Shear Coupling Research Articles

Shear-coupling of graphene grain boundaries: Elementary mechanisms, effects of topology, and role of buckling

Engineering grain boundary structure is a promising method for rational control of the microstructure and mechanical properties of two-dimensional materials. In bulk materials, shear stresses can drive grain boundary migration through the dislocations in grain boundaries. However, while shear coupling of grain boundaries has been studied in bulk materials like nanocrystalline copper, its translation to two-dimensional materials where out-of-plane deformation can relieve in-plane shear is not yet established. We investigate how the low flexural rigidity of graphene effects shear coupled grain boundary motion using atomic scale simulations of flat and buckled grain boundaries. We define the coupling shear strain as the strain at which a grain boundary has advanced by one Burgers vector and is at equilibrium and the critical shear strain as the strain at which migration of the first dislocation in the grain boundary becomes thermodynamically favorable. We show that the out-of-plane deformation does not influence the coupling shear strain and is governed only by the grain boundary topology. While the critical shear strain is altered somewhat by the low flexural rigidity due to buckling induced softening, it is also still dominated by the grain boundary topology. Our atomic scale results are synthesized into two models that predict the coupling and critical shears.

A rosette approach for the determination of the compliance matrix

The computation of the Young's moduli and Poisson's ratio using finite element analysis is comparatively straight forward in the case of systems with non-orthogonal lattice vectors. However, the corresponding calculation of the shear coupling coefficients and the shear modulus is more demanding and less readily attainable. Yet these are needed in order to determine the compliance matrix, which is essential in order to obtain a complete description of the mechanical properties of a structure in any direction. Based on these considerations, this work aims at providing a general methodology for the computation of the complete compliance matrix for systems with non-orthogonal lattice vectors from measurements of the Young's modulus and Poisson's ratio obtained using a suitable rosette of unit cells. The theoretical framework will be outlined and then applied on an accordion-like honeycomb that does not possess a rectangular unit cell and has potential applications in cellular scaffolding, particularly of heart muscle tissue. For the computation, the values of the Young's moduli and Poisson's ratio from three differently-orientated non-rectangular unit cells were obtained using finite element simulations allowing the determination of the complete compliance matrix. The results were validated by comparison with numerical simulations carried out on another unit cell having a different orientation from the other three.

Influence of PVB Interlayer Mechanical Properties on Laminated Glass Elements Design in Dependence of Real Time-Temperature Changes.

Most used laminated glass is composed of float glass plies bonded together with a viscoelastic Polyvinyl Butyral (PVB) interlayer. The shear stiffness of the polymeric interlayer is the key factor in the behavior of laminated glass. Structural engineers in the past were designing laminated glass regardless of the shear coupling of the plies. This approach with a high level of reliability led to expensive laminated glass structures due to insufficient knowledge of foil properties. Most of the current standards suggest methods that consider the shear coupling of the plies. This paper presents the experimental data from a static loading test performed on a laminated glass panel exposed to changing temperatures. The deformations were observed for 48 h. The measured results were compared with the known analytical design approaches and in addition with the finite element modeling (FEM) analysis in the available software for laminated glass design. A simplified design approach that simulates foil behavior in dependence on load duration and temperature change was adopted in this study. Design approaches that use effective thickness calculations are used with the Young and shear relaxation modulus provided by the foil producer. The imprecision of the Eurocode standards for glass design, and the propensity to change the approach to the calculation by introducing more precise parameters were expounded. The results when combining the time-temperature superposition (TTS) and the Wölfel–Bennison approach were found to be in very good agreement with the FEM analysis of 3D solid elements in Abaqus and measured data.

