Strain Gradient Research Articles

The spectral methods for the propagation of thermoelastic waves in multilayer cylinders based on nonlocal strain gradient elasticity

The spectral methods for the propagation of thermoelastic waves in multilayer cylinders based on nonlocal strain gradient elasticity

Buckling behavior of nickel microbeams based on reformulated strain gradient theory

Buckling behavior of nickel microbeams based on reformulated strain gradient theory

Microstrain partitioning, transformation induced plasticity, and damage evolution of a third generation medium Mn advanced high strength steel

An experimental Medium Mn (med-Mn) steel (0.15C-5.8Mn-1.8Al-0.71Si) with a martensitic starting microstructure, intercritically annealed at 685 °C for 120s, was discovered to have a large true strain at fracture (ɛf = 0.61) while also meeting established (strength x elongation) targets (28,809 MPa%), sustained monotonic work hardening and prolonged Transformation Induced Plasticity (TRIP) kinetics. This was found by varying the intercritical annealing (IA) temperature within a narrow temperature interval in order to isolate its impact on TRIP kinetics and damage development on such med-Mn steel. A comprehensive understanding of the microstructural damage processes leading to fracture is presented using quasi in-situ Scanning Electron Microscope tensile testing as well as X-ray Computed Microtomography. In addition, we precisely evaluated the TRIP kinetics of this steel using a combined Digital Image Correlation (DIC) and synchrotron-sourced High Energy X-ray Diffraction technique. With these methods, we demonstrate that an abundance of voids nucleate during deformation, but their growth can be suppressed by prolonging TRIP over a large strain range. Moreover, novel post-processing techniques to assess DIC acquired data at the microscopic scale have been used to gauge the severity of strain partitioning amongst phases and strain gradient evolution across dissimilar phase interfaces. By comparing it to another 3G TRIP-assisted steel and an ultrafine grained Dual Phase steel. Overall, it has been found that, in addition to carefully moderating TRIP kinetics, the introduction of polygonal ferrite, as is conventional in med-Mn steels, enhances the local forming properties and damage tolerance in 3G TRIP-assisted microstructures.

Hamiltonian System-Based Symplectic Framework for Analytical Vibration Analysis of Microplates

Abstract The classical elasticity is inadequate for the dynamic analysis of microplates due to the size effect. This study incorporates a higher-order strain gradient theory into the Hamiltonian system-based symplectic framework and derives new analytical solutions for the free vibration of microplates. The analytical solutions are obtained using rigorous mathematical techniques, including separation of variables, symplectic eigen expansion, and superposition, without relying on predetermined solution forms. Hence, they are not restricted to Lévy-type boundary conditions. Using these analytical solutions, we present comprehensive vibration results for microplates and perform detailed parametric studies to explore the impact of length scale parameters on the natural frequencies. Given the growing demand for microplates in advanced engineering applications, the obtained analytical solutions are expected to facilitate their design and performance optimization.

Bioinspired Hierarchical Porous Architecture for Enhanced Kinetics and Mechanical Integrity in Thick Cathode.

Increasing the thickness of the electrodes is considered the primary strategy to elevate battery energy density. However, as the thickness increases, rate performance, cycling performance, and mechanical stability are affected due to the sluggish ion transfer kinetics and compromised structural integrity. Inspired by the natural hierarchical porous structure of trees, electrodes with bioinspired architecture are fabricated to address these challenges. Specifically, electrodes with aligned columns consist of tree-inspired vertical channels, and hierarchical pores are constructed by screen printing and ice-templating, imparting enhanced electrochemical and mechanical performance. Employing an aqueous-based binder, the LiNi0.8Mn0.1Co0.1O2 cathode achieves a high areal energy density of 15.1 mWh cm-2 at a rate of 1C at mass loading of 26.0mg cm-2,benefitting from the multiscale pores that elevated charge transfer kinetics in the thick electrode. The electrodes demonstrate capacity retention of 90% at the 100th cycle at a high current density of 5.2mA cm-2. To understand the mechanisms that promote electrode performance, simplified electro-chemo-mechanical models are developed,the drying process and the charge-discharge process are simulated. The simulation results suggested that the improved performance of the designed electrode benefits from the lower ohmic overpotential and less strain gradient and stress concentration due to the hierarchical porous architecture.

