Strain Gradient Research Articles

On the Applications of a New Advanced PEPFG Mathematical Model for HTM Dynamic Behavior of SDF Sandwich Plates

Considering the crucial role of the flexoelectricity phenomena (the electrical polarization–strain gradient coupling) in the mechanical behavior of different structures on the micro/nanoscale, this paper is derives the motion equations of a size-dependent flexoelectric (SDF) sandwich plate to study its hygro-thermo-mechanical (HTM) dynamic behavior. The model is a three-layer microplate including a porous exponential and power–law functionally graded (PEPFG) mid-layer, and two flexoelectric face sheets. The whole structure is under hygrothermal loading and the Vlasov foundation serves as the stand for the structure. Then, Hamilton’s principle and modified couple stress theory (MCST) are implemented to derive the motion equations. The new PEPFG utilization besides evaluating the impact of the length scale parameter, hygrothermal loading, materials composition, porosity, foundation parameter, and boundary conditions on the normalized natural frequency (NNF) of such an SDF sandwich model is the novelty of this paper. It is revealed that the lateral ratio enhancement causes NNF and stiffness reduction in the model. Furthermore, among all considered boundary types, simply supported and clamped refer to the lowest and the highest NNFs, respectively. This paper serves as a good source to provide a better understanding of the dynamic response of high stiffness-to-weight ratio structures to different variable variations.

The influence of material gradation parallel to two unequal mode-III cracks in functionally graded materials via strain gradient elasticity theory

In this article, the strain gradient elasticity (SGE) theory is used to investigate the mechanical behaviour of a functionally graded material (FGM) weakened by two unequal collinear mode-III cracks. The SGE theory uses two material characteristic lengths, ℓ and ℓ′, to account for volumetric and surface strain-gradient factors, respectively. The directions of both cracks coincide with the material gradation, which is oriented parallel to the x-axis. The numerical outcomes of the problem are obtained by constructing the system of equations using the hyper-singular integral-differential equation technique. The influence of the material gradation parameter on various fracture parameters, including the stress intensity factor (SIF), strain and crack surface displacement (CSD), is numerically shown. In addition, different loads are considered while analysing CSD profiles in connection to the gradation parameter β. Furthermore, the effect of inter-crack distance on CSD profiles is comprehensively explored, showing information between crack geometry and material gradation.

A size-dependent nonlinear isogeometric approach of bidirectional functionally graded porous plates

Recent progress in materials science and fabrication technologies, such as additive manufacturing (AM) or 3D printing, has facilitated the design and production of intricate multi-directional functionally graded (FG) materials which are playing a pivotal role in interdisciplinary engineering applications. Developing mathematical modeling for such nanostructures, however, remains challenging. The primary objective of this research, therefore, is to present a mathematical model for studying the static bending characteristics considering the geometric nonlinearity of bidirectional FG nanoplates with internal pores. The mathematical formulations are established by utilizing the first-order shear deformation theory and the von-Kármán assumption within the framework of an isogeometric approach based on NURBS basis functions. To account for the influence of both strain gradient and nonlocal elasticity, we adopt the nonlocal strain gradient theory including two independent material length scale parameters to predict the geometric nonlinearity performance of structures at small-scale levels. The mechanical properties of multi-directional FG material models are assumed to be continuously graded in two directions based on power law, while internal pores can be dispersed into two typical distribution patterns. Several numerical investigations are performed to evaluate the substantial impact of certain parameters on the nonlinear deflections of bidirectional FG nanoplates with pores under various conditions. Compared to existing studies, the key contribution is to present a robust numerical model aimed at elucidating both the stiffness-softening and stiffness-hardening mechanisms of multi-directional FG nanostructures under static bending conditions with geometric nonlinearity. These findings enhance our insights into nonlinear bending performance and contribute valuable design guidelines for future small-scale engineering structures. These innovative designs have become popular and are now crucial in state-of-the-art engineering applications, such as aerospace, nuclear systems, or thermal resistance devices.