A finite deformation theory for grain boundary plasticity based on geometrically necessary disconnections

Grain boundary processes such as shear coupling and sliding are a consequence of plastic distortion accompanying grain boundary motion. Atomic scale studies using molecular dynamics (MD) and phase field crystal simulations demonstrate non-unique and stress-dependent shear coupling, a key feature that recently motivated the introduction of disconnections as the primary carriers of grain boundary plasticity. In this work, we develop a diffuse-interface finite deformation theory for grain boundary plasticity based on the notion of geometrically necessary disconnections (GND), with a discrete collection of intrinsic coupling factors, defined by the bicrystallography, as inputs to the model. It is emphasized that disconnection density is not a primary variable of the theory, instead it is the plastic slip rate associated with shear coupling that is a fundamental variable, and the resulting incompatibility is measured by the GND density. As an interesting consequence of this framework, we discover that in the presence of grain rotation, plastic shear that is commonly associated with the glide of disconnections, is insufficient to describe grain boundary plasticity, and it must be augmented with an additional plastic rotation. The disconnections-based continuum model can describe phenomena such as state-dependent shear coupling, mode switching, grain boundary sliding and grain rotation. Using finite elements, we simulate grain boundaries driven by shear and synthetic driving forces in bicrystals under various boundary conditions.

A method for generating dynamic compression shear coupled stress loading on living cells.

Changes in the mechanical properties of single cells are related to the physiological state and fate of cells. The construction of cell constitutive equations is essential for understanding the material characteristics of single cells. With the help of atomic force microscopy, bio-image processing algorithms, and other technologies, research investigating the mechanical properties of cells during static/quasi-static processes has developed rapidly. A series of equivalent models, such as viscoelastic models, have been proposed to describe the constitutive behaviors of cells. The stress-strain relations under dynamic processes are essential to completing the constitutive equations of living cells. To explore the dynamic mechanical properties of cells, we propose a novel method to generate a controllable dynamical compression shear coupling stress on living cells. A CFD model was established to visualize this method and display the theories, as well as assess the scope of the application. As the requirements or limitations are met, researchers can adjust the details of this model according to their lab environment or experimental demands. This micro-flow channel-based method is a new tool for approaching the dynamic mechanical properties of cells.

The theory of compression–shear coupled composite wave propagation in rock

AbstractThe wave velocity analysis of rock medium is the main method used to explore the internal compositions in the crust and research seismic. In this paper, a compression–shear coupled nonlinear elastic constitutive relation is established, which is consistent with the mechanical properties of rock and mineral medium under high pressure. On this basis, numerical solutions of the wave equation and plane wave analytical solutions for the primary and secondary wave velocities are obtained. As is indicated by the comparison with the linear elastic constitutive theory, the results reflect the compression–shear coupling characteristics of the rock, including the stress path effect and the compression–shear coupling wave effect. With different parameter values, the velocity of the secondary wave changes from lower than that of the elastic shear wave, to higher than that of the elastic shear wave. The research results are expected to provide meaningful explanations for the physical mechanisms of the supershear wave and sub‐Rayleigh wave, and guidance for the detection of rock and soil composition and the observation of seismic waves.

Effects of handedness ratio and handedness distribution on the mechanical properties of Bi-chiral mechanical metamaterials

The elastic mechanical properties of bi-chiral mechanical metamaterials are explored via systematic finite element simulations. Designs of bi-chiral mechanical metamaterials with both periodic and complete random handedness distributions for various handedness ratio and domain size and length aspect ratios were investigated. It is found that in general, because of the interactions at the ‘twinned’ intercellular boundaries between neighboring domains, the handedness ratio, handedness distribution, domain size and length aspect ratio significantly influence the overall mechanical properties of bi-chiral designs. Specifically, when handedness ratio increases and domain size decreases, the effective stiffness and the auxetic effects increases, while the effective shear modulus is much less sensitive to either the handedness ratio or the domain size. The chirality-induced normal shear coupling effect is solely determined by the handedness ratio. An empirical mechanical model was proposed to quantify the influences of ‘twinned’ intercellular boundaries on the effective stiffness and effective Poisson’s ratio of bi-chiral designs. In addition, both upper and lower limits of the effective stiffness and the effective Poisson’s ratio of bi-chiral designs are identified.