Linear strain gradient-regulated bifurcation of circular bilayer plates

Bilayer structures with controllable self-folding capability have found applications in a variety of cutting-edge fields such as flexible electrics, wearable devices and soft robotics. The folding of bilayer structures occurs when the mismatch strain between the two layers exceeds the bifurcation threshold, resulting in a deformation transition from an axisymmetric to a folded state. Previous efforts have predominantly focused on bilayer structures with uniform and/or anisotropic strain distributions. However, the role of non-uniform in-plane strain distributions in regulating the bifurcation of bilayer structures has not been fully understood. In this study, the effects of linear in-plane strain gradients on the bifurcation of circular bilayer plates, both with and without geometric mismatch, are systematically investigated by combining theoretical analysis, finite element simulations and experiments. Our results reveal that both the mismatch strain gradient and the geometric mismatch between the two layers play crucial roles in regulating bifurcation. Notably, linear mismatch strain gradients with larger strain at the center delay bifurcation, while those with larger strain along the edge promote bifurcation. This work offers new insights into the design of controllable self-folding bilayer structures, which is of great significance for advanced applications.

Effective flexoelectric properties of inclusion-based composites based on strain gradient theory and homogenization technique

This study focuses on enhancing flexoelectricity in composites and develops a new micromechanical analytical framework to determine the effective electromechanical properties of inclusion-based flexoelectric composites within the context of SGE. Initially, we specialize in studying isotropic materials and derive the governing Navier equations for the problem. Subsequently, we streamline these differential equations by introducing a Laplacian-type gradient state variable, departing from higher-order gradient-enrichment treatments. The study employs Green’s functions and stress polarization tensors for spherical inhomogeneities, deriving homogenized material properties through volumetric averages of microscopic properties weighted by displacement localization operators. The analytical scheme’s relevance is validated against results from reference models and experimental data. Effective composite properties are evaluated using numerical methods, with an emphasis on assessing the impact of reinforcement on these properties. Our findings lay the foundation for developing a micromechanical method to predict the electromechanical behavior of composites. Specifically, we demonstrate the efficacy of our proposed theory by deriving effective flexoelectric properties of particulate composites.

Strain energy density maximization principle for material design and the reflection in trans-scale continuum theory

Traditional efforts in the design of damage-tolerant structural materials were largely exercises in optimizing the combination of strength and ductility. However, the simultaneous consideration of these two conflicting mechanical indices, improving one inevitably sacrifices the other, makes the design extremely complex and difficult, due to the dilemma of choosing between them. Here, physically guided by the energy variational expression in trans-scale continuum mechanics theory, we propose a general mechanics principle for material design that involving only one index: towards strong and tough material the strain energy density limit (w) should be maximized, i.e., strain energy density maximization principle, referred to as wmax principle. It aims to guide the attainment of exceptional comprehensive mechanical properties, while circumventing the dual-index dilemma by employing a singular index w. Extensive experimental data analyses prove that (i) the maximum wmax always exists, at a critical dimension of characteristic microstructure dc,micro, and (ii) w can effectively index strength-ductility synergy and the wmax is conjugated with both high strength and high ductility, verifying the validity of wmax principle. The universality, practicality and downward compatibility are also examined. The dc,micro approaches twice the span of strain gradient region around internal boundary, suggesting that the microstructure state with wmax is the critical state with strongest strain gradient. Importantly, the w improvement as a function of the characteristic size of either microstructure or deformation field can be well captured by strain gradient theory, confirming the consistence between the wmax principle, experimental results and trans-scale continuum theories. This principle opens up a new design concept for advanced structural materials from the perspective of microstructure-w-mechanical properties relationship.

Unconventional mechanical responses and mechanisms of Ti-6Al-4V sheet subjected to electrically-assisted cyclic loading-unloading: Thermal and athermal effects

For the sake of unveiling the macro-micro behaviors and underlying control mechanisms of electroplastic effect (EPE) of sheet metals during recent thriving electrically-assisted incremental forming (EAIF) processes, electrically-assisted cyclic loading-unloading tension (EACT) experiments were carried out at a current density of 14～20A/mm2 followed by forced and unforced cooling. The electro-thermo-mechanical responses and the evolution rules of dislocation configurations, fracture modes, phase composition and local orientation distribution were characterized by IR imaging, SEM, quantitative EBSD and TEM tests. Moreover, the thermal and athermal components of the electrically-induced stress drop throughout the EACT processes were decoupled and systematically analyzed via temperature control tests and isothermal correction. The results show that thermal effect of electric current possesses a great proportion of 75 % in the overall stress drop and plays a key role in elastic modulus degradation and ductility enhancement by activating pyramidal {101‾1}⟨12‾10⟩ slip systems, weakening (0001) texture and promoting dynamic recrystallization (DRX) and α→β→α′ phase transformation. While the athermal effect only operates after reaching both threshold current density and plastic strain, it increases monotonically with current density, brings about “hot spots” effect, local charge imbalance and weakened atomic bonding, and further causes intensified local strain gradient, substructure formation and DRX nucleation. The ratio of athermal stress drop first decreases and then increases significantly with loading cycle at the later stage of EACT under the combined effect of local Joule heating effect and flow localization. Additionally, the athermal effect only activates short-range solute diffusion and localized diffusional α→β phase transformation, while the combined thermal and athermal effects promote long-range solute diffusion and an increasing rate in β content of 261.8 %. The present work provides theoretical basis for optimizing the EAIF forming process and realizing extreme manufacture of light-weight thin-walled complex components.

