the spectrum of flexophysics and has potential applications in flexoelectrics.

Two-dimensional (2D) semiconductors such as monolayer WSe2 have attracted significant interest for their quantum properties and potential as scalable single-photon emitters. However, conventional microphotoluminescence (μ-PL) techniques are fundamentally limited by optical diffraction, hindering access to critical nanoscale features such as strain gradients and localized quantum confinement. In this study, we utilize tip-enhanced photoluminescence (NanoPL) with a spatial resolution of ≈10 nm to directly image the emission landscape of monolayer WSe2 on top of nanopillars at room temperature. Our results reveal two distinct localization regimes associated with leading theoretical models for single-photon activation and provide guidelines for deterministic nanoengineering of quantum light sources.

• Phase-field model with strain-gradient elasticity for ferroelectric domain switching. • New Q84 finite element enables C0-continuous discretization. • Non-linear strain effects in polycrystalline ceramics with random initial polarization. • Strong strain gradients at grain boundaries and at intragranular domain walls. • Larger material length scale suppresses switching and shifts ferroelectric domains. Ferroelectric materials are widely used in industries, and accurately predicting their response under external loading is essential for both research and applications. With the miniaturization trend driving the size of electronic components to micro- and nanoscale, strain gradient effects become increasingly important. This paper presents a phase-field material model and governing equations for ferroelectrics that account for strain gradients and derive the associated weak forms. To circumvent the C 1 -continuity requirement of gradient elasticity, we employ a mixed finite-element formulation and present the discretization of a newly developed Q84 element for phase-field modeling, together with its element residuals, tangent matrix, and pseudocode for a user element subroutine. The implementation is verified by reproducing known results for monocrystalline and honeycomb ferroelectric specimens and, for the first time, we demonstrate strain gradient effects in these idealized settings. We then simulate a polycrystalline microstructure and analyze the influence of strain gradient elasticity for both uniform and random initial polarization. The results highlight the interplay between higher-order (strain gradient) effects and non-linear electromechanical coupling.

Kerr Foundation-Induced Mode Jumping and Shielding Effects in Nanobeams Analyzed by Modified Strain Gradient Theory

Coupled nonlocal–strain gradient effects on the dynamic stability of functionally graded nanoplates resting on elastic foundations

Contact in strain gradient elasticity: The rigid flat punch problem