Biaxial Model Research Articles

Small fatigue crack behavior of CP-Ti in thin-walled cruciform specimens under biaxial loading

This study investigates the small fatigue crack propagation behavior of commercially pure titanium (CP-Ti) using thin-walled cruciform specimens under in-plane biaxial loading, considering the effects of biaxial ratio and phase angle. Increasing phase angle results in more secondary cracks merging with main cracks perpendicular to the rolling direction (RD) and transverse direction (TD), a phenomenon attributed to the rise in shear stress that accelerates main crack growth. Higher loading biaxiality or a lower phase angle leads to decreased crack propagation rates and increased biaxial fatigue life. Electron backscatter diffraction (EBSD) analysis reveals that when the maximum normal stress aligns with the RD, prismatic slip primarily governs crack propagation, thereby accelerating crack propagation rates. Conversely, alignment with the TD reduces prismatic slip activity and crack propagation rates. Under equi-biaxial loading, prismatic slip activity decreases further, and crack propagation is dominated by multiple slip and twinning, consequently resulting in the slowest propagation rates. Additionally, a higher proportion of prismatic slip under high phase angle also accelerates crack propagation. Finally, incorporating Findley equivalent stress into the Chapetti model, which considers the crack length-dependent threshold effect, a highly accurate biaxial small fatigue crack propagation rate model is proposed.

Exchange-biased quantum tunneling of magnetization in a nanomagnetic dimer via a Josephson current

We investigate a Josephson junction where the weak link consists of a nanomagnetic dimer, featuring two large, antiferromagnetically coupled spins under simple easy-axis anisotropy. In this setup, the exchange coupling constant serves as a transverse anisotropy constant, and the quantum tunneling of the magnetization is influenced by the supercurrent, which behaves like an external magnetic field applied along the hard axis. Our results demonstrate that the superconducting current induces non-Kramers freezing and unfreezing of the magnetic moment’s tunneling within a biaxial spin model driven by exchange interaction. We derive an exact expression for the quenching condition caused by the exchange coupling. Additionally, we extend our analysis to tunneling phenomena in two antiferromagnetically or ferromagnetically coupled spins biased by the anisotropic exchange interaction, revealing more varied cases of tunnel splitting.

Grain-based coupled thermo-mechanical modeling for stressed heterogeneous granite under thermal shock

Microscopic damage and macroscopic mechanical properties of granite under the coupling effect of thermal load and initial stress are crucial considerations for the safe construction of underground geo-energy engineering. However, visualizing real-time micro-crack processes in rocks under high-temperature and high-pressure conditions using the current experimental techniques remains challenging. In this study, a numerical method is developed to analyze the thermally induced damage in heterogeneous granite under the coupled influence of initial stress and thermal loading. A biaxial thermo-mechanical grain-based model considering real mineral distribution is established based on digital image processing technology, the grain-based modeling method, and heat conduction theory. The microscopic parameters are calibrated and the effectiveness of the model is verified based on thermal shock and uniaxial compression experiments. The thermal destruction mechanism of granite under initial stress from a microscopic perspective was unveiled for the first time. During the thermal shock process, the stress within the rock does not remain constant at the initial stress value. Instead, it changes continuously with the progression of heat conduction. The impact of the initial stress on the thermally induced cracks is relatively minor. Cooling causes more damage to the rock than heating during thermal shock. The intragranular cracks of quartz consistently outnumber other intragranular or intergranular cracks during thermal shock. The initial stress and thermal shock damage enhance and weaken the biaxial peak strength of granite, respectively. The weakening effect of thermal shock on the peak strength becomes more pronounced at a higher initial stress. These research findings and proposed research techniques contribute to the management and optimization of underground geo-energy engineering.

