Biaxial Shear Research Articles

Biaxial shear behaviour of HDNR with Mullins effect and deformation-induced anisotropy

High damping natural rubber (HDNR) bearings, commonly employed to isolate structures, are subjected to biaxial horizontal deformations by the seismic motion. If they have virgin material properties, biaxial models including the stress softening due to the Mullins effect should be used for describing their force–deformation behaviour. Specific studies oriented at characterizing and modelling the biaxial behaviour of HDNR bearings accounting for the stress-softening are very few in number because they would require a large number of virgin isolators or long times of rest between two consecutive tests. Moreover, available studies consider the Mullins effect as an isotropic phenomenon, whereas experimental investigations have shown that it is direction-dependent and thus induces anisotropy of the rubber behaviour. This paper describes an extensive experimental campaign carried out on a large number of small material test pieces aimed at achieving a satisfactory characterization of the biaxial anisotropic response of a highly dissipative rubber compound. These results are then used to develop a two-dimensional constitutive model for the virgin HDNR material accounting for the direction-dependence of the Mullins effect, based on the concept of representative directions applied to the biaxial shear deformation state. Because for commonly employed laminated HDNR bearings under design actions the approximation of uniform simple shear is realistic, the proposed material model can also be used to simulate the global bidirectional horizontal response of the bearings.

Shear-induced mechanical failure of β−Ga2O3 from quantum mechanics simulations

Monoclinic gallium oxide ($\ensuremath{\beta}\text{\ensuremath{-}}\mathrm{G}{\mathrm{a}}_{2}{\mathrm{O}}_{3}$) has important applications in power devices and deep UV optoelectronic devices because of such novel properties as a wide band gap, high breakdown electric field, and a wide range of $n$-type doping conductivity. However, the intrinsic failure mechanisms of $\ensuremath{\beta}\text{\ensuremath{-}}\mathrm{G}{\mathrm{a}}_{2}{\mathrm{O}}_{3}$ remain unknown, which limits the fabrication and packaging of $\ensuremath{\beta}\text{\ensuremath{-}}\mathrm{G}{\mathrm{a}}_{2}{\mathrm{O}}_{3}$-based electronic devices. Here we used density-functional theory at the Perdew-Burke-Ernzerhof level to examine the shear-induced failure mechanisms of $\ensuremath{\beta}\text{\ensuremath{-}}\mathrm{G}{\mathrm{a}}_{2}{\mathrm{O}}_{3}$ along various plausible slip systems. We found that the $(001)/\ensuremath{\langle}010\ensuremath{\rangle}$ slip system has the lowest ideal shear strength of 3.8 GPa among five plausible slip systems, suggesting that $(001)/\ensuremath{\langle}010\ensuremath{\rangle}$ is the most plausible activated slip system. This slip leads to an intrinsic failure mechanism arising from breaking the longest Ga\ensuremath{-}O bond between octahedral Ga and fourfold-coordinated O. Then we identified the same failure mechanism of $\ensuremath{\beta}\text{\ensuremath{-}}\mathrm{G}{\mathrm{a}}_{2}{\mathrm{O}}_{3}$ under biaxial shear deformation that mimics indentation stress conditions. Finally, the general stacking fault energy (SFE) surface is calculated for the (001) surface from which we concluded that there is no intrinsic stacking fault structure for $\ensuremath{\beta}\text{\ensuremath{-}}\mathrm{G}{\mathrm{a}}_{2}{\mathrm{O}}_{3}$. The deformation modes and SFE calculations are essential to understand the intrinsic mechanical processes of this semiconductor material, which provides insightful guidance for designing high-performance semiconductor devices.