Crack propagation arrest by the Joule heating in micro/nano-sized structures

The Joule heating technique is utilized to arrest the crack propagation so to protect some important structures being further damaged. In this approach there are created compression stresses at the crack tip vicinity due to a specific temperature distribution induced by the electric current. The Joule heating is amulti-physical problem which is applied here to micro/nano-sized structures. The size-effects are considered for description of both the elastic and the thermal fields. The heat conduction can’t be well described by classical Fourier’s law in nano-sized structures. A novel gradient theory is developed in such structures adopting the size effect of heat conduction. Besides, the strain gradients and double stresses are introduced into the constitutive laws. Then, the governing equations are given by partial differential equations with order of derivatives being higher than in classical theory. The principle of virtual work is the base of weak formulation and derivation of the discretized finite element equations for ageneral 2d boundary value problem with cracks. The collocation mixed FEM with large strain gradients is developed for numerical solution, where the C0 continuous approximation is applied independently to displacements and strains and also to temperature and temperature gradients. Kinematic constraints between strains and displacements are satisfied by the collocation method at selected interior points. The collocation mixed FEM is applied to solve 2D crack problems with Joule heating.

Tensile mechanical behavior of functionally graded NiTi alloy manufactured via laser powder bed fusion

Laser powder bed fusion (LPBF) offers the potential to modify the characteristics of NiTi alloys, allowing for the creation of bespoke solutions tailored to specific applications. In this study, four functionally graded NiTi alloys with varying martensite/austenite distributions were designed and manufactured. A comprehensive investigation was conducted into the local microstructure, phase transformation behaviour, and tensile mechanical behaviour. The findings illustrate that, in comparison to homogeneous NiTi, gradient NiTi displays a propensity for preferential deformation within the martensitic region, attributable to the presence of localised performance variations. Gradient NiTi exhibits evident strain hardening and a wider range of plateau stress due to its intricate step-by-step phase transformation behaviour. The strain gradient strengthening near the interface between martensite and austenite endows gradient NiTi with enhanced fracture strength. Furthermore, while ensuring a discernible gradient in strain, the design of the interface with narrow spacing and parallel to the tensile direction can effectively enhance the mechanical properties of gradient NiTi. This study validates that gradient design based on LPBF is an effective approach for controlling the macroscopic mechanical behavior of NiTi alloy.

Phase velocity shifts of shear surface waves in flexoelectric wave-guide clamped on piezomagnetic base

Surface acoustic wave devices featuring periodic layers of piezomagnetic and piezoelectric-flexoelectric layers are subject to intense investigation. In miniaturized devices, large strain gradients are possible that produce significant flexoelectric fields in piezoelectric components. In the present theoretical research, surface acoustic wave transference has been manifested in a flexoelectric waveguide clamped over a piezomagnetic base. This endeavor involves the formulation and solution of coupled magneto-electro-elastic field equations governing the structure’s behavior. Coupled magneto-electro-elastic field equations for the structure have been derived and solved utilizing analytical techniques. By accounting for pertinent boundary conditions, the dispersion relations characterizing the velocity of surface waves, both in scenarios with and without electrodes have been obtained. Based on proper numerical examples, the frequency and phase velocity spectrum have been plotted offering insights into key parameters i.e. modal frequency, phase velocity, and wave attenuation. The outcomes of the theoretical study may be helpful in providing insights into mechanical wave propagation in coupled piezoelectric/piezomagnetic structures.

Wave solutions in nonlocal integral beams

Wave propagation in slender beams is addressed in the framework of nonlocal continuum mechanics. The elastodynamic problem is formulated exploiting consistent methodologies of pure integral, mixture and nonlocal strain gradient elasticity. Relevant wave solutions are analytically provided, with peculiar attention to reflection and near field phenomena occurring in presence of boundaries. Notably, the solution field is got as superimposition of incident, reflected, primary near field and secondary near field waves. The latter contribution represents a further effect due to the size dependent mechanical behaviour. Limit responses for vanishing nonlocal parameter are analytically evaluated, consistently showing a zero amplitude of the secondary near field wave. Parametric analyses are carried out to show how length scale parameter, amplitude of incident wave and geometric and elastic properties of the beam affect the amplitudes of reflected, primary near field and secondary near field waves. The results obtained exploiting different nonlocal integral elasticity approaches are compared and discussed.

Sensor Systems for Measuring Force and Temperature with Fiber-Optic Bragg Gratings Embedded in Composite Materials

Currently, there is a lot of interest in smart sensors and integrated composite materials in various industries such as construction, aviation, automobile, medical, information technology, communication, and manufacturing. Here, a new conceptual design for a force and temperature sensor system is developed using fiber-optic Bragg grating sensors embedded within composite materials, and a mathematical model is proposed that allows one to estimate strain and temperature based on signals obtained from the optical Bragg gratings. This is important for understanding the behaviors of sensors under different conditions and for creating effective monitoring systems. Describing the strain gradient distribution, especially considering different materials with different Young’s modulus values, provides insight into how different materials respond to applied forces and temperature changes. The shape of the strain gradient distribution was obtained, which is a quadratic function with a maximum value of 1500 µ, with a maximum value at the center of the lattice and a symmetrically decreasing strain value with distance from the central part of the fiber Bragg grating. With the axial strain at the installation site of the Bragg grating sensor under applied force values ranging from 10 to 11 N, the change in strain was linear. As a result of theoretical research, it was found that the developed system with fiber-optic sensors based on Bragg gratings embedded in composite materials is resistant to external influences and temperature changes.