Modeling and compensation of a hollow XY stage based on hybrid reluctance actuators

In the field of beam pointing and optoelectronic imaging, there is a growing demand for control mechanisms that offer large stroke, and high bandwidth. These are precisely the characteristics of hybrid reluctance actuator, which therefore is increasingly being used in XY stage to replace piezo-actuator and voice coil motor. This study presents a hollow XY stage utilizing hybrid resistance actuators, aiming to adapt to optical applications with inherent nonlinearity and biaxial coupling, which are further modeled and compensated to mitigate their impacts. Firstly, the basic composition and working principle of the hollow XY stage are described, and the impact of its nonlinearity and biaxial coupling characteristics is elucidated. Secondly, the sources of nonlinearity and biaxial coupling are analyzed, and an analytical model of hybrid reluctance actuators is established. The magnetic leakage coefficient of the model is determined, and the accuracy of the model is verified by Finite Element Method (FEM) and experiment, demonstrating consistency with the analytical model's results. Furthermore, based on the nonlinear and biaxial coupling model, a compensator based on feedback linearization method is established, and verified through experiment. The results show that this method has a significant suppression effect on nonlinear and biaxial coupling, and the tracking error and cross-talk is obviously reduced, which proves the effectiveness of this compensation method.

Coupled wind-induced response of inter-story isolated eccentric tall buildings with friction-pendulum bearings

The isolation technology is widely used to protect structures against strong earthquake. For the inter-story isolated tall building located in strong wind-prone area, the soft isolation layer prolongs the structural period, which can make the wind effects significant. This study presents an analytical framework for assessing three-dimensional coupled wind-induced response of inter-story isolated eccentric tall buildings employing friction-pendulum bearings. The framework utilizes a biaxial Bouc-Wen hysteresis model and a velocity-dependent friction coefficient to describe the coupled frictional forces at each bearing. To enhance the computational efficiency, a simplified model with reduced degrees of freedom is proposed to represent the building. This study investigates eighty combinations of stiffness and mass eccentricities of lower and upper structures relative to isolation layer to analyze their impact on building acceleration. A spherical and two aspheric sliding surfaces of the bearing are examined to understand their effects on building response. The findings suggest that the stiffness eccentricity of either lower or upper building solely affects its own response without influencing other part of the structure. Conversely, the mass eccentricity of upper building induces significant mode coupling, resulting in noticeable impact on the accelerations of both upper and lower buildings. Moreover, the acceleration of the story conner farther from the mass eccentric position experiences significantly amplification. The proposed aspherical bearing demonstrates the capability to substantially reduce the bearing displacement, although with a limited increase in other building responses not exceeding 20 %.

Performance of Simplified Damage-Based Concrete Models in Seismic Applications

Significant progress in the finite-element (FE) modeling at the member-level of reinforced-concrete (RC) structures under seismic excitation has been achieved in the past decades; however, reliable and accurate analysis models for full-scale 3D system-level RC structures validated with experimental data are scarce. As the development of a complete nonlinear model is expensive and time consuming, simpler models, typically elastic or lumped-plastic in nature, are employed in practice with additional provisions prescribed to account for nonlinear behavior. Depending on the assumptions made by the analyst, there may be substantial uncertainties related to the response of a complete structure. Capturing global failure modes is challenging, and the assessment of strength and ductility capacities may be inaccurate, resulting in potentially unsafe designs. The objective of this research is to assess the performance of simplified damage-based concrete biaxial models in analyzing and capturing the structural behavior of full-scale RC systems. Damage-based models for concrete require minor input from the analyst, facilitating their use in a design setting, while their explicit, non-conditional convergence formulations allow for non-iterative solutions. This results in damage-based models featuring efficient computational analysis while accounting for complex phenomena such as the capacity to account for stiffness recovery in reversal loading (crack closing) and permanent strains in the concrete. A comparison between analytical and experimental data at both the element- and system-levels is conducted, and a viable damage-based model is proposed for a full-scale structure analysis. The results of the study show that damage-based models are a viable alternative to developing efficient analysis models for elements and whole structures.

Experimental and numerical investigation of the fracture behavior in granite specimens with two co-planar side flaws under biaxial loading