Wrinkling of Functionally Graded Sandwich Structures Subject to Biaxial and In-Plane Shear Loads

Benefits of a functionally graded core increasing wrinkling stability of sandwich panels have been demonstrated in a recent paper (Birman, V., and Vo, N., 2017, “Wrinkling in Sandwich Structures With a Functionally Graded Core,” ASME J. Appl. Mech., 84(2), p. 021002), where a several-fold increase in the wrinkling stress was achieved, without a significant weight penalty, using a stiffer core adjacent to the facings. In this paper, wrinkling is analyzed in case where the facings are subject to biaxial compression and/or in-plane shear loading, and the core is arbitrary graded through the thickness. Two issues addressed are the effect of biaxial or in-plane shear loads on wrinkling stability of panels with both graded and ungraded core, and the verification that functional grading of the core remains an effective tool increasing wrinkling stability under such two-dimensional (2D) loads. As follows from the study, biaxial compression and in-plane shear cause a reduction in the wrinkling stress compared to the case of a uniaxial compression in all grading scenarios. Accordingly, even sandwich panels whose mode of failure under uniaxial compression was global buckling, the loss of strength in the facings or core crimpling may become vulnerable to wrinkling under 2D in-plane loading. It is demonstrated that a functionally graded core with the material distributed to increase the local stiffness in the interface region with the facings is effective in preventing wrinkling under arbitrary in-plane loads compared to the equal weight homogeneous core.

Quantification of particle crushing in consideration of grading evolution of granular soils in biaxial shearing: A probability‐based model

SummaryA probability‐based model is presented to estimate particle crushing and the associated grading evolution in granular soils during isotropic compression and prepeak shearing in biaxial tests. The model is based on probability density functions of interparticle and intraparticle stress (ie, particle normalized maximum shear stress and particle average maximum shear stress) derived from discrete element method simulations of biaxial tests. We find that the probability density functions of normalized maximum shear stress are dependent on the current sample grading, implying coupling effects between particle crushing and sample grading such that the particle crushing is affected by the current sample grading, and the grading change is also dependent on the current particle crushing extent. To incorporate these coupling effects into the model, particle crushing and grading change are calculated for each load increment, in which the crushing probability of a particle during any loading increment is denoted as the corresponding increment of probability of the internal maximum shear stress exceeding its maximum shear strength. The model shows qualitative agreement with published experimental data. The effects of the model parameters, including initial porosity, particle strength, initial grading, and crushing mode, on the calculated results are discussed and compared with previous studies. Finally, the strengths and limitations of the model are discussed.

Solving Problems in Geomechanics: Comparison of the Fidesys Strength Analysis System and the Plaxis Software Package

This article is devoted to solving problems with known theoretical solutions in the Fidesys software package. Within the framework of the work, modeling of a biaxial shear test of the ground and simulating a draft of a flexible foundation was done. The solutions obtained were correlated with the solutions of such problems in the Plaxis software package. According to the results of the study, it can be concluded that the Fidesys software complex allows solving problems in the field of geomechanics. At the same time, it is not inferior to recognized solutions in terms of functionality.

An integrated inverse model-experimental approach to determine soft tissue three-dimensional constitutive parameters: application to post-infarcted myocardium.

Knowledge of the complete three-dimensional (3D) mechanical behavior of soft tissues is essential in understanding their pathophysiology and in developing novel therapies. Despite significant progress made in experimentation and modeling, a complete approach for the full characterization of soft tissue 3D behavior remains elusive. A major challenge is the complex architecture of soft tissues, such as myocardium, which endows them with strongly anisotropic and heterogeneous mechanical properties. Available experimental approaches for quantifying the 3D mechanical behavior of myocardium are limited to preselected planar biaxial and 3D cuboidal shear tests. These approaches fall short in pursuing a model-driven approach that operates over the full kinematic space. To address these limitations, we took the following approach. First, based on a kinematical analysis and using a given strain energy density function (SEDF), we obtained an optimal set of displacement paths based on the full 3D deformation gradient tensor. We then applied this optimal set to obtain novel experimental data from a 1-cm cube of post-infarcted left ventricular myocardium. Next, we developed an inverse finite element (FE) simulation of the experimental configuration embedded in a parameter optimization scheme for estimation of the SEDF parameters. Notable features of this approach include: (i) enhanced determinability and predictive capability of the estimated parameters following an optimal design of experiments, (ii) accurate simulation of the experimental setup and transmural variation of local fiber directions in the FE environment, and (iii) application of all displacement paths to a single specimen to minimize testing time so that tissue viability could be maintained. Our results indicated that, in contrast to the common approach of conducting preselected tests and choosing an SEDF a posteriori, the optimal design of experiments, integrated with a chosen SEDF and full 3D kinematics, leads to a more robust characterization of the mechanical behavior of myocardium and higher predictive capabilities of the SEDF. The methodology proposed and demonstrated herein will ultimately provide a means to reliably predict tissue-level behaviors, thus facilitating organ-level simulations for efficient diagnosis and evaluation of potential treatments. While applied to myocardium, such developments are also applicable to characterization of other types of soft tissues.