Cold Seeded Epitaxy and Flexomagnetism in GdAuGe Membranes Exfoliated From Graphene/Ge(111).

Remote and van der Waals epitaxy are promising approaches for synthesizing single crystalline membranes for flexible electronics and discovery of new properties via extreme strain; however, a fundamental challenge is that most materials do not wet the graphene surface. We develop a cold seed approach for synthesizing smooth intermetallic films on graphene that can be exfoliated to form few nanometer thick single crystalline membranes. Our seeded GdAuGe films have narrow X-ray rocking curve widths of 9-24 arc seconds, which is 2 orders of magnitude lower than their counterparts grown by typical high temperature methods, and have atomically sharp interfaces observed by transmission electron microscopy. Upon exfoliation and rippling, strain gradients in GdAuGe membranes induce an antiferromagnetic to ferri/ferromagnetic transition. Our smooth, ultrathin membranes provide a clean platform for discovering new flexomagnetic effects in quantum materials.

Flexoelectric Enhancement of Strain Gradient Elasticity Across a Ferroelectric-to-Paraelectric Phase Transition.

We study the temperature dependent elastic properties of Ba0.8Sr0.2TiO3 freestanding membranes across the ferroelectric-to-paraelectric phase transition using an atomic force microscope. The bending rigidity of thin membranes can be stiffer compared to stretching due to strain gradient elasticity (SGE). We measure the Young's modulus of freestanding Ba0.8Sr0.2TiO3 drumheads in bending and stretching dominated deformation regimes on a variable temperature platform, finding a peak in the difference between the two Young's moduli obtained at the phase transition. This demonstrates a dependence of SGE on the dielectric properties of a material and alludes to a flexoelectric origin of an effective SGE.

Active shape programming drives Drosophila wing disc eversion.

How complex 3D tissue shape emerges during animal development remains an important open question in biology and biophysics. Here, we discover a mechanism for 3D epithelial shape change based on active, in-plane cellular events that is analogous to inanimate "shape programmable" materials, which undergo blueprinted 3D shape transformations from in-plane gradients of spontaneous strains. We study eversion of the Drosophila wing disc pouch, when the epithelium transforms from a dome into a curved fold, quantifying 3D tissue shape changes and mapping spatial patterns of cellular behaviors on the evolving geometry using cellular topology. Using a physical model inspired by shape programming, we find that active cell rearrangements are the major contributor to pouch eversion and validate this conclusion using a knockdown of MyoVI, which reduces rearrangements and disrupts morphogenesis. This work shows that shape programming is a mechanism for animal tissue morphogenesis and suggests that patterns in nature could present design strategies for shape-programmable materials.

Exact solution for free vibration analysis of non-uniform thickness functionally graded porous nanosheet with surface effect based on variable nonlocal and length-scale parameters

In this article, the analytical solution for free oscillation of non-uniform thickness functionally graded porous (FGP) rectangular nanosheets resting on a Pasternak foundation with various boundary conditions (BCs) based on the nonlocal strain gradient theory and surface effect are discovered. The nonlocal stress and strain effects are captured on the nonlocal strain gradient hypothesis, while the surface energy effects are based on the surface elasticity hypothesis. The FGP nanosheet has a nonlinear thickness change in both x and y directions and is placed on the Pasternak elastic foundation. The unique point of this study is to investigate the change of nonlocal and length-scale coefficients along the thickness as mechanical properties of the material. Applying classical shear deformation theory (ignore the effect of shear deformation) combined with Hamilton’s principle, the motion balance equation of non-uniform thickness nanosheets is established. The accuracy of the proposed method is verified through reliable publications. A set of results of natural vibration frequencies of variable thickness FGP nanosheets under the influence of factors are discovered and discussed. The results of this study can be used in design calculations of MEM and NEMs systems in mechanics.