It is well known that the structural plane plays a decisive role in the mechanical properties of rock mass. To better understand the cracking mechanism and stress characteristics of co-planar intermittent double-flawed granite specimens with various dip angles (Abbreviated as flawed specimens), two co-planar flaws were prefabricated on both sides of the granite, and biaxial compression tests were conducted. The failure characteristics and local microstrain were recorded by the camera and strain acquisition instrument. The evolution law of mechanical parameters of flawed specimens was analyzed. Simultaneously, a two-dimensional particle flow code (PFC2D) was used to establish a biaxial compression model of flawed specimens. The crack initiation and propagation of the specimens were explained by the crack hot spot, the evolution law of crack, and the evolution law of the number of microcracks. It is found that (a) as flaw dip angle (α) increases, peak strength and elastic modulus initially decrease and then increase, with reductions ranging from 17.6% to 46.1% and 15.6% to 48.2%, respectively. (b) Increasing lateral stress (σ2) triggers a shift in failure mode from a tensile-shear mixed failure to a shear failure. The cohesion (c) and friction angle (φ) of flawed specimens were notably smaller compared to those of intact specimens, with reductions correlating with the α. (c) Flawed specimens exhibit pronounced contact force concentration and stress concentration at the flaw tip. The analysis of the microstrain confirms stress concentration at the flaw tip, leading to failure. However, various σ2 induces the differences in the magnitude and extent of tip stress.

NONLINEAR FINITE ELEMENT ANALYSIS OF COMPOSITE CONCRETE BEAMS

To study the nonlinear response of composite concrete beams, a finite element analysis is presented. Material nonlinearities as a result of nonlinear response of concrete in compression, crushing and cracking of concrete, strain softening and stiffening after cracking, yielding of reinforcement, bond- slip, shear-slip, and dowel action between the precast concrete beams and the cast-in-situ slabs are considered.A biaxial concrete model is adopted. Concrete is treated as an orthotropic material with smeared rotating crack model. The steel reinforcement is assumed to be in a uniaxial stress state and is modeled as a bilinear material. I A two-dimensional plane stress finite element type is used to model the concrete Reinforcement is represented by one-dimensional bar elements. Bond-slip and dowel action is modeled by using fictitious linkage elements with two springs at right angles. Shear-slip is modeled by using shear transfer in face elements with appropriate stiffness values Comparison between the results obtained by the finite element and available experimental results of composite concrete beams is made. The results compare satisfactorily with the experimental ones

Complete integrability and equilibrium thermodynamics of biaxial nematic systems with discrete orientational degrees of freedom

We study a discrete version of a biaxial nematic liquid crystal model with external fields via an approach based on the solution of differential identities for the partition function. In the thermodynamic limit, we derive the free energy of the model and the associated closed set of equations of state involving four order parameters, proving the integrability and exact solvability of the model. The equations of state are specified via a suitable representation of the orientational order parameters, which imply two-order parameter reductions in the absence of external fields. A detailed exact analysis of the equations of state reveal a rich phase diagram where isotropic versus uniaxial versus biaxial phase transitions are explicitly described, including the existence of triple and tricritical points. Results on the discrete models are qualitatively consistent with their continuum analogue. This observation suggests that, in more general settings, discrete models may be used to capture and describe phenomena that also occur in the continuum for which exact equations of state in closed form are not available.

Biaxial bending moments calculation model based on stress distribution for H-section steel members under different loading paths

To explore the biaxial bending development mechanism of H-section steel members under different cyclic loading paths, we conducted a parametric analysis involving various axial force ratios, plate width-to-thickness ratios, and loading angles. Three loading paths were considered, including linear, rectangular, and triangular loading paths. Finite element models were established in ABAQUS and validated for accuracy using existing experimental data. Based on the finite element analysis results, a methodology for determining the form of normal stress distribution was derived by analyzing the mechanism of biaxial interactions in H-section steel members. By establishing a relationship between the normal stress distribution and the biaxial bending moments, a semi-empirical semi-theoretical calculational model was developed to simulate the entire process of biaxial bending and compression loading at reverse point in H-section steel members under different loading paths. The validity of this model was confirmed, as it demonstrated effective prediction of the complete development trends of biaxial bending moments for H-section steel members. This model establishes the basis for seismic design of H-section steel members subjected to biaxial loading conditions.

