In-plane Strain Field Research Articles

A MITC3+ element improved by edge-based smoothed strains for free vibration and buckling analyses of porous plates based on the first-order shear deformation theory

This paper presents the free vibration and critical buckling analyses of porous plates based on the first-ordershear deformation theory by the proposed three-node triangular element. The bending strain fields of the suggested element are enriched by the bubble node located at the centroid of the triangular element. The shear locking phenomenon is eliminated by the independent interpolations of the transverse shear strains following the MITC3+ technique. The edge-based smoothed (ES) strain method is employed to improve the in-plane strain fields. The influence of the porosity distributions, length-to-thickness ratios, porous coefficient, and boundary conditions on the free vibration and critical buckling load of the porous plates are evaluated through several numerical examples by the proposed element, namely ES-MITC3+ element. The obtained results are compared with other references to perform the efficiency of the proposed element.

Tunable Band Alignment and Optoelectronic Structure of Cu2Se/PtX2 (X=Se,Te) Heterostructures: under Strain and Electric Field

Two-dimensional (2D) material-based van der Waals heterostructures (vdWHs) are an emerging strategy for regulating the electronic properties of two-dimensional materials. This study investigated the effects of a vertical electric field and strain on the band alignment transition and optoelectronic properties of Cu2Se/PtSe2 (PtTe2) vdWHs using density functional theory calculations. Cu2Se/PtSe2 vdWHs exhibited type-I to type-II band alignment transformation under an in-plane strain, interlayer distance, and electric field of 2%, 2.40 Å, and -0.40 V/Å, respectively. Moreover, Cu2Se/PtTe2 vdWH demonstrated a rich transition of types I, II, and III band alignments with in-plane strain. The absorption spectra of Cu2Se/PtSe2 (PtTe2) vdWHs show a certain degree of blue and red shift phenomenon upon the application of strain and electric fields. The predicted power conversion efficiencies at 3% in-plane strain with an interlayer distance of 3.40 Å for Cu2Se/PtSe2 (PtTe2) vdWHs were observed to be as high as 22.58% (19.80%). Thus, our work demonstrated that both strain and electric field can effectively and flexibly control the electronic properties of Cu2Se/PtSe2 (PtTe2) vdWHs, making them a promising candidate material for applications in photodetectors and field-effect transistors.

Homogenization of non-rigid origami metamaterials as Kirchhoff–Love plates

Origami metamaterials have gained considerable attention for their ability to control mechanical properties through folding. Consequently, there is a need to develop systematic methods for determining their effective elastic properties. This study presents an energy-based homogenization framework for non-rigid origami metamaterials, effectively linking their mechanical treatment with that of traditional materials. To account for the unique mechanics of origami systems, our framework incorporates out-of-plane curvature fields alongside the usual in-plane strain fields used for homogenizing planar lattice structures. This approach leads to a couple-stress continuum, resembling a Kirchhoff–Love plate model, to represent the homogeneous response of these lattices. We use the bar-and-hinge method to assess lattice stiffness, and validate our framework through analytical results and numerical simulations of finite lattices. Initially, we apply the framework to homogenize the well-known Miura-ori pattern. The results demonstrate the framework’s ability to capture the unconventional relationship between stretching and bending Poisson’s ratios in origami metamaterials. Subsequently, we extend the framework to origami lattices lacking centrosymmetry, revealing two distinct neutral surfaces corresponding to bending along two lattice directions, unlike in the Miura-ori pattern. Our framework enables the inverse design of metamaterials that can mimic the unique mechanics of origami tessellations using techniques like topology optimization.

Mesoscopic Stacking Reconfigurations in Stacked van der Waals Film.

Mesoscopic-scale stacking reconfigurations are investigated when van der Waals (vdW)films are stacked. A method to visualize complicated stacking structures and mechanical distortions simultaneously in stacked atom-thick films using Raman spectroscopy is developed. In the rigid limit, it is found that the distortions originate from the transfer process, which can be understood through thin film mechanics with a large elastic property mismatch. In contrast, with atomic corrugations, the in-plane strain fields are more closely correlated with the stacking configuration, highlighting the impact of atomic reconstructions on the mesoscopic scale. It is discovered that the grain boundaries do not have a significant effect while the cracks are causing inhomogeneous strain in stacked polycrystalline films. This result contributes to understanding the local variation of emerging properties from moiré structures and advancing the reliability of stacked vdW material fabrication.