Second-order Willis metamaterials: Gradient elasto-momentum coupling in flexoelectric composites

Willis materials are composites whose the overall constitutive relations exhibit coupling between momentum and strain. Recently, piezoelectric Willis materials have been studied, allowing the macroscopic momentum to be additionally coupled to the non-mechanical stimulus. Such metamaterials classified as first-order Willis materials generate cross-couplings due to their asymmetric microstructures in order to realize novel phenomena in wave propagation. In this work, we study Willis materials that are flexoelectric and offer an electric field induced by a strain gradient. We show that in the case of flexoelectric Willis materials, the momentum also gets coupled to the strain gradient term under an effective description. Hereby, an ensemble averaging-based dynamic homogenization theory is developed for flexoelectric composites to compute constitutive relations of the macroscopic fields. This second-order Willis metamaterial offers a novel coupling termed gradient elasto-momentum coupling. The presence of non-uniform strain that can break the inversion symmetry of a unit cell is thus significant in generating the imaginary portion of all cross-couplings in the absence of asymmetric microstructures.

Fluid-Solid Interaction Analysis for Developing In-Situ Strain and Flow Sensors for Prosthetic Valve Monitoring.

Transcatheter aortic valve implantation (TAVI) was initially developed for adult patients, but there is a growing interest to expand this procedure to younger individuals with longer life expectancies. However, the gradual degradation of biological valve leaflets in transcatheter heart valves (THV) presents significant challenges for this extension. This study aimed to establish a multiphysics computational framework to analyze structural and flow measurements of TAVI and evaluate the integration of optical fiber and photoplethysmography (PPG) sensors for monitoring valve function. A two-way fluid-solid interaction (FSI) analysis was performed on an idealized aortic vessel before and after the virtual deployment of the SAPIEN 3 Ultra (S3) THV. Subsequently, an analytical analysis was conducted to estimate the PPG signal using computational flow predictions and to analyze the effect of different pressure gradients and distances between PPG sensors. Circumferential strain estimates from the embedded optical fiber in the FSI model were highest in the sinus of Valsalva; however, the optimal fiber positioning was found to be distal to the sino-tubular junction to minimize bending effects. The findings also demonstrated that positioning PPG sensors both upstream and downstream of the bioprosthesis can be used to effectively assess the pressure gradient across the valve. We concluded that computational modeling allows sensor design to quantify vessel wall strain and pressure gradients across valve leaflets, with the ultimate goal of developing low-cost monitoring systems for detecting valve deterioration.

Evaluating non-intrinsic contribution in flexoelectric measurements

The characterization of the flexoelectric coefficient is a fundamental issue for the studies of the flexoelectric effect, which describes the coupling between strain gradient and polarization. However, the contribution from non-intrinsic flexoelectricity cannot be ignored in the flexoelectric measurements, bringing challenges for the determination of intrinsic flexoelectric coefficients. In this work, we propose a non-intrinsic flexoelectric factor to evaluate the non-intrinsic flexoelectric contributions to the measured coefficient, based on the crystal-orientation-dependent flexoelectric coefficients measured by cantilever-bending method. The cubic magnesium oxide single crystals with different surface statuses are chosen to obtain the effective flexoelectric coefficients through the cantilever-bending method and first-principles. The results verify the effectiveness of the proposed non-intrinsic flexoelectric factor. This work provides an effective way to evaluate the non-intrinsic flexoelectric contributions in flexoelectric measurements.

Grain boundary-mediated strain response mechanism of AZ31 gradient- structure Mg alloy plate under uniaxial tensile loading

The changes in strain gradient induced by grain boundaries are crucial for enhancing the plasticity of gradient magnesium (Mg) alloys. The change of strain distribution influence by grain boundaries during plastic deformation of the gradient structure was examined. In this paper, the gradient structure AZ31 Mg-alloy plate with the surface fine grain (FG) to the center coarse grain (CG) was fabricated using hard plate rolling (HPR). The microstructure and strain distribution of Mg-alloy with a gradient structure were analyzed by electron backscatter diffraction (EBSD) and Digital image correlation (DIC) during uniaxial tensile. The findings indicate that the gradient structure sample (GS sample) displays a uniform strain distribution during the tensile process. Coarse-grain sample (CG sample) have obvious strain concentration, which leads to premature fracture. Based on EBSD characterization, low-angle grain boundaries (LAGBs) accumulates in the CG during plastic deformation. Orientation of CG tends to the (0001) basal. At the same time, the density of geometrically necessary dislocations (GNDs) inside CG has changed, which improves the Heterogeneous deformation induced (HDI) stress of gradient structure. During the uniaxial tensile, LAGBs accumulates in CG and changes the strain distribution of the gradient structure, which induces the accumulation of GNDs, and hence improving the properties of the GS Mg-alloy. These findings unveil the mechanism of strength-plasticity synergism of GS alloys from a new perspective and offer insights into the application of GS in Mg-alloys.