Rapid-Transfer Matrix Method for Analysis of Electromagnetic Properties of Uniaxial/Biaxial Biaxially Anisotropic Media

The employment of uniaxial/biaxial bianisotropic materials in the field of optical device manufacturing is widespread due to the distinctive electromagnetic response characteristics exhibited by such materials. To effectively analyze the electromagnetic properties of uniaxial/biaxial bianisotropic materials, rapid-transfer matrix method (R-TMM) is proposed to investigate the propagation process of plane waves in the media. Starting from the Maxwell’s equations in the time domain, the homogeneous differential equation about the electric field is constructed by processing the matrix containing dielectric and magnetic conductivity, electric and magnetic loss, tellegen and chirality carrier parameters, and the complex matrix operation is applied to that equation to get the booker quartic equation, and then the formulae method are utilized to obtain the eigenvalues in the uniaxial/biaxial bianisotropic media. Subsequently, the tangential continuity of layered media at the interface is employed to establish a transfer matrix for single-layered media. In the case of multi-layered media, the transfer matrix of plane waves propagating in multi-layered uniaxial/biaxial bianisotropic media can be obtained by means of a continuous iteration process based on the transfer matrix of single-layered media. The formula for calculating the propagation coefficient of uniaxial/biaxial bianisotropic materials can be derived based on the different upward and downward waves in the reflection/transmission region. Finally, the reliability and efficiency of R-TMM is verified from two numerical experiments with the plane waves incident at different angles on a uniaxial/biaxial bianisotropic media. The first experiment is designed as a single-layered biaxial bianisotropic model with more general electromagnetic parameters, and the second experiment is designed as a double-layered uniaxial and biaxial bianisotropic model consisting of common optical materials, which are composed of two non-magnetic materials, lithium niobate (LiNbLO<sub>3</sub>) and cadmium sulfide (CdS). The experimental results demonstrate that, in comparison with the conventional conventional-transfer matrix method (C-TMM), the R-TMM reduces the computational memory and CPU time required for calculating the reflection and transmission coefficients of the uniaxial/ biaxial bianisotropic model by over 98%, while maintaining the accuracy of the reflection and transmission coefficients calculation. Therefore, R-TMM provides an efficient and dependable approach for the design of complex optical devices and the analysis for uniaxial/biaxial bianisotropic propagation characteristics.

Differential model of biaxial hysteresis with coupled principal strengths and cyclic deterioration for reinforced-concrete elements

Structural analysis often is multidirectional because simultaneous load components are severer than single components. However, current models need improvement to cover various inelastic interactions. Herein a uniaxial hysteretic model of the Bouc–Wen class is extended to two dimensions by double formulation for principal axes, proper to general loading histories, as opposed to one formulation projected from a skewed axis. Coupling of strengths in terms of stress resultants is implemented for arbitrary degree of interaction, also different between principal directions. Coupling of cyclic deterioration of stiffness and strength is incorporated consistently with phenomenological application of the model at the element scale. The proposed model is assessed by fibre analysis of symmetric and asymmetric cross-sections, and by experimental outcome in the literature. The latter concerns reinforced-concrete square columns under constant axial load and rectangular columns under varying axial load, each subjected to cyclic square and rhombic displacement paths. Based on residual displacement, final energy, and transverse force, the proposed biaxial model is reasonably less accurate than the background uniaxial model. However, it proves to be adequate to simulate force-displacement loops and hysteretic energy of columns and piers.

A compressive-shear biaxial stress field model for analyzing the anisotropic mechanical behavior of nanotwinned diamond

Synthetic nanotwinned diamond (Nt-D) with unprecedented hardness and toughness is an ideal material for manufacturing ultra-precision cutting tools. It is urgent to investigate the surface formation mechanism of Nt-D under complex stress fields. Here, we developed a compressive-shear biaxial stress field model to study the extreme anisotropic mechanical behavior of Nt-D. It was found that graphitization occurred in all shear directions of the Nt-D (0001) plane through the microstructure evolution of 2H-diamond, 4H-diamond, 6H-diamond, and 9R-diamond, in which the stress release mechanism was accompanied by partial slips in certain specific crystal directions such as 〈1010〉. In addition, the generalized stacking fault energy calculation indicates that the partial slip in 6H- and 9R-diamonds is mainly attributed to the low slip energy barrier between adjacent interlayer. These results expand our understanding of the surface formation mechanism of Nt-D and will contribute to the manufacturing of new-generation ultra-precision tools.