Active control for higher order micro sandwich beam with various cores integrated by piezoelectric layers based on MSGT on the Pasternak foundation

In the present article, the vibration suppression of higher order micro sandwich beams based on modified strain gradient beam theory (MSGT) and Reddy/Timoshenko beam theories is developed. Three types of core, including honeycomb, foam, and porous for a micro sandwich beam, are considered. The core’s top and bottom are integrated by piezoelectric layers as actuator and sensor, respectively. Displacement fields are defined via third-order shear deformation beam theory (TSDBT) (or Reddy beam theory (RBT)) and first-order shear deformation beam theory (FSDBT) (or Timoshenko beam theory (TBT)). The governing equations of motion are derived using MSGT to consider the small-scale effect. To optimal approaches for the controller, state feedback is designed based on a linear quadratic regulator (LQR) in the state-space form. Moreover, the effect of various parameters, including small-scale parameters, three types of core, temperature changes, Pasternak foundation, density of core, dimensionless cell thickness ([Formula: see text]), and internal aspect ratio ([Formula: see text]), angles ([Formula: see text]) of honeycomb, and the porosity parameter is performed on the active control of the smart micro sandwich beam. The numerical results indicate that the parameters mentioned significantly affect the optimal vibration control of the smart micro sandwich beam. It is found that the lightweight cores have more attenuation of the transient response and faster settling time. By analyzing the effect of temperature changes on active vibration control of lighter core, it was found that the frequency decreases as the temperature increases. Also, by considering the Pasternak foundation, it is found that the time period without considering the elastic foundation is longer than when considering the elastic foundation, and the natural frequency is vice versa. Also, the settling time by considering the elastic foundation occurs earlier. In the active control field of smart micro beams, this theoretical investigation developed widely as a benchmark for experimental research and the manufacturing process.

Band gaps of elastic waves in 1-D dielectric phononic crystal with the flexoelectric and strain gradient effects consideration

The propagation of Bloch waves in one dimensional phononic crystal consisting of dielectric elastic solids is studied with consideration of the strain gradient, inertial gradient and flexoelectric effects. The transfer matrixes for single layer and one-cell of phononic structure are derived based on the constitutive equations and the governing equations of dielectric elastic solids. The dispersion equation for Bloch waves is obtained by the application of periodic conditions for the generalized displacements and tractions considered within strain gradient theory of electro-elasticity. Based on the numerical solution of the derived dispersion equation, the influences of the micro-stiffness length scale, micro-inertial length scale and flexoelectric coefficients on the dispersion and the bandgap are discussed.

Strongly Enhanced Electronic Bandstructure Renormalization by Light in Nanoscale Strained Regions of Monolayer MoS2/Au(111) Heterostructures.

Understanding and controlling the photoexcited quasiparticle (QP) dynamics in monolayer (ML) transition metal dichalcogenides (TMDs) lays the foundation for exploring the strongly interacting, nonequilibrium two-dimensional (2D) QP and polaritonic states in these quantum materials and for harnessing the properties emerging from these states for optoelectronic applications. In this study, scanning tunneling microscopy/spectroscopy (STM/scanning tunneling spectroscopy) with light illumination at the tunneling junction is performed to investigate the QP dynamics in ML MoS2 on an Au(111) substrate with nanoscale corrugations. The corrugations on the surface of the substrate induce nanoscale local strain in the overlaying ML MoS2 single crystal, which result in energetically favorable spatial regions where photoexcited QPs, including excitons, trions, and electron-hole plasmas, accumulate. These strained regions exhibit pronounced electronic bandstructure renormalization as a function of the photoexcitation wavelength and intensity as well as the strain gradient, implying strong interplay among nanoscale structures, strain, and photoexcited QPs. In conjunction with the experimental work, we construct a theoretical framework that integrates nonuniform nanoscale strain into the electronic bandstructure of a ML MoS2 lattice using a tight-binding approach combined with first-principle calculations. This methodology enables better understanding of the experimental observation of photoexcited QP localization in the nanoscale strain-modulated electronic bandstructure landscape. Our findings illustrate the feasibility of utilizing nanoscale architectures and optical excitations to manipulate the local electronic bandstructure of ML TMDs and to enhance the many-body interactions of excitons, which is promising for the development of nanoscale energy-adjustable optoelectronic and photonic technologies, including quantum emitters and solid-state quantum simulators for interacting exciton polaritons based on engineered periodic nanoscale trapping potentials.