Optimization of finite plates with polygonal cutout under in-plane loading by gray wolf optimizer

This article investigates the optimum design of isotropic finite plates with different polygonal cutouts under in-plane loading (uniaxial tensile, biaxial, and pure shear load). This purpose is pursued by a gray wolf optimization algorithm. The important features of this algorithm include flexibility, simplicity, short solution time, and the ability to avoid local optimums. The objective function used for this algorithm seeks to minimize the value of stress concentration factor around different cutouts. The method used for the calculation of stress concentration is based on analytical solution of Muskhelishvili complex variable and conformal mapping with plane stress assumption. The plate is assumed to be isotropic, linear elastic, and finite (the ratio of cutout side to plate’s longest side in the square and triangular cutouts and the ratio of diameter of circle circumscribing other n-gonals to the plate’s longest side are greater than 0.2). Results show that by selecting the aforementioned parameters properly, less amounts of stress could be achieved around the polygonal cutout leading to an increase in load-bearing capacity of the structure.

Analytical solution for buckling of Mindlin plates subjected to arbitrary boundary conditions

The study investigates the buckling behavior of isotropic plates subjected to axial, biaxial and pure shear loads. The effect of transverse shear deformation is taken into account by adopting the Mindlin first order shear theory. By applying the extended Kantorovich method, an exact solution is presented without any approximation on the boundary conditions. The procedure is proposed for thin, moderately thick and thick isotropic plates. The obtained results are in good agreement with those available in literature and they demonstrate the accuracy of the proposed procedure.

Applying the Artificial Neural Network to Predict the Soil Responses in the DEM Simulation

This paper aims to bridge the soil properties and the soil response in the discrete element method (DEM) simulation using the artificial neural network (ANN). The network was designed to output the stress-strain-volumetric response from inputting the soil properties. 31 biaxial shearing tests with varying soil parameters were generated using the DEM simulations. Based on these 31 training samples, a three-layer neural network was established. 2 extra samples were generated to examine the validity of the network, and the predicted curves using the ANN were well matched with those from the DEM simulations. Overall, the ANN was found promising in effectively modelling the soil behaviour.

Nonlinear mechanical behaviour of γ-graphyne through an atomistic finite element model

A non-linear finite element model for the simulation of the mechanical in-plane behaviour of γ-graphyne is presented in this paper. Different types of bonds (Single CC, Aromatic CC, Triple CC) are simulated by means of non-linear springs, which accurately take into account the different behaviour of interatomic forces in tension and compression at 0K temperature. Then, the finite element model is used to conduct six tests (two uniaxial tension–compression tests, one biaxial tension–compression test, two uniaxial shear tests, one biaxial shear test) to evaluate the non-linear mechanical behaviour of γ-graphyne. After that, a set of linear elastic properties (Young’s modulus, Poisson’s ratio, shear modulus, bulk modulus) and non-linear elastic properties (limit of proportionality stress and strain, ultimate stress and strain) is reported and compared with values reported in the literature (mostly linear elastic properties). This validation shows that the developed finite element model is able to predict accurately the linear and non-linear mechanical properties of γ-graphyne (i.e. stiffness and strength). Additionally, some remarks are drawn regarding the anisotropy of γ-graphyne and its distinct behaviour under tension and compression.