A shear–flexure interaction model for column elements with biaxial loading

This research develops a 3D macroscopic model to capture the shear and flexural behavior of square and rectangular reinforced concrete columns under biaxial lateral loads. This efficient-shear-flexure-interaction (E-SFI)–BIAXIAL model, based on the E-SFI two-dimensional macro model, reformulates the materials and elements to a 3D domain. Reinforced concrete prisms with three-dimensional behavior are incorporated using a rotating-angle approach and calibrated expression of the two-dimensional model to calculate the horizontal strain in each orthogonal direction (ɛx and ɛz). This approach reduces the number of iterative processes and analysis time. Model validation employed an extensive database of 56 reinforced concrete column tests with shear failure under cyclic biaxial loading conditions, 41 square and 15 rectangular, as reported in the literature. The validation demonstrated that the model accurately captures the hysteretic response and shear failure mode of the tests. The results are verified against the experimental data regarding the load–displacement response and the contribution of flexural and shear displacements. The model’s estimated shear strength agreed well with experimental data, with average ratios of measured to calculated maximum shear strength of 0.91 and 0.95 for square and rectangular columns with coefficients of variation of 0.078 and 0.12, respectively. The onset of strength degradation was also compared, achieving average ratios of the measured to calculated drift for square and rectangular columns of 1.02 in both cases, with coefficients of variation of 0.32 and 0.4, respectively. Furthermore, the normalized biaxial shear strength results from the experimental tests and the model fit the circular interaction curve and validate the proposed ACI 318-19 code provisions to capture the biaxial shear effect through a trilinear curve.

Identification of subject-specific fibrillar disposition in healthy rabbit cornea through birefringence analysis

The cornea is an essential component in ocular biomechanics. The modifications in the collagen microstructure of the cornea affect its biomechanical behavior in various ocular conditions. Birefringence is an indicator of the microstructural changes in the cornea. The characterization of birefringence can benefit the patient-specific assessment of disease and surgically driven effects. According to the existing literature, optical birefringence of the cornea is best described as of biaxial nature. However, the biaxial model does not concur with the varying degree of birefringence observed amongst individuals. Using digital photoelasticity, the present study explores the applicability of birefringence of the healthy rabbit cornea as a benchmark model for human cornea. Eight freshly excised healthy rabbit corneas are imaged using the polariscope in the transmission mode. A fringe analysis is performed for each configuration of the polariscope to discern the collagen fiber distribution in the cornea. The birefringence of the rabbit corneas showed inter-corneal variability with varying degrees of biaxiality like the human corneas. Based on the fringe analysis, the fiber families in the cornea were identified in the form of geometric patterns distributed over the corneal surface and incorporated in the finite element model of the cornea. The present study envisages the utilization of birefringence-derived structural information to develop a reliable treatment design based on microstructural features of the cornea.

Improved simpler R/C hysteresis model considering biaxial interaction

From practical point of view, it is evident that the seismic wave acted on structures through two mutually orthogonal components which have significant combined effect on inelastic demands of the structure. Usually a smaller amount of ground motion generally applied in only one direction than the other and in most of the cases the studies considered only limited inelasticity. Therefore, further research is needed that considers ground motion in both horizontal directions with corresponding bi-directional intensities. Study shows, the combined effects cause significant amount of degradation of strength and stiffness which in turn cause early yielding of R/C(Reinforced Concrete) structural member. Conventional uni-axial model does not consider this type of bi-directional interaction. Some existing simpler bi-axial hysteresis model which can capture biaxial interaction shows satisfactory results, but still the deviation from experimental results are very prominent. On the other hand, some existing sophisticated bi-axial hysteresis model shows better accuracy in predicting response of R/C structural elements but these types of models require large number of calibrated test results which makes them case-specific. In this backdrop, by using principle of yield surface, this study aims to incorporate bi-directional interaction over a simpler hysteresis model which primarily able to capture uni-directional loading effects. Detailed computational scheme of the enhanced simpler uni-axial hysteresis model and extension of the model to capture bi-directional interaction with its performance in prediction of inelastic cyclic behaviour of R/C structural members are presented in this paper. From the performance point of view, it is clearly visible that the proposed simple bi-axial hysteresis model can predict experimental load–displacement curves of R/C structural members under bi-directional reversible loading with acceptable accuracy. The requirement of limited number of input parameters for the present proposed bi-axial hysteresis model make it more convenient to assess the progressive seismic damage under bi-directional ground motion.