Strength analysis of composite envelope structures considering the tension–shear coupling and cutting pattern effect

Various strength criteria have been extensively used in the structural design of stratospheric airships. However, it is still a critical challenge to accurately predict the failure strength for ensuring structural safety due to the complex mechanical behaviors of multi-layer composite envelope materials under various loading environments. This article thus aims to establish refined numerical models for the strength prediction of envelope structures. Firstly, the mechanical properties of envelope materials were tested and investigated comprehensively. The creative concept of tension–shear​ coupling is demonstrated by the shear constitutive relation and failure criterion. Secondly, with consideration of the cutting pattern effect originating from the manufacturing procedure, a new equal-diameter flattening method for cutting gores is proposed. Finally, inflation-bursting tests of spherical and ellipsoidal envelopes were conducted to validate the proposed refined numerical models. The maximum deviation of strengths predicted by the novel criterion is less than 8% for both envelope structures, indicating that the tension–shear effect plays a significant role in the failure mechanism of flexible thin-walled envelope structures.

Pressure-bearing performance of sliding poly-p-phenylene benzobisoxazole-rope-reinforced spherical composite envelope structures

Stratospheric airships require a lightweight envelope to contain lighter-than-air (LTA) buoyancy gas, making the lightweight design and pressure-bearing performance of the envelope structure a key research issue. This paper proposes a structural design scheme for a sliding poly-p-phenylene benzobisoxazole (PBO) fiber-rope-reinforced spherical envelope. The aims were to reduce envelope weight and improve pressure-bearing performance while solving the challenges of envelope structural strength. Two types of spherical envelope structures were constructed from Vectran fabric with PBO rope placed in various positions for reinforcement, and subjected to inflatable burst tests. Strain in the seam tape and envelope gores were measured by digital image correlation. A refined envelope structure model was established to simulate the bursting process with consideration of the cutting pattern effect and the mechanical properties of the weld seams. Comparison of the simulation and test results, combined with observations of the tear textures of damaged envelopes, enabled the determination of failure positions. The envelope material at the failure point was disassembled and the micromorphology and microstructure of the bearing layer were observed by scanning electron microscopy (SEM). The process and characteristics of damage origination, propagation, and collection in the envelope material are explained, and the stress behavior and state of the damage positions are analyzed. Based on the study of the mechanical behavior at the failure position, design suggestions for PBO-rope-reinforced spherical envelopes are provided. A strength criterion to incorporate tensile–shear coupling is proposed, which bridges the gap between the uniaxial tensile strength (UTS) and biaxial tensile mechanical properties of the envelope structure.

Compression Deformation Prediction of Chiral Metamaterials: A Compression–Shear Coupling Model

A category of metamaterials consisting of chiral cytosolic elements assembled periodically, in which the introduction of a rotatable annular structure gives metamaterials the ability to deform in compression–shear, has been a focus of research in recent years. In this paper, a compression–shear coupling model is developed to predict the compressive deformation behaviour of chiral metamaterials. This behaviour will be analysed by coupling the rotation of the annular node and the bending characteristics of ligament beam, which are obtained as a function of the length of ligament beam and the angle of rotation at the end of the beam. The shape function of the ligament beam under large deformation is obtained based on the elliptic integral theory; the function characterises the potential relationship between key parameters such as displacement and rotation angle at any point on the ligament beam. By simulating the deformation of cells under uniaxial compression, the reasonableness of the large deformation model of the ligament beam is verified. On this basis, a chiral cell-compression mechanical model considering the ductile deformation of the annular node is established. The compression–shear deformation of two-dimensional planar chiral metamaterials and three-dimensional cylindrical-shell chiral metamaterials was predicted; the offset displacements and torsion angles agreed with the experimental and finite element simulation results with an error of less than 10%. The developed compression–shear coupling model provides a theoretical basis for the design of chiral metamaterials, which meet the need for the precise control of shapes and properties.