Evolution of in-plane strain fields onset of a plastically deforming crack in zirconium

Understanding the fracture behaviour of a material is essential for the sustainable design of structural components. The complex nature of microscale mechanical testing techniques makes identifying the fracture behaviour experimentally challenging at a microscopic scale. Validating microscale simulations with experimental studies can be difficult using traditional experimental techniques. High-resolution digital image correlation combined with electron backscatter diffraction describes the total in-plane deformation field at a microstructural scale, which can be compared against finite element models for verification. The present study determines the in-plane strain distribution ahead of a plastically deforming crack during an in-situ experiment. A crystal plasticity-based finite element model is used to simulate the experimental crack tip behaviour, after which quantitative and qualitative comparisons are made. A concentration of normal strains ahead of the crack tip is observed in both experimental and simulated results, defining the fracture process zone. Slip localization behaviour around the crack is also evaluated using Schmid factor analysis. A good correlation between the experimental slip bands and theoretical predictions has been observed. The strain path dependence on slip activation is also identified. Strain localization in deforming zirconium is initially limited with dense and low-intensity slip occurring up to a maximum in-plane shear strain of 0.2. Formation of well-defined equidistant slip bands occurs with further deformation. Equidistant slip bands are observed for prismatic <a> and pyramidal <c+a> slip systems, having an interplane distance of ∼0.60±0.05 µm and ∼0.46±0.04 µm, respectively.

Dynamic Behavior of Aluminum Plates Subjected to Sequential Fragment Impact and Blast Loading: An Experimental Study

This paper presents a study on the dynamic behavior of thin aluminum plates subjected to consecutive fragment impact and blast loading. To this end, two separate experimental setups are used. In the first setup, 2 mm thick aluminum plates EN-AW-1050A-H24 were subjected to the ballistic impact of fragment-simulating projectiles (FSPs). Experiments were carried out for FSP calibers of 7.62 mm and 12.7 mm considering both single impact and triple impacts with variations in the spacing of the impact locations. The out-of-plane displacement and in-plane strain fields were measured using digital image correlation (DIC) coupled to a pair of high-speed cameras in a stereoscopic setup. In the second setup, a subsequent blast loading was applied to the perforated plates using an explosive-driven shock tube (EDST). After the plates are perforated, the strain field around the holes depended on the caliber, the impact orientation of the FSP, and the distance between the impact locations. When the blast loading was applied, cracks tended to appear in areas of strain concentration between the perforated holes. It was found that the relative distance between the holes significantly influences the target’s response mode.

Microscale experimental results and their implications for mesoscale modeling of damage initiation in cross-ply fiber reinforced composites

The results from a combined experimental and computational study to evaluate local in-plane variations of elastic properties (at the microscale fiber/matrix level) in mesoscale progressive failure analysis models of composites due to local fiber volume fraction variations are reported. A rectangular cross-ply specimen subjected to tensile loading is used as a case study in this investigation. Experimental results in support of understanding the correlation between local fiber volume fraction and in-plane strain field variations, by using specimens with small length scales is reported. A micromechanics computational model is used to understand and explain the experimental findings. The microscale finite element results suggest that the strain variations on the surface of the outer 90 plies prior to damage initiation are caused by local geometrical changes caused by the fibers non-uniformly packed and lying closest to the surface and not by the through-ply thickness local fiber volume fraction variations. Implications of this finding for homogenized mesoscale models for damage and failure are discussed.

Design Optimization by Virtual Prototyping Using Numerical Simulation to Ensure Thermomechanical Reliability in the Assembly and Interconnection of Electronic Assemblies

Abstract A methodology is presented that allows the evaluation of the thermomechanical reliability of electronic packages using “virtual prototyping.” Here, a virtual flip chip ball grid array (FC-BGA) is examined in comparison to a reference chip scale package (CSP). The comparison is performed using finite element simulation. A combined measurement-simulation technique is used to calibrate the finite element simulations on a reference object. The adjustment is based on the in-plane deformation field obtained by both simulation and optical measurement. For the latter, an optical sensor is used for in-plane deformation and strain field analysis based on the gray-scale correlation method. The findings obtained can be extrapolated to alternative package types with different but similar design to evaluate their suitability for the desired application before physical fabrication.