Validation of discrete element method by simulating a 2D assembly of randomly packed elliptical rods

This paper aims at establishing the predictive capability of the discrete element method (DEM) by validating the simulated responses of granular systems against experimental observations at both the macroscale and the microscale. A previously published biaxial shearing test on a 2D assembly of randomly packed elliptical rods was chosen as the benchmark test. In carrying out the corresponding DEM simulations herein, the contact model was derived and then validated using finite element analysis; the associated parameters were calibrated experimentally. The flexible (membrane) boundary was modeled by a bonded-particle string with experimentally calibrated parameters. An iteration procedure was implemented to replicate the initial packing and also to satisfy the boundary conditions in the experiment. Overall, the DEM simulation is found effective in reproducing the stress–strain–volumetric response, the statistical observation on the fabric anisotropy and the strain localization. Furthermore, the closer the numerical packing is to the experimental one, the closer the response is reproduced, demonstrating the significance of the initial packing reconstruction. Still, there are some minor differences between the experiment and simulation, reflecting the limitations associated with the particle number and the measurement resolution used in the experiment when reproducing the initial packing.

Nanotwins soften boron-rich boron carbide (B13C2)

Extensive studies of metals and alloys have observed that nanotwins lead to strengthening, but the role of nanotwins in ceramics is not well established. We compare here the shear strength and the deformation mechanism of nanotwinned boron-rich boron carbide (B13C2) with the perfect crystal under both pure shear and biaxial shear deformations. We find that the intrinsic shear strength of crystalline B13C2 is higher than that of crystalline boron carbide (B4C). But nanotwins in B13C2 lower the strength, making it softer than crystalline B4C. This reduction in strength of nanotwinned B13C2 arises from the interaction of the twin boundary with the C-B-C chains that connect the B12 icosahedra.

Simulating stick‐slip failure in a sheared granular layer using a physics‐based constitutive model

AbstractWe model laboratory earthquakes in a biaxial shear apparatus using the Shear‐Transformation‐Zone (STZ) theory of dense granular flow. The theory is based on the observation that slip events in a granular layer are attributed to grain rearrangement at soft spots called STZs, which can be characterized according to principles of statistical physics. We model lab data on granular shear using STZ theory and document direct connections between the STZ approach and rate‐and‐state friction. We discuss the stability transition from stable shear to stick‐slip failure and show that stick slip is predicted by STZ when the applied shear load exceeds a threshold value that is modulated by elastic stiffness and frictional rheology. We also show that STZ theory mimics fault zone dilation during the stick phase, consistent with lab observations.

The effect of strain on the electronic properties of MoS2 monolayers

We utilize first-principles calculations within density-functional theory to investigate the possibility of strain engineering in the tuning of the band structure of two-dimensional <TEX>$MoS_2$</TEX>. We find that the band structure of <TEX>$MoS_2$</TEX> monolayers transits from direct to indirect when mechanical strain is applied. In addition, we discuss the change in the band gap energy and the critical stains for the direct-to-indirect transition under various strains such as uniaxial, biaxial, and pure shear. Biaxial strain causes a larger change, and the pure shear stain causes a small change in the electronic band structure of the <TEX>$MoS_2$</TEX> monolayer. We observe that the change in the interaction between molecular orbitals due to the mechanical strain alters the band gap type and energy.

The effect of strain on the electronic propertiesof MoS2 monolayers

We utilize first-principles calculations within density-functional theory to investigate the possibility of strain engineering in the tuning of the band structure of two-dimensional MoS2. We find that the band structure of MoS2 monolayers transits from direct to indirect when mechanical strain is applied. In addition, we discuss the change in the band gap energy and the critical stains for the direct-to-indirect transition under various strains such as uniaxial, biaxial, and pure shear. Biaxial strain causes a larger change, and the pure shear stain causes a small change in the electronic band structure of the MoS2 monolayer. We observe that the change in the interaction between molecular orbitals due to the mechanical strain alters the band gap type and energy.