Strain-gradient and damage failure behavior in particle reinforced heterogeneous matrix composites

A strain gradient plasticity model with strengthening effect and damage effect (SGSED) is developed under the continuum medium framework for particle-reinforced heterogeneous matrix composites (PRHMCs). Boron carbide (B4C) particle-reinforced ultrafine-grained (UFG)/fine-grained (FG) heterogeneous matrix composites (B4Cp/(UFG/FG)) are fabricated, in which the UFG region consisted of carbon nanotubes (CNTs)/6061 aluminum (Al) flakes with grains in the ultrafine range and the FG region is processed via 6061Al. The SGSED model is written into the user subroutines using commercial finite element (FE) calculation software, and the three-dimensional (3D) FE representative volume element (RVE) for B4Cp/(UFG/FG) composites is established, from which the distribution of the interface-affected-zone (IAZ) formed of the strain gradient caused by the uncoordinated deformation of the UFG-FG heterogeneous matrix and reinforced phase-matrix is calculated. The evolution of the strain gradient in the deformation process of composites and the influence of the strain gradient on the progressive damage and crack evolution of composites are analyzed, and the strain gradient strengthening-toughening mechanism of composites is revealed. It is found that the IAZ has a considerable strengthening-toughening effect on the composites, which can reduce stress concentration at the interface between the reinforced phase and the matrix, and slow down the crack propagation of the matrix.

Plane dilatational and shear waves in a chiral porous thermoelastic medium under strain gradient theory

Purpose This study aims to investigate time-harmonic wave propagation in a chiral porous thermoelastic solid under strain gradient theory (SGT), focusing on identifying and characterizing distinct wave modes within the medium. Design/methodology/approach Using Iesan's gradient theory, which incorporates chiral effects and accommodates second sound phenomena, the authors derive mathematical formulations for the velocities and attenuations of eight propagating waves: four dilatational waves and two pairs of coupled shear waves (one left circularly polarized, the other right). Numerical simulations are performed for a specific model, exploring the influence of various parameters on wave propagation. Findings The authors establish that the medium supports four dilatational waves, including a microstretch-associated wave, and four shear waves, distinguished by their chiral-induced characteristics. The results highlight the frequency-dependent dispersive nature of all propagating waves and establish connections with existing theoretical frameworks, demonstrating the broader applicability of our findings. Practical implications The characteristics of wave propagation in chiral media examined here can enhance our understanding of chiral medium behavior. This knowledge is crucial for developing materials with pronounced chiral effects, surpassing those found in natural chiral materials like bone, quartz, sugar and wood. Advances in artificial chiral materials are driven by their superior toughness, durability and other beneficial properties. Consequently, this study has potential applications across various fields, including the design of chiral broadband absorbers and filters, the production of artificial bones and medical devices, aeronautical engineering and beyond. Originality/value This research extends existing theories and deepens the understanding by exploring wave behaviors in chiral media, advancing this emerging field.

A microsphere-homogenized strain gradient elasticity model for polymers

A microsphere-homogenized strain gradient elasticity model for polymers

A size‐dependent model of strain gradient elastic laminated micro‐beams with a weak adhesive layer

AbstractA size‐dependent model for a laminated micro‐beam with a soft adhesive is developed in the framework of strain gradient elasticity theory. The layered beam is constituted by two Euler–Bernoulli strain gradient elastic isotropic beams, joined through a strain gradient spring‐type contact law at the adhesive level. The governing bending and extensional equations and boundary conditions are obtained by using the variational principle. The differential system shows a coupling between the flexural and axial behaviors of the upper and lower beams, due to the presence of interface terms related to shear and peeling stresses. Two benchmark problems have been presented through their closed‐form solutions, namely a simply‐supported laminated beam subjected to a uniform distributed load and a mode 2‐type loading configuration of a layered axially deformable beam. Size effects and non‐local phenomena, due to high strain concentrations, are highlighted. Though simple in their features, the examples prove the efficiency of the proposed approach in designing micro‐scale layered beams.