Tunable electronic structure and Rashba spin splitting of WSe2/WS2 van der Waals heterostructure via strain and electric-field

Suitable band structure, effective carrier separation and spin-charge locking are critical for further development and application of nanoscale spintronic devices. In this work, the effects of in-plane biaxial strain and electric field on the electronic structures and Rashba spin splitting of WSe 2 /WS 2 van der Waals heterostructure are investigated by the first principles calculations. The results show that considering the SOC effect, an observable Dresselhaus spin splitting of 424.5 meV and Rashba spin splitting can be observed at the K and Γ point in the valence band, respectively. At the same time, unexpected circle-type Berry curvature occurs due to a broken mirror structure for the WSe 2 /WS 2 heterostructure. A largest Rashba parameter α R with 0.503 eV Å can be achieved at the strain of −4% and the positive electronic field tend to weaken the strength of Rashba spin splitting. The linear Rashba spin splitting strength of WSe 2 /WS 2 heterostructure is tried to clarify, and coexistence of valley-contrasting property and Rashba effect enables spintronics and valleytronics application can be achieved. These results provide a way to engineer the electronic structure and Rashba spin splitting of WSe 2 /WS 2 heterostructure and open up the possibilities for exploring spin logic electronic devices as well as valleytronic devices. • Effects of strain and electric field on the electronic structures of WSe2/WS2van der Waals heterostructure are studied. • The WSe 2 /WS 2 heterostructure exhibits type-II band alignment and tunable Rashba spin splitting. • Unexpected circle-type Berry curvature occurs due to broken mirror structure. • A largest Rashba parameter α R of 0.507 eV Å can be obtained at the strain of −4%.

Inversion of elastic constants of composite materials by single test based on virtual fields method

In this paper, a method of obtaining four elastic constants of orthotropic composites by single tensile test is proposed. The principle of this method is to obtain the full field strain on the surface of the specimen through the tensile test of the specimen with a specific geometry, and to invert the measured in-plane strain field into the virtual fields method (VFM) to obtain the elastic constants. Based on the deformation field data generated by finite element numerical simulation, the effects of design parameters such as effective length, notch position, notch size and fillet radius on the identification results of elastic parameters of V-notch tensile specimen are studied. The results show that the inversion results of symmetrical V-notch specimen with 50 mm length, 12 mm notch size and 3.1 mm fillet radius are the best, and the sum of absolute relative errors of four elastic constants is less than 3%, which verifies the feasibility of the method.

Tri-wavelength simultaneous ESPI for 3D micro-deformation field measurement.

Electronic speckle pattern interferometry (ESPI), a well-established technique for micro-deformation measurement, can be used to determine both in-plane and out-of-plane displacement components. Although many works in ESPI have been reported for three-dimensional (3D) displacement measurement, few works have focused on the simultaneous measurement of 3D deformation fields. Here we present an ESPI system that consists of three sub-interferometers for simultaneous measurement of all three displacement components and in-plane strain fields. A 3CCD color camera, a specially designed shifting stage, and three lasers with optimal wavelengths are used in this system. The lasers and 3CCD camera provide independent interferograms with different color signals, while the shifting stage allows the sub-interferometers to achieve simultaneous phase shifting. The results of color separation and experimental measurement demonstrate the utility of the system.

Promoted photocarrier separation by dipole engineering in two-dimensional perovskite/C2N van der Waals heterostructures.