Biaxial shear in RC square beams: Experimental, numerical and analytical program

There are limited studies about the effect of biaxial shear in reinforced concrete (RC) elements. However, this load condition is quite common in columns subjected to horizontal forces. Moreover, the design and evaluation methods reported in codes do not consider any interaction between the shear strength in the two principal directions of inertia.This paper presents the results of an experimental program on six beams, with square section, subjected to inclined shear, which have been tested in order to understand the influence of the load inclination on the shear failure envelope.Based on the experiments, a new analytical formulation was proposed, with the aim to extend the prescriptions presented in fib-Model Code 2010 and ACI Code to the biaxial shear force.The proposed formulation was finally validated against results from experiments and non-linear finite element analyses (NLFEA).

The Connection between Biaxial Orientation and Shear Thinning for Quasi-Ideal Rods.

The complete orientational ordering tensor of quasi-ideal colloidal rods is obtained as a function of shear rate by performing rheo-SANS (rheology with small angle neutron scattering) measurements on isotropic fd-virus suspensions in the two relevant scattering planes, the flow-gradient (1-2) and the flow-vorticity (1-3) plane. Microscopic ordering can be identified as the origin of the observed shear thinning. A qualitative description of the rheological response by Smoluchowski, as well as Doi–Edwards–Kuzuu theory is possible, as we obtain a master curve for different concentrations, scaling the shear rate with the apparent collective rotational diffusion coefficient. However, the observation suggests that the interdependence of ordering and shear thinning at small shear rates is stronger than predicted. The extracted zero-shear viscosity matches the concentration dependence of the self-diffusion of rods in semi-dilute solutions, while the director tilts close towards the flow direction already at very low shear rates. In contrast, we observe a smaller dependence on the shear rate in the overall ordering at high shear rates, as well as an ever-increasing biaxiality.

An applicable formula for elastic buckling of rectangular plates under biaxial and shear loads

As thin plates have relatively big thickness ratios, their elastic buckling usually occurs before the yielding. From beginning of the previous century, many researchers have considered various in-plane loading states on thin plates and have strived to find simple equations to predict the buckling load. However, there are few valid equations with negligible errors for a thin plate, when it is under all of in-plane loads. In this paper, using energy method, an applicable formula is suggested for a simply supported rectangular plate, which is under biaxial and shear loads. The biaxial loads can be applied in the compressive/compressive, compressive/tensile, and tensile/tensile states on the plate. Generally, 15 129 examples are considered for this problem. The aspect ratio of plates varies from 1 to 5 and for each case and with the known load ratios, the plate buckling coefficient is calculated. Then, by using the regression techniques and interpolation, it is tried to estimate a simple equation with minimum error to predict the buckling load. The confirmed results show that for the biaxial compression and shear state, the maximum error is 8% and for the compression–tension–shear and biaxial tension and shear states, it increases until 20%.

Erratum to: Impact of Bi-Axial Shear on Atherogenic Gene Expression by Endothelial Cells

Erratum to: Impact of Bi-Axial Shear on Atherogenic Gene Expression by Endothelial Cells

Optimization design of unitized panels with stiffeners in different formats using the evolutionary strategy with covariance matrix adaptation

Curvilinear stiffener concept has been introduced to aircraft panel structures most recently for possible further weight reduction during optimization design. However, due to enlarged design space and high design complexity, more computational time is needed to optimize curvilinearly stiffened panels. Considering the requirement for both lighter structure and less design time, optimization designs of a unitized panel with stiffeners in three different formats, i.e. curvilinear, oblique, and evenly distributed straight, are conducted under various loading conditions to figure out which stiffener format should be selected in a real design environment. Four single loading cases with different compression-shear ratios and a set of multiple load cases are considered. Evolution strategy with covariance matrix adaption is combined with sequential quadratic programming to seek out the optimum structure with minimum mass taking into account buckling and strength constraints. Comparative analysis of the optimization results indicates that evenly distributed straight format is suitable for compression-dominant loading conditions whereas curvilinear format become superior in case that shear loading is considerable or multiple biaxial compression and shear loads are applied. Besides, curvilinear format adds more design flexibilities to the stiffeners, which enables them to play a more important role in the optimized structures. Furthermore, evolution strategy with covariance matrix adaption is found to be more efficient than particle swarm optimization for this optimization problem. This study can provide a useful guidance for future optimization design of aircraft structures.