Effect of annealing temperature on microstructure and mechanical properties of Mg-Zn-Zr-Nd alloy with large final rolling deformation

In this study,the Mg-3Zn-0.5Zr-χNd(χ=0,0.6)alloys were subjected to final rolling treatment with large deformation of 50%.The impact of annealing temperatures on the microstructure and mechanical properties was investigated.The rolled Mg-3Zn-0.5Zr-0.6Nd alloy exhibited an ultimate tensile strength of 386 MPa,a yield strength of 361 MPa,and an elongation of 7.1%.Annealing at different temperatures resulted in reduced strength and obviously increased elongation for both alloys.Optimal mechanical properties for the Mg-3Zn-0.5Zr-0.6Nd alloy were achieved after annealing at 200℃,with an ultimate tensile strength of 287 MPa,a yield strength of 235 MPa,and an elongation of 26.1%.The numerous deformed microstructures,twins,and precipitated phases in the rolled alloy could impede the deformation at room temperature and increase the work hardening rate.After annealing,a decrease in the work hardening effect and an increase in the dynamic recovery effect were obtained due to the formation of fine equiaxed grains,and the increased volume fraction of precipitated phases,which significantly improved the elongation of the alloy.Additionally,the addition of Nd element could enhance the annealing recrystallization rate,reduce the Schmid factor difference between basal and prismatic slip systems,facilitate multi-system slip initiation and improve the alloy plasticity.

Case study on the mechanics of NPR anchor cable compensation for large deformation tunnel in soft rock in the Transverse Mountain area,China

A study was conducted to analyze the deformation mechanism of strongly weathered quartz schist in the Daliangshan Tunnel,located in the western Transverse Mountain area.A large deformation problem was experienced during the tunnel construction.To mitigate this problem,a support system was designed incorporating negative Poisson ratio(NPR)anchor cables with negative Poisson ratio effect.Physical model experiments,field experiments,and numerical simulation experiments were conducted to investigate the compensation mechanical behavior of NPR anchor cables.The large deformations of soft rocks in the Daliangshan Tunnel are caused by a high ground stress,a high degree of joint fracture development,and a high degree of surrounding rock fragmentation.A compensation mechanics support system combining long and short NPR anchor cables was suggested to provide sufficient counter-support force(approximately 350 kN)for the surrounding rock inside the tunnel.Comparing the NPR anchor cable support system with the original support system used in the Daliangshan tunnel showed that an NPR anchor cable support system,combining cables of 6.3 m and 10.3 m in length,effectively prevented convergence of surrounding rock deformation,and the integrated settlement convergence value remained below 300 mm.This study provides an effective scientific basis for resolving large deformation problems in deeply buried soft rocks in western transverse mountain areas.

Topology Optimization of Metamaterial Microstructures for Negative Poisson’s Ratio under Large Deformation Using a Gradient-Free Method

Negative Poisson’s ratio(NPR)metamaterials are attractive for their unique mechanical behaviors and potential applications in deformation control and energy absorption.However,when subjected to significant stretching,NPR metamaterials designed under small strain assumption may experience a rapid degradation in NPR performance.To address this issue,this study aims to design metamaterials maintaining a targeted NPR under large deformation by taking advantage of the geometry nonlinearity mechanism.A representative periodic unit cell is modeled considering geometry nonlinearity,and its topology is designed using a gradient-free method.The unit cell microstructural topologies are described with the material-field series-expansion(MFSE)method.The MFSE method assumes spatial correlation of the material distribution,which greatly reduces the number of required design variables.To conveniently design metamaterials with desired NPR under large deformation,we propose a two-stage gradient-free metamaterial topology optimization method,which fully takes advantage of the dimension reduction benefits of the MFSE method and the Kriging surrogate model technique.Initially,we use homogenization to find a preliminary NPR design under a small deformation assumption.In the second stage,we begin with this preliminary design and minimize deviations in NPR from a targeted value under large deformation.Using this strategy and solution technique,we successfully obtain a group of NPR metamaterials that can sustain different desired NPRs in the range of[−0.8,−0.1]under uniaxial stretching up to 20% strain.Furthermore,typical microstructure designs are fabricated and tested through experiments.The experimental results show good consistency with our numerical results,demonstrating the effectiveness of the present gradientfree NPR metamaterial design strategy.