Due to the aggravation of environmental pollution and the energy crisis, it is urgent to develop and design environment-friendly and efficient photocatalysts for water splitting. van der Waals heterostructures composed of different two-dimensional materials offer an easily accessible way to combine properties of individual materials for applications. Herein, a novel Cs3Bi2I9/C2N heterostructure is proposed through first-principles calculations. The structural, electronic, and optical properties, as well as the charge transfer mechanism at the interface of Cs3Bi2I9/C2N are systematically investigated. Due to the difference between the work functions of Cs3Bi2I9 and C2N monolayers, when they are constructed into heterostructures, redistribution of charge occurs in the whole structure, and some of the charge transfer occurs at the interface due to the formation of an internal electric field. The band structure of Cs3Bi2I9/C2N has type-II band alignment, and the band edge position as well as the band-gap value of the heterostructure are suitable for visible light water splitting. The in-plane biaxial strain, interfacial spacing, and external electric field can effectively modulate the electronic structure and photocatalytic performance of the heterostructure. Under certain conditions, the heterostructure can be changed from type-II to type-I band alignment, accompanied by the transition from an indirect band-gap semiconductor to a direct band-gap semiconductor. Moreover, the intrinsic anion defect (I vacancy) at different positions, as donor defects, can introduce defect levels near the conduction band edge, which affects the transition of photogenerated carriers in these systems. Our findings provide a theoretical design for strategies to improve the performance of two-dimensional perovskites/C2N in photocatalytic and optoelectronic applications.

Nondestructive Assessment of Elastomeric Bridge Bearings Using 3D Digital Image Correlation

Elastomeric bridge bearings are installed between the bridge superstructure and substructure to accommodate translational and rotational deformations. The manufacturing quality of elastomeric bridge bearings is of high significance because manufacturing defects (such as variations in rubber layer thickness and nonparallel steel laminates) may jeopardize their short- and long-term structural behavior and integrity. Current quality control procedures involve destructive testing of samples of bearings from a lot. This type of testing is time consuming and costly, and thus limited to a relatively small sample size, which may undermine confidence in the quality of remaining bearings in the lot. This paper presents an alternative, vision-based assessment methodology for the nondestructive identification of the internal structure of elastomeric bridge bearings. The methodology capitalizes on the high deformability of rubber and the near inextensibility of the steel laminates, which together result in a unique deformation pattern on the vertical surfaces of a bearing when it is subjected to axial load. This deformation pattern features local extrema in in-plane strain and horizontal displacement fields on the vertical surfaces. These local extrema are analyzed to deduce the thicknesses of the rubber layers and rubber side covers. The methodology is developed based on three-dimensional finite-element analyses (3D-FEA). Then, three-dimensional digital image correlation (3D-DIC) is used in experimental tests to evaluate its capability to identify manufacturing defects in elastomeric bridge bearings. Finally, the methodology is validated against destructive tests. The nondestructive method presented in this study is conducted in conjunction with compressive tests that departments of transportation carry out routinely and is therefore expected to facilitate rapid and cost-effective qualification of elastomeric bridge bearings.

Quasi-static and low-velocity impact biaxial flexural fracture of aluminosilicate glass — An experimental and numerical study

In this study, the quasi-static biaxial fracture behavior of aluminosilicate glass is investigated via Ball-On-Ring (BOR) and Ring-On-Ring (ROR) tests aided by a three-dimensional Digital Image Correlation (3D-DIC) technique. In-plane strain field and out of plane deformation distribution during the loading process can be obtained by this test system, overcoming the problem of inaccurate displacement data provided by the loading machine. During the loading process, a uniform strain distribution field is formed below the load ring of the ROR specimen while a gradient strain distribution is built for the BOR specimens. For dynamic loading conditions, low-velocity impact BOR tests are conducted at velocities of 2 m/s and 4 m/s showing a dynamic strengthening effect and high-speed cameras provide detailed fracture and failure sequences of the glass plates. Finite Element Method (FEM) simulations with the JH-2 material model are carried out showing good consistency with experimental results for the quasi-static loading conditions. FEM coupled to Smooth Particle Hydrodynamics (FEM-SPH) technique is utilized for dynamic simulations to solve the element distortion and non-physical problems. The influence of the tensile strain rate effect on low-velocity impact behavior of aluminosilicate glass is analyzed in detail. The original JH-2 model does not provide a reasonable prediction of the dynamic tensile response of brittle materials and the model requires further modifications to describe the dynamic tensile fracture behavior. By introducing rate-dependence maximum hydrostatic tensile strength σt,max to the updated model, better predictions for the contact force and projectile residual velocity histories of low-velocity impact tests can be provided.

