Review on dynamic analysis of road pavements under moving vehicles and plane strain conditions

This paper reviews works on the dynamic analysis of flexible and rigid pavements under moving vehicles on the basis of continuum-based plane strain models and linear theories.The purpose of this review is to provide in-formation about the existing works on the subject,critically discuss them and make suggestions for further research.The reviewed papers are presented on the basis of the various models for pavement-vehicle systems and the various methods for dynamically analyzing these systems.Flexible pavements are modeled by a homogeneous or layered half-plane with isotropic or anisotropic and linear elastic,viscoelastic or poroelastic material behavior.Rigid pavements are modeled by a beam or plate on a homogeneous or layered half-plane with material properties like the ones for flexible pavements.The vehicles are modeled as concentrated or distributed over a finite area loads moving with constant or time dependent speed.The above pavement-vehicle models are dynamically analyzed by analytical,analytical/numerical or purely numerical methods working in the time or frequency domain.Representative examples are presented to illustrate the models and methods of analysis,demonstrate their merits and assess the effects of the various parameters on pavement response.The paper closes with con-clusions and suggestions for further research in the area.The significance of this research effort has to do with the presentation of the existing literature on the subject in a critical and easy to understand way with the aid of representative examples and the identification of new research areas.

Two-dimensional plane strain consolidation of unsaturated soils considering the depth-dependent stress

In practical engineering,the total vertical stress in the soil layer is not constant due to stress diffusion,and varies with time and depth.Therefore,the purpose of this paper is to investigate the effect of stress diffusion on the two-dimensional(2D)plane strain consolidation properties of unsaturated soils when the stress varies with time and depth.A series of semi-analytical solutions in terms of excess pore air and water pressures and settlement for 2D plane strain consolidation of unsaturated soils can be derived with the joint use of Laplace transform and Fourier sine series expansion.Then,the inverse Laplace transform of the semi-analytical solution is given in the time domain using a self-programmed code based on Crump’s method.The reliability of the obtained solutions is proved by the degeneration.Finally,the 2D plots of excess pore pressures and the curves of settlement varying with time,considering different physical parameters of unsaturated soil stratum and depth-dependent stress,are depicted and analyzed to study the 2D plane strain consolidation properties of unsaturated soils subjected to the depthdependent stress.

Analysis of plane strain bending of a strain hardening curved beam based on unified yield criterion

The analysis of plane strain elastic-plastic bending of a linear strain hardening curved beam with a narrow rectangular cross section subjected to couples at its end is conducted based on a unified yield criterion. The solutions for the mechanical properties of plane strain bending are derived, which are adapted for various kinds of non-strength differential materials and can be degenerated to those based on the Tresca, von Mises, and twin-shear yield criteria. The dependences of the two critical bending moments, the radii of the interfaces between the elastic and plastic regions and the radial displacements of the points at the symmetrical plane on different yield criteria and Poisson’s ratios are discussed. The results show that the influences