Mesoscopic coupled plasticity-damage model of rough surface considering size-dependent plasticity

Metallic materials exhibit significant size effect at mesoscopic scale have been revealed by many experiments. Thus, it is essential to consider size effect when conducting mesoscopic scale studies in tribology. However, there is no constitutive model considering both ductile fracture and size effects of rough surface in the literature. At the same time, the simulation of friction and wear at the mesoscopic scale suffer from computational inefficiency using the conventional theory of mechanism-based strain gradient (CMSG) plasticity theory. To address the aforementioned challenges, we propose a mesoscopic coupled plasticity-damage model by combining the coupled plasticity-damage model and the simplified CMSG plasticity theory. This model can take into account not only the effect of stress state, temperature, strain rate on plasticity and fracture, but also the effect of the effective plastic strain gradient. Meanwhile, the model is able to solve the effective plastic strain gradient by a simplified method, thereby enhancing the computational efficiency. Then, model parameters for bearing bushing material of an engine are calibrated. Finally, scratch simulation and scratch tests of bearing bushing material at the mesoscopic scale are conducted to validate the effectiveness of the mesoscopic constitutive model. The residual scratch depth and width, coefficient of friction at different normal loads are investigated by experiment and simulation, respectively. Results proved the effectiveness of mesoscopic coupled plasticity-damage model, which is applicable for investigating issues related to wear, friction, and contact.

Flexomagnetoelectric Effect in Sr_{2}IrO_{4} Thin Films.

Symmetry engineering is explicitly effective to manipulate and even create phases and orderings in strongly correlated materials. Flexural stress is universally practical to break the space-inversion or time-reversal symmetry. Here, by introducing strain gradient in a centrosymmetric antiferromagnet Sr_{2}IrO_{4}, the space-inversion symmetry is broken accompanying a nonequivalent O p-Ir d orbital hybridization along the z axis. Thus, an emergent polar phase and out-of-plane magnetic moment have been simultaneously observed in these asymmetric Sr_{2}IrO_{4} thin films, which both are absent in its ground state. Furthermore, upon the application of a magnetic field, such polarization can be controlled by modifying the occupied d orbitals through spin-orbit interaction, giving rise to a flexomagnetoelectric effect. This Letter provides a general strategy to artificially design multiple symmetries and ferroic orderings in strongly correlated systems.

Analyzing flexoelectric polarization of suspended membrane by nonlinear bending theory of plate

Strain gradient breaks inversion symmetry and induces flexoelectric polarization as well as electromechanical coupling in all material systems, though the effect is usually only significant at the nanoscale. Two-dimensional (2D) materials and thin membranes thus provide an ideal platform to explore flexoelectricity, which has been widely pursued, yet quantitative theoretical analysis is needed to guide the rapid experimental developments. In this work, we develop 2D flexoelectric model for suspended membrane based on von Kármán plate theory, and implement it into finite element computation using conforming BCIZ element. Numerical results and discussions on flexoelectric polarization in suspended membrane under uniform pressure or concentrated load are presented, which are validated by piezoresponse force microscopy (PFM) experiments under a range of membrane thicknesses and loading forces showing good agreement with computations. Since large strain gradient often exists in samples with small size in one or two dimensions, the method we develop provides a powerful tool to study a wide range of low-dimensional materials and structures with flexoelectric effect.

Free vibrations and dynamic behavior of the three layered flexoelectric functionally graded microbeam under moving load

In this study, free vibrations and the dynamic responses of the three layered flexoelectric functionally graded microbeam under the effect of moving load are investigated. Using the first order shear deformation and the size-dependent piezoelectricity theories in the framework of Hamilton's principle, the governing equations of motion and the corresponding classical and non-classical boundary conditions are obtained. Next, the equations of motion were discretized and solved using the finite element method. In order to validate the governing equations and the solution method, the obtained results have been compared with the results of previous studies, which shows a good convergence between the current and previous results. The obtained results demonstrate the dynamic behavior of the microbeam is strongly influenced by the geometrical ratios, the flexoelectric layers thickness, the functionally graded power index, the flexoelectric coefficient and the load velocity. So that the escalation in the strain gradient from the augmentation of the flexoelectric layers' thickness leads to a corresponding rise in the electric potential function. Moreover, as the flexoelectric coefficient increases, the microbeam becomes more responsive to polarization, thereby generating a greater amount of electrical energy. In addition, changes in the velocity of the moving load significantly affect the dynamic behavior of the structure in such a way that with the increase in the load velocity, the dynamic deflection of the structure increases.