In-Plane Shear-Axial Strain Coupling Formulation for Shear-Deformable Composite Thin-Walled Beams

This paper presents an improved description of the in-plane strain coupling in Librescu-type shear-deformable composite thin-walled beams (CTWB). Based on existing descriptions for Euler-type CTWB, an analogous formulation for shear-deformable CTWB is here developed by building, via the Mindlin–Reissner theory and an orthotropic constitutive law of the shell wall, an alternate equation for the in-plane shear force which effectively couples the axial and shear in-plane strains. It is observed that this strain coupling formulation includes some of the transversal (out-of-plane) shear strain terms, thus also functioning as a path for transferring transversal shear energy to the in-plane strain field and therefore improving shear-deformability. The performance of the new CTWB model is compared against that of previously available CWTB (i.e. Euler-type with strain coupling and Timoshenko-type without strain coupling) for several aspect ratios, fibre-orientations and laminate types. Error measures are calculated by comparing several relevant stiffness coefficients and displacement shapes to reference results provided by corresponding 3D shell-based ANSYS finite-element models. Results indicate that for cases involving significant shear energy (i.e. short aspect ratios) and/or in-plane shear-axial strain coupling (i.e. off-axis or asymmetric/unbalanced laminates), the new CTWB model proposed in this work can attain an accuracy level comparable to that associated to more sophisticated models, two to three orders of magnitude larger, at a fraction of the computational cost.

Tunable electronic properties of SnS2/WSe2 hetero-structure: A frist principle study

The two-dimensional van der Waals hetero-structures have excellent electronic properties, which provide a new platform for the development of nanoscale electronic devices in the future. Utilizing the first principle calculation based on density functional theory, we systematically study the electronic properties of SnS 2 /WSe 2 hetero-bilayer systems. We mainly focused on the effect of the in-plane biaxial strain and external electric field on the energy band structures of hetero-bilayer SnS 2 /WSe 2 . As a contrast, corresponding calculations of monolayer (or bilayer) SnS 2 and WSe 2 were also implemented. It is shown that monolayer SnS 2 and WSe 2 are direct (1.583 eV) and indirect (1.476 eV) band gap semiconductors, respectively. For hetero-bilayer SnS 2 /WSe 2 , among six considered independent stacking structures, the most stable system is manifested as type-II band alignment with a bandgap of 0.269 eV. Moreover, a tunable band gap in hetero-bilayer SnS 2 /WSe 2 can be realized by implying in-plane compressing/stretching strain and external electric field. Our results are useful complement to experimental studies of SnS 2 -based (or WSe 2 -based) hybrid systems and provide a new route to facilitate fabricate optoelectronic devices where controllable bandgap are needed. • Structural and electrical properties of SnS 2 /WSe 2 hetero-bilayers are investigated using DFT-D2 and HSE06 functionals with GGA approximation. • The SnS 2 /WSe 2 hetero-bilayer is an indirect semiconductor with type-II band alignment. • Band gaps of SnS 2 /WSe 2 hetero-bilayers could be modulated by in-plane biaxial compressing/stretching and vertical electric field. • Interlayer interactions of SnS 2 /WSe 2 hetero-bilayers could induce the type–II–to-type-I band alignment transition and semiconductor-to-metal transition.