The Conjugate Beam Effective Thickness Method

The structural performance of laminated glass is strongly dependent on the shear coupling offered by the interlayer between the bounding layered and monolithic limits of the glass plies. The most common simplified design approach consists of defining the effective thickness, i.e., the thickness of a monolithic section with equivalent flexural section properties. The Enhanced Effective Thickness (EET) method has been verified to estimate deflection in laminated glass for a range of load and boundary conditions for two-, three-, and multi-ply beams; however, for some static schemes, the EET method is less accurate for predicting stress. The recently proposed Conjugate Beam Effective Thickness (CBET) method, initially developed for cantilevered laminated glass balustrade applications, accounts for the relative displacement of glass plies across the interlayer for a range of loads and statically determinate boundary conditions. In this paper, the CBET method is extended to the evaluation of two-ply simply supported beams under concentrated, uniformly, and tapered distributed out-of-plane loads. Predicted deflection- and stress-effective thickness obtained from effective thickness methods is compared with finite element model results in illustrative examples, demonstrating improved accuracy. Closed-form formulas are summarized in tables to facilitate the practical application of the CBET method in the design practice.

Interstitial hydrogen enhances the mobility of some grain boundaries in tungsten

Segregation of interstitials at a grain boundary (GB) is known to generally lower its mobility. This phenomenon, called ‘solute-drag’, has important ramifications on the process of recrystallization and microstructural evolution. In this manuscript, we present predictions from molecular dynamics (MD) simulations which demonstrate that interstitial hydrogen in tungsten can in fact increase the mobility of some GBs which exhibit shear coupling. Assuming a disconnection-based mechanism, activation energies and pre-factors for disconnection nucleation are predicted from simulations of shear-coupled motion. In GBs where enhanced mobility is predicted, interstitial H reduces both the activation energy and the pre-factor for disconnection nucleation, thus effectively increasing the mobility. For GBs with diminished mobility, MD predicts that presence of interstitial H reduces the pre-factor and, in some cases, increases the activation energy. The reduction in the activation energy inferred from MD simulations are confirmed by nudged elastic band calculations. Temperature-dependent structural transitions are observed for some GBs, and the effect of interstitial H is found to change with the changes in structure. The effect of interstitial H is predicted to be complex and highly variable, providing some plausible explanations for experimental observations on the recrystallization of tungsten in presence of H-loaded plasma.

Interlayer shear coupling in bilayer graphene

The interfacial shear coupling (ISC) governs the relative in-plane deformations of layered two-dimensional (2D) van der Waals (vdW) materials, which is significant for both the fundamental theory of solid mechanics and the stability design of 2D devices. Here we study the representative ISC of 2D vdW stacks using bilayer graphene (BLG) and isotope-labeled Raman spectroscopy. The results show that under uniaxial tensile strain, the ISC between two graphene layers evolves sequentially with bonding, sliding and debonding process, and the corresponding interfacial shear strength is inversely proportional to the sample size. Molecular dynamics (MD) simulations demonstrate the origin of this inverse proportionality as stronger interlayer vdW interaction induced by the edge lattices and atoms of BLG that have more degrees of freedom. These results not only provide new fundamental insights into the multiscale interpretation of macroscopic interfacial shear properties of 2D vdW stacks but also have great potential in guiding the design of graphene-based composite materials and flexible 2D electronics.

Simulating the non-monotonic strain response of nanoporous multiferroic composites under electric field control