Calculating real-time surface deformation for large active surface radio antennas using a graph neural network

This paper presents an innovative surrogate modeling method using a graph neural network to compensate for gravitational and thermal deformation in large radio telescopes.Traditionally,rapid compensation is feasible for gravitational deformation but not for temperature-induced deformation.The introduction of this method facilitates real-time calculation of deformation caused both by gravity and temperature.Constructing the surrogate model involves two key steps.First,the gravitational and thermal loads are encoded,which facilitates more efficient learning for the neural network.This is followed by employing a graph neural network as an end-to-end model.This model effectively maps external loads to deformation while preserving the spatial correlations between nodes.Simulation results affirm that the proposed method can successfully estimate the surface deformation of the main reflector in real-time and can deliver results that are practically indistinguishable from those obtained using finite element analysis.We also compare the proposed surrogate model method with the out-of-focus holography method and yield similar results.

Development of the rolling extrusion rock bolt with constant resistance and large deformation

With the increasing excavation depth of underground engineering,engineering problems such as large deformation and rock burst caused by high geo-stress brings new challenges to the excavation and reinforcement of surrounding rock in deep underground engineering.The traditional rock bolt is prone to brittle fracture under high geo-stress due to its low elongation.Therefore,this work aims to develop a novel energy-absorbing bolt with constant resistance and large displacement to reinforce the surrounding rock with a risk of large deformation or rockburst.The novel energy-absorbing bolt refereed as rolling extrusion rock bolt(RE bolt)is mainly consists of sleeve tube with a variable cross-section,energy absorption slider with steel balls embedded,steel bar connected with the energy absorption slider.The rolling extrusion is adopted to produce the resistance force of the RE bolt,which avoids the sudden attenuation of resistance force and the abrasion of the energy absorption slider.The static pull test is conducted to study the resistance force and deformation characteristics of the RE bolt with different specifications.Results imply that the RE bolt has higher resistance force,larger deformation capacity and energy absorption capacity.The work of this study provides an effective solution for the reinforcement of surrounding rock in deep rock engineering.

LARGE DEFORMATION OF CIRCULAR MEMBRANE UNDER THE CONCENTRATED FORCE

Making use of basic equation of large deformation of circular membrane under the concentrated force and its boundary conditions and Hencky transformation, the problems of nonlinear boundary condition were solved. The Hencky transformation was extended and a exact solution of large deformation of circular membrane under the concentrated force has been obtained.

Application of MLPG in large deformation analysis

Two-dimensional large deformation analysis of hyperelastic and elasto-plastic solids based on the Meshless Local Petrov-Galerkin method （MLPG） is presented. A material configuration based the nonlinear MLPG formulation is introduced for the large deformation analysis of both path-dependent and path-independent materials. The supports of the MLS approximation functions cover the same sets of nodes during material deformation, thus the shape function needs to be computed only in the initial stage. The multiplicative hyperelasto-plastic constitutive model is adopted to avoid objective time integration for stress update in large rota- tion. With this constitutive model, the computational formulations for path-dependent and path-independent materials become identical. Computational efficiency of the nonlinear MLPG method is discussed and optimized in several aspects to make the MLPG an O（N） algorithm. The numerical examples indicate that the MLPG method can solve large deformation problems accurately. Moreover, the MLPG computations enjoy better convergence rate than the FEM under very large particle distortion.

Nonlinear formulation for flexible multibody system with large deformation

In this paper, nonlinear modeling for flexible multibody system with large deformation is investigated. Absolute nodal coordinates are employed to describe the displacement, and variational motion equations of a flexible body are derived on the basis of the geometric nonlinear theory, in which both the shear strain and the transverse normal strain are taken into account. By separating the inner and the boundary nodal coordinates, the motion equations of a flexible multibody system are assembled. The advantage of such formulation is that the constraint equations and the forward recursive equations become linear because the absolute nodal coordinates are used. A spatial double pendulum connected to the ground with a spherical joint is simulated to investigate the dynamic performance of flexible beams with large deformation. Finally, the resultant constant total energy validates the present formulation.