3D Strain Field Evolution and Failure Mechanisms in Anisotropic Paperboard

BackgroundExperimental analyses of the 3D strain field evolution during loading allows for better understanding of deformation and failure mechanisms at the meso- and microscale in different materials. In order to understand the auxetic behaviour and delamination process in paperboard materials during tensile deformation, it is essential to study the out-of-plane component of the strain tensor that is, in contrast to previous 2D studies, only achievable in 3D.ObjectiveThe main objective of this study is to obtain a better understanding of the influence of different out-of-plane structures and in-plane material directions on the deformation and failure mechanisms at the meso- and microscale in paperboard samples.MethodsX-ray tomography imaging during in-situ uniaxial tensile testing and Digital Volume Correlation analysis was performed to investigate the 3D strain field evolution and microscale mechanical behaviour in two different types of commercial paperboards and in two material directions. The evolution of sample properties such as the spatial variation in sample thickness, solid fraction and fibre orientation distribution were also obtained from the images. A comprehensive analysis of the full strain tensor in paperboards is lacking in previous research, and the influence of material directions and out-of-plane structures on 3D strain field patterns as well as the spatial and temporal quantification of the auxetic behaviour in paperboard are novel contributions.ResultsThe results show that volumetric and deviatoric strain, dominated by the out-of-plane normal strain component of the strain tensor, localize in the out-of-plane centre already in the initial linear stress-strain regime. In-plane strain field patterns differ between samples loaded in the Machine Direction (MD) and Cross Direction (CD); in MD, strain localizes in a more well-defined zone close to the notches and the failure occurs abruptly at peak load, resulting in angular fracture paths extending through the stiffer surface planes of the samples. In CD, strain localizes in more horizontal and continuous bands between the notches and at peak load, fractures are not clearly visible at the surfaces of CD-tested samples that appear to fail internally through more well-distributed delamination.ConclusionsIn-plane strain localization preceded a local increase of sample thickness, i.e. the initiation of the delamination process, and at peak load, a dramatic increase in average sample thickening occurred. Different in-plane material directions affected the angles and continuity of the in-plane strain patterns as well as the sample and fracture properties at failure, while the out-of-plane structure affected how the strain fields distributed within the samples.

Investigation of the biaxial flexural fracture of aluminosilicate glass by smeared fixed crack method

Ball-On-Ring (BOR) and Ring-On-Ring (ROR) tests are experimental methods used to characterize biaxial flexural strength of brittle materials. In this study, the quasi-static biaxial fracture behavior of aluminosilicate glass is investigated via BOR and ROR tests aided by a three-dimensional Digital Image Correlation (3D-DIC) technique. The in-plane strain field and out of plane deformation distribution during the loading process can be obtained by this special-designed test system. A finite element modeling approach incorporating smeared crack model is chosen to represent the discontinuous macrocrack brittle behavior of aluminosilicate glass. The simulations are conducted using the commercial software LS-DYNA with the implemented material model MAT280_GLASS. This numerical method is carefully assessed, and the capability of this model is evaluated by comparing the results of the numerical simulations with the corresponding experimental results.

A MITC3+ element improved by edge-based smoothed strains for analyses of laminated composite plates using the higher-order shear deformation theory

In this paper, a new three-node triangular plate element is proposed to analyze laminated composite plates based on the higher-order shear deformation theory (HSDT). Originating from the MITC3+ shell finite elements, the displacement fields of the HSDT are interpolated by usual linear functions of the three-node triangular element and a cubic supplemented function associated with a node located at the centroid of the element. The transverse shear strain fields are separately approximated according to the MITC3+ shear-locking removal technique. The edge-based smoothed (ES) strain method is employed to improve the in-plane strain fields. Applying the divergence theorem, the surface integration of the in-plane stiffness matrices is transformed into the line integration on the boundary of the smoothing domains. The performance of the so-called ES-MITC3+ plate elements is validated through several numerical examples. The numerical results of the static, frequency and buckling analyses when this new element is used converge to the exact solutions and agree well with those given in other references.

Dipole control of Rashba spin splitting in a type-II Sb/InSe van der Waals heterostructure

InSe monolayer, belonging to group III–VI chalcogenide family, has shown promising performance in the realm of spintronic. Nevertheless, the out-of-plane mirror symmetry in InSe monolayer constrains the electrons' degrees of freedom, and this will confine its spin-related applications. Herein, we construct Sb/InSe van der Waals heterostructure to extend the electronic and spintronic properties of InSe. The density functional theory is utilized to verify the tunable electronic properties and Rashba spin splitting (RSS) of Sb/InSe heterostructure. According to the obtained results, the Sb/InSe heterostructure can be considered as a direct band gap semiconductor with typical type-II band alignment, where the electrons and holes are localized in the InSe and Sb layers, respectively. The RSS is recognized at conduction band minimum around Γ point in Sb/InSe, which is induced by the spontaneous internal electric field with electric dipole moment of 0.016 e Å from Sb to InSe. The vertical strain, in-plane strain, and external electric field are employed to modulate the strength of RSS. The Rashba coefficient and dipole moment exhibit the similar variation tendency, suggesting the strength of RSS depends on the magnitude of dipole moment. The controllable RSS makes Sb/InSe heterostructure become an appropriate candidate material for spintronic devices.