In this work, we simulate and analyze the mechanical response of a class of multiferroic materials consisting of a templated porous nanostructure made out of cobalt ferrite (CFO) partially filled by atomic layer deposition (ALD) with a ferroelectric phase of lead zirconate titanate (PZT). The strain in the device is measured when an electric field is applied for varying ALD thicknesses, displaying a non-monotonic dependence with a maximum strain achieved for a coating thickness of 3 nm. To understand this behavior, we apply finite element modeling to the smallest repeatable unit of the nanoporous template and simulate the mechanical response as a function of PZT coating thickness. We find that this non-monotonic response is caused by the interplay between two driving forces opposing one another. First, increased porosity works toward increasing the strain due to a reduced system stiffness. Second, decreased porosity involves a larger mass fraction of PZT, which drives the electro-mechanical response of the structure, thus leading to a larger strain. The balance between these two driving forces is controlled by the shear coupling at the CFO/PZT interface and the effective PZT cross section along the direction of the applied electric field. Our numerical results show that considering a nonlinear piezoelectric response for PZT leads to an improved agreement with the experimental data, consistent with ex situ poling of the nanostructure prior to magnetic measurements.

Study on shear buckling failure of laser-welded dissimilar aluminum alloy (Al-Li-2099/Al-Li-S4) stiffened panel

Laser welding of L-shaped aluminum alloy joints is of great significance in lightweight and efficient manufacturing of thin-wall reinforced aerospace structures. Shear performance is an important reference index for the structural design of aluminum alloy-reinforced panels. In this study, in-plane shear experiments of a continuous double-sided laser welded dissimilar Al-Li alloy (Al-Li-2099/Al-Li-S4) stiffened thin-walled panels were carried out. The deformation and buckling mode evolution of the stiffened panel were measured by the combination of fringe projection profilometry and strain gauge measurement. The results show that in the macroaspect, the stiffened panel first exhibits local skin buckling and then develops into overall buckling along the diagonal tensile direction. Finally, the stiffened panel shows weld desoldering failure. Metallographic examination and scanning electron microscopy were performed on the L-shaped joints at different positions of the stiffened panel. The microstructure observation shows that the weld was composed of a nondendritic equiaxed zone, a columnar dendritic zone, and an equiaxed dendritic zone. The failure mode of the weld is mainly brittle fracture with a small amount of shear dimples, indicating that the welded seam of the stiffened panel under the shear load is tensile shear coupling. After the force reaches material strength, the crack nucleates in the weld and extends along the weld until it penetrates the whole weld. This shows that the mechanical properties of the weld microstructure are closely related to the macroshear properties of the stiffened panel.

Direct observation of edge modes in zigzag granular chains

As a new class of artificial elastic materials, granular crystals are mechanical structures of elastic beads arranged in contact through a lattice. One important feature of wave dynamics in granular crystals is that it highly relies on the contact mechanics, allowing for exotic wave transport properties such as rotational waves, solitary waves, slow edge waves, topological edge waves, etc. Realizing granular structures with well-predicted wave physics not only renders these new properties to mechanical systems, but provides also significant possibilities for advanced elastic wave control scenarios. Here, we theoretically and experimentally study the linear wave dynamics in one-dimensional (1D) zigzag granular chains constructed with macroscopic spherical stainless steel/tungsten beads. A spring–mass model including normal, shear and bending mechanical couplings between beads is proposed to characterize the wave dynamics in the chain, which turns out to exhibit remarkable agreement with the experimental measurements. Our work confirms the existence of localized translational–rotational coupled modes at the ends of granular chains, and it might motivate future studies for novel topological wave effects in granular structures.

Universally characterizing atomistic strain via simulation, statistics, and machine learning: Low-angle grain boundaries

When applied to catalysis and related materials phenomena, grain boundary (GB) engineering optimizes over many currently disparately defined properties. Such properties include GB mobility, solute diffusivity, and catalytic footprints correlating current density with dislocation-induced strain. A recent universalizing framework has systematically classified low-Σ GBs in relation to analogous high-angle references, distinguishing them using footprints formed from the directional straining needed to reversibly yield bicrystals from their separated grains. Correlating the elastic work profiles derived from this thermodynamic process with matching changes in GB dislocations, strain footprints can comprehensively link formerly disparate catalytic properties and materials phenomena. This research investigates such structure-energy correlations to evaluate differences between low-angle (LAGBs) and high-angle (HAGBs) GBs, systematically delineating LAGB-HAGB transitions, explaining their origins, and connecting transitions to materials phenomena. A hierarchical statistical model, nesting GB degrees of freedom within one another, systematically detects such transitions via simplified strain footprints without failure of a single unique GB structure and material combination. A more comprehensive analysis of footprint directional components and discontinuities links transitions to catalytically relevant materials phenomena, describing thermal grooving, shear coupling, complexions, and defect migration under a single universal atomistic framework. With machine learning and spatially generalized strain footprints, this framework reconciles such phenomena via more comprehensive geometry-energy correlations.