Two-Dimensional Large Deformation Finite Element Analysisfor the Pulling-up of Plate Anchor

Based on mesh regeneration and stress interpolation from an old mesh to a new one, a large deformation finite element model is developed for the study of the behaviour of circular plate anchors subjected to uplift loading. For the deterruination of the distributions of stress components across a clay foundation, the Recovery by Equilibrium in Patches is extended to plastic analyses. ABAQUS, a commercial finite element package, is customized and linked into our program so as to keep automatic and efficient running of large deformation calculation. The quality of stress interpolation is testified by evaluations of Tresca stress and nodal reaction forces. The complete pulling-up processes of plate anchors buried in homogeneous clay arc simulated, and typical pulling force-displacement responses of a deep anchor and a shallow anchor are compared. Different from the results of previous studies, large deformation analysis is of the capability of estimating the breakaway between the anchor bottom and soils. For deep anchors, the variation of mobilized uplift resistance with anchor settlement is composed of three stages, and the initial buried depths of anchors affect the separation embedment slightly. The uplift bearing capacity of deep anchors is usually higher than that of shallow anchors.

Compensation excavation method control for large deformation disaster of mountain soft rock tunnel

In recent years,the mine tunneling method and the new Austrian tunneling method have been considered the main theories of tunneling approaches in China.It is difficult for the traditional technique to overcome the large deformation problems imposed by complex geological conditions of mountain soft rock tunneling.Hence,the compensation excavation method has been proposed to solve this issue under the consideration that all damage in tunneling originates from the excavation.It uses supportive strategies to counteract the excavation effects successfully.This paper provides an overview of the fundamental ideas of the compensation excavation method,methodologies,and field applications.The scientific validity and feasibility of the compensation excavation method were investigated through the practical engineering study of the Muzhailing and Changning tunnels.

Isogeometric analysis of free-form Timoshenko curved beams including the nonlinear effects of large deformations

In the present paper, the isogeometric analysis（IGA） of free-form planar curved beams is formulated based on the nonlinear Timoshenko beam theory to investigate the large deformation of beams with variable curvature. Based on the isoparametric concept, the shape functions of the field variables（displacement and rotation） in a finite element analysis are considered to be the same as the non-uniform rational basis spline（NURBS） basis functions defining the geometry. The validity of the presented formulation is tested in five case studies covering a wide range of engineering curved structures including from straight and constant curvature to variable curvature beams. The nonlinear deformation results obtained by the presented method are compared to well-established benchmark examples and also compared to the results of linear and nonlinear finite element analyses. As the nonlinear load-deflection behavior of Timoshenko beams is the main topic of this article, the results strongly show the applicability of the IGA method to the large deformation analysis of free-form curved beams. Finally, it is interesting to notice that, until very recently, the large deformations analysis of free-form Timoshenko curved beams has not been considered in IGA by researchers.

Numerical modeling of large deformation and nonlinear frictional contact of excavation boundary of deep soft rock tunnel

Roadways excavated in soft rocks at great depth are difficult to be maintained due to large deformation of surrounding rocks, which greatly influences the safety and efficiency of deep resources exploitation. During the excavation process of a deep soft rock tunnel, the rock wall may be compacted due to large deformation. In this paper, the technique to address this problem by a two-dimensional (2D) finite element software, large deformation engineering analyses software (LDEAS 1.0), is provided. By using the Lagrange multiplier method, the kinematic constraint of non-penetrating condition and static constraint of Coulomb friction are introduced to the governing equations in the form of incremental displacement. The numerical example demonstrates the efficiency of this technology. Deformations of a transportation tunnel in inclined soft rock strata at the depth of 1 000 m in Qishan coal mine and a tunnel excavated to three different depths are analyzed by two models, i.e. the additive decomposition model and polar decomposition model. It can be found that the deformation of the transportation tunnel is asymmetrical due to the inclination of rock strata. For extremely soft rock, large deformation can converge only for the additive decomposition model. The deformation of surrounding rocks increases with the increase in the tunnel depth for both models. At the same depth, the deformation calculated by the additive decomposition model is smaller than that by the polar decomposition model.