Application of Numerical Simulation Technology in New Intelligent Reinforcing Method of Shield Tunnel End in Seaside Environment

The instability of the soil at the shield end is an important safety hazard in shield tunnel construction. In loose and weak strata, the risk of instability and damage is higher, and the loss is greater. In this paper, the instability and failure of the end soil in loose and weak strata are studied. To ensure the smooth start and arrival of the shield and avoid engineering accidents such as end soil instability, surface subsidence, landslides, etc., during the construction process, this paper summarizes the commonly used reinforcement technology and characteristics of the shield in and out of the tunnel. Through numerical simulation, the influence of the thickness of the added solid on the formation and diaphragm wall is analyzed. It is found that the reinforcement effect increases with the increase in thickness of the added solid, but the change rate becomes smaller and smaller. The indoor triaxial test is used to find out the physical and mechanical properties of loose sand and soft clay. The biaxial compression numerical model is built with PFC2D (Particle Flow Code 2D PFC 6.0), and the wall constraint type is improved. With the help of the PFC biaxial test, the influence of model parameters on the macroscopic properties of the simulated material was analyzed. The research has certain reference values for the actual construction of the project.

A practical biaxial time-dependent material model of PVDF-coated polyester fabrics for structural applications

The utilization of air-supported fabric structures as formwork to construct concrete shells has attracted increasing attention in recent decades. An example of such an airform is the air-supported structure at Dahaize, which consists of a cylindrical part and a hemispherical part, and is 66 m in diameter and 65 m in height. The precise forming analysis of large-span air-supported structures requires the use of a reasonable material model that considers the biaxial stress condition and the creep behavior of the fabric. In this paper, a practical approach to modeling the biaxial time-dependent material behavior of composite fabrics is proposed based on the uniaxial linear viscoelastic theory and the plane stress orthotropic assumption. The multi-Kelvin physical model is developed to the two-dimensional form for the simulation of biaxial creep compliances. Biaxial tensile and biaxial creep tests are conducted on PVDF-coated polyester fabrics to calibrate the material parameters. The experimental stress conditions were determined according to the pre-estimated actual membrane stress distribution. The established material model is employed for the forming analysis of the Dahaize airform under conditions of varying creep times. The simulation results agree well with the on-site measured data, and this validates the accuracy and efficiency of the proposed material model.

On Flexure-Shear Interaction in Fibre Model for the Analysis of RC Section

This paper investigates the effects of flexure-shear interaction on the force-deformation response of RC section. The analysis is performed using an improved version of fibre section model to consider the interaction of shear force. The model uses a supplementary shear strain field, in addition to the ‘plane-section’ hypothesis, for section kinematics. The concrete is modelled using a bi-axial stress-strain model based on a rotating, smeared-crack model with equivalent uniaxial stress-strain relation in principal directions. The confining effect of stirrups is considered by using Mander model. The reinforcing bars are modelled using a uniaxial stress-strain relation. The use of bi-axial model allow the flexure-shear interaction to reflect at the material point. The fibre section model is used to analyse an RC section to study the moment-curvature and shear force-shear strain response for increasing levels of shear forces and bending moments. The results shows that the moment-curvature and shear force-shear strain diagrams are significantly influenced by the presence of large shear force and bending moment respectively.

3D coupled wind-induced inelastic response of base-isolated tall buildings with eccentricity and biaxial interaction of hysteretic restoring base forces

This study presents an analysis framework for coupled inelastic response of base-isolated tall buildings with eccentricities of mass and resistance and coupled hysteretic restoring forces of base isolation system. The upper building motion is represented by lower modal displacements. The translational hysteretic restoring forces of base isolation system are described by a biaxial hysteretic model and the torsional restoring moment by a linear elastic model. The stochastic story wind forces of the upper building are represented in their cross power spectral matrix. Response history analysis is carried out to characterize the coupled responses of a square-shaped tall building with eccentricity in the center of resistance. The results showed that the eccentricity amplifies the alongwind response but has relatively less influence on the larger crosswind and torsional responses. The eccentricity has less influence on the inelastic response of based-isolated building as compared to the fixed-base building. The base isolation with inelastic response is more effective for building with eccentricity as compared to building without eccentricity. The biaxial interaction reduces the effect of eccentricity on base displacements but increases the effect on upper building response. The eccentricity and biaxal interaction result in fast growth of time-varying mean alongwind base displacement.