Study on Seismic Performance of Connecting Prefabricated Coupling Beam and Shear Wall with Equivalent Bars

This study proposes a new type of method for the connection of the prefabricated coupling beam and shear wall to solve the problems in the construction of assembled frame‐shear wall structures. To investigate the seismic properties of this new type of assembled coupling beam, experiments with 2 groups of test pieces under low‐period cycling loads were completed. Furthermore, this study studied some important influence factors. Results show that this novel coupling beam has a similar performance to the cast‐in‐place coupling beam. The bearing capacity and energy dissipation capacity of cast‐in‐place structures increase with the increase in end block thickness and the ductility inversely, yet the bearing capacity, seismic energy dissipation capacity, and ductility of assembled coupling beam structure decrease with the increase in end block thickness. Numerical simulation shows that increasing the area of equivalent steel bars will increase its yield load but will also reduce the seismic energy dissipation capacity and ductility. The thicker the shear wall thickness, the higher specimen’s bearing capacity, the stronger the seismic energy dissipation capacity, and the worse the ductility is.

Investigations on the viscoelastic material behaviour and linearity limits of PVB

The consideration of the shear bond via the intermediate layer in the design of laminated glass is of great interest, as this can lead to a considerable reduction of the maximum stresses in the glass, depending on the load and static system. Polyvinyl butyral based interlayers show a typical polymeric thermo‐viscoelastic material behaviour, which means that the shear coupling depends on the load (duration and magnitude) and the prevailing temperature. With small distortions below the linearity limit, the time‐dependent material behaviour of the intermediate layer can be mapped using the Prony‐Series. However, the linear viscoelastic range is exceeded at latest in the post‐fracture behaviour and hence the Prony‐Series can no longer be used straightforwardly. This article shows the experimentally determined limits of the linear viscoelastic range using the example of PVB. In addition, the Prony parameters for the linear viscoelastic range are determined.

On the Behavior of Coupled Shear Walls: Numerical Assessment of Reinforced Concrete Coupling Beam Parameters

Modern construction of high-rise and tall buildings depends on coupled shear walls system to resist the lateral loads induced by wind and earthquake hazards. The lateral behavior of this system depends on the structural behavior of its components including coupling beams and shear walls. Although many research studies in the literature investigated coupling beams and shear walls, these studies stopped short of investigating the coupled shear walls as a system. Therefore, in this research, the effect of the coupling beam parameters on the nonlinear behavior of the coupled shear walls system was investigated. The full behavior of a 10-story coupled shear wall system was modeled using a series of finite element analyses. The analysis comprised of testing several coupling beam parameters to capture the effect of each parameter on system response including load-deflection behavior, coupling ratio, crack pattern, and failure mechanism. The results indicated that a span-to-depth ratio equal to two is a turning point for the coupling beam behavior. Specifically, the behavior is dominated by ordinary flexure for a ratio of more than two and deep beam behavior for a ratio of less than two. This study showed that the coupling beam width does not have a significant effect on the coupled shear wall response. Additionally, it was concluded that the excessive coupling beam diagonal reinforcement could significantly affect the coupled shear walls behavior and therefore an upper limit for the diagonal reinforcement was provided. Moreover, limitations on the longitudinal and diagonal reinforcement and stirrups are presented herein. The analysis results presented in this paper can provide guidance for practitioners in terms of making decisions about the coupling ratio of the coupled shear walls.