Damping Characteristics of Nonlocal Strain Gradient Waves in Thermoviscoelastic Graphene Sheets Subjected to Nonlinear Substrate Effects

Damping Characteristics of Nonlocal Strain Gradient Waves in Thermoviscoelastic Graphene Sheets Subjected to Nonlinear Substrate Effects

Self-limiting stacks of curvature-frustrated colloidal plates: Roles of intraparticle versus interparticle deformations.

In geometrically frustrated assemblies local intersubunit misfits propagate to intra-assembly strain gradients, giving rise to anomalous self-limiting assembly thermodynamics. Here we use theory and coarse-grained simulation to study a recently developed class of "curvamer" particles, flexible shell-like particles that exhibit self-limiting assembly due to the build up of curvature deformation in cohesive stacks. To address a generic, yet poorly understood aspect of frustrated assembly, we introduce a model of curvamer assembly that incorporates both intraparticle shape deformation as well as compliance of interparticle cohesive gaps, an effect we can attribute to a finite range of attraction between particles. We show that the ratio of intraparticle (bending elasticity) to interparticle stiffness not only controls the regimes of self-limitation but also the nature of frustration propagation through curvamer stacks. We find a transition from uniformly bound, curvature-focusing stacks at small size to gap opened, uniformly curved stacks at large size is controlled by a dimensionless measure of inter- versus intracurvamer stiffness. The finite range of interparticle attraction determines the range of cohesion in stacks that are self-limiting, a prediction which is in strong agreement with numerical studies of our coarse-grained colloidal model. These predictions provide critical guidance for experimental realizations of frustrated particle systems designed to exhibit self-limitation at especially large multiparticle scales.

Flexoelectric influence on crack propagation in ferroelectric single crystals: a phase-field approach

Ferroelectric materials, known for their inherent brittleness, are prone to brittle fracture. This limitation not only curtails the materials’ operational lifespan but also impinges on the reliability of the associated devices. Notably, the pronounced strain gradient present at the crack tip necessitates consideration of the flexoelectric effect—the interaction between strain gradient and electric polarization—in the fracture mechanics of ferroelectric materials. This study introduces a phase-field model incorporating the flexoelectric effect to elucidate its role on crack growth and domain evolution in ferroelectric single crystals. Our findings demonstrate that both crack trajectory and domain switching phenomena at the crack’s forefront are substantially influenced by the magnitude and sign of the flexoelectric coefficient, as well as the initial polarization direction. Depending on the computational scenarios, the flexoelectric effect can either exacerbate or impede crack propagation. Through meticulous examination of the mechanical field distributions and their temporal progression, we have uncovered the underlying mechanisms by which the flexoelectric effect governs crack propagation in ferroelectric single crystals. These insights pave the way for improving the fracture resistance and thereby enhancing the reliability of ferroelectric devices.

Electrical Detection of Acoustic Antiferromagnetic Resonance in Compensated Synthetic Antiferromagnets.

Compensated synthetic antiferromagnets (SAFs) stand out as promising candidates to explore various spintronic applications, benefitting from high precession frequency and negligible stray field. High-frequency antiferromagnetic resonance in SAFs, especially the optic mode (OM), is highly desired to attain fast operation speed in antiferromagnetic spintronic devices. SAFs exhibit ferromagnetic configurations above saturation field; however in that case, the intensity of OM is theoretically zero and hard to be detected in well-established microwave resonance experiments. To expose the hidden OM, the exchange symmetry between magnetic layers must be broken, inevitably introducing remanent magnetization. Here, we experimentally demonstrate a feasible method to break the symmetry via surface acoustic waves with the maintenance of compensated SAF structure. By introducing an out-of-plane strain gradient inside the Ir-mediated SAFs, we successfully reveal the hidden OM. Remarkably, the OM intensity can be effectively modulated by controlling strain gradients in SAFs with different thicknesses, confirmed by finite-element simulations. Our findings provide a feasible scheme for detecting the concealed OM, which would trigger future discoveries in magnon-phonon coupling and hybrid quasiparticle systems.