Anchoring effect and energy-absorbing support mechanism of large deformation bolt

To research the anchoring effect of large deformation bolt,tensile and drawing models are established.Then,the evolution laws of drawing force,bolt axial force and interfacial shear stress are analyzed.Additionally,the influence of structure element position on the anchoring effect of large deformation bolt is discussed.At last,the energy-absorbing support mechanism is discussed.Results show that during the drawing process of normal bolt,drawing force,bolt axial force and interfacial shear stress all gradually increase as increasing the drawing displacement,but when the large deformation bolt enters the structural deformation stage,these three values will keep stable;when the structure element of large deformation bolt approaches the drawing end,the fluctuation range of drawing force decreases,the distributions of bolt axial force and interfacial shear stress of anchorage section are steady and the increasing rate of interfacial shear stress decreases,which are advantageous for keeping the stress stability of the anchorage body.During the working process of large deformation bolt,the strain of bolt body is small,the working resistance is stable and the distributions of bolt axial force and interfacial shear stress are steady.When a rock burst event occurs,the bolt and bonding interface cannot easily break,which weakens the dynamic disaster degree.

Characteristics of microseismic b-value associated with rock mass large deformation in underground powerhouse caverns at different stress levels

Rock mass large deformation in underground powerhouse caverns has been a severe hazard in hydropower engineering in Southwest China.During the development of rock mass large deformation,a sequence of fractures was generated that can be monitored using microseismic(MS)monitoring techniques.Two MS monitoring systems were established in two typical underground powerhouse caverns featuring distinct geostress levels.The MS b-values associated with rock mass large deformation and their temporal variation are analysed.The results showed that the MS bvalue in course of rock mass deformation was less than 1.0 in the underground powerhouse caverns at a high stress level while larger than 1.5 at a low stress level.Prior to the rock mass deformation,the MS b-values derived from both the high-stress and low-stress underground powerhouse caverns show an incremental decrease over 10%within 10 d.The results contribute to understanding the fracturing characteristics of MS sources associated with rock mass large deformation and provide a reference for early warning of rock mass large deformation in underground powerhouse caverns.

Similar simulation study on the deformation and failure of surrounding rock of a large section chamber group under dynamic loading

Large and super-large section chamber groups in coal mines are frequently affected by dynamic loads resulting from production activities such as roadway driving and blasting.The stability of the surrounding rock is poor,and it is difficult to control.In this paper,a similar simulation test was used to study the deformation and evolution laws of the surrounding rock of a triangle-shaped chamber group under different dynamic loads.The results showed that under dynamic loading,the vertical stress of the surrounding rock of the chamber group increased in an oscillatory form.The maximum stress concentration coefficient reached 4.09.The damage degree of the roof was greater than that of the two sides.The deformation of the roof was approximately 1.2 times that of the two sides.For the chamber closer to the power source,the stress oscillation amplitude of the surrounding rock was larger,and the failure was more serious.The force of the anchorage structure showed a phased increasing characteristic;additionally,the force of the anchorage structure on the adjacent side of the chambers was greater than that on the other side.This study reveals the deformation and failure evolution laws of the surrounding rock of large section chamber groups under dynamic loading.

Behavior of large post-liquefaction deformation in saturated Nanjing fine sand

Laboratory tests on the large post-liquefaction deformation of saturated Nanjing fine sand were performed by using a hollow cylinder apparatus. The stress-strain responses and the characteristics of excess pore water pressure after liquefaction were studied. It was found that the relationship between deviatoric stress and axial strain presented a sigmoid curve, and there was a good linearity relationship between normalized pore water pressure and deviatoric stress. On this basis, a constitutive model of stress-strain responses and a dissipation model of excess pore water pressure were established. It was found that the results predicted by the two models were in good agreement with the experimental data. The influence of relative densities and confining pressure on the characteristics of liquefied soil were studied, The results showed the relative densities and initial effective confining pressure all had an important influence on the stress-strain responses of liquefied saturated Nanjing fine sand. However, the dissipation model of excess pore water pressure after liquefaction was only affected by the confining pressure.

Large deformation and failure mechanism analyses of Tangba high slope with a high-intensity and complex excavation process

The Tangba high slope is mainly composed of coarse soils and supplies core wall materials for the construction of the Changheba dam. Since the filling intensity of the Changheba dam is high, the Tangba high slope suffers from a high-intensity excavation process, and reinforcement measures are usually not implemented immediately. Moreover, the distribution of useful materials is uneven and insufficient, and the mixing of different soil materials is necessary; thus, multiple simultaneous excavations and secondary excavation are inevitable. In the construction period from 2012 to 2016, large deformations occurred in this area, and one of the largest monitored horizontal deformations whose direction points to the opposite side of the valley even reached more than 8000 mm. According to field investigation, site monitoring and theoretical analysis, the large deformation in the Tangba high slope can be divided into two phases. In the first phase, the excavation construction breaks the original stress equilibrium state; in the second phase, the precipitation infiltration accelerates the deformation. Thus, the excavation construction and precipitation infiltration are the two major factors promoting the deformation, and the high-intensity and complex excavation process is the fundamental cause. Notably, rate of slope deformation significantly accelerated in rainy seasons due to precipitation infiltration; the rate also accelerated in early 2016 due to the high-intensity, complex excavation process. Comprehensively considering the above factors, timely and effective reinforcement measures are essential.

Experimental analysis of crack tip fields in rubber materials under large deformation

A three-nested-deformation model is proposed to describe crack-tip fields in rubber-like materials with large deformation. The model is inspired by the distribution of the measured in-plane and out-of-plane deformation. The in- plane displacement of crack-tip fields under both Mode 1 and mixed-mode （Mode I-II） fracture conditions is measured by using the digital Moir6 method. The deformation character- istics and experimental sector division mode are investigated by comparing the measured displacement fields under differ- ent fracture modes. The out-of-plane displacement field near the crack tip is measured using the three-dimensional digital speckle correlation method.

Large deformation analysis of a cantilever beam made of axially functionally graded material by homotopy analysis method

Large deformation of a cantilever axially functionally graded (AFG) beam subject to a tip load is analytically studied using the homotopy analysis method (HAM). It is assumed that its Young’s modulus varies along the longitudinal direction according to a power law. Taking the solution of the corresponding homogeneous beam as the initial guess and obtaining a convergence region by adjusting an auxiliary parameter, the analytical expressions for large deformation of the AFG beam are provided. Results obtained by the HAM are compared with those obtained by the finite element method and those in the previous works to verify its validity. Good agreement is observed. A detailed parametric study is carried out. The results show that the axial material variation can greatly change the deformed configuration, which provides an approach to control and manage the deformation of beams. By tailoring the axial material distribution, a desired deformed configuration can be obtained for a specific load. The analytical solution presented herein can be a helpful tool for this procedure.

The effect of large deformation and material nonlinearity on gel indentation

A gel, an aggregate of polymers with solvents, has dual attributes of solid and liquid as solvent migrates in and out of the polymer network. Indentation has recently been used to characterize the mechanical properties of gels. This paper evaluates the effects of large deformation and material nonlinearity on gel indentation through theoretical modeling and finite element analysis. It is found that large deformation significantly affects the interpretation of the experimen- tal observations and the classical relation between indenta- tion force and depth has limitations for large deformation. The material nonlinearity does not play a very important role on indentation experiment so that the poroelasticity is a good approximation. Based on these observations, this paper proposes an alternative approach to measure the mechanical properties of gels, namely, uniaxial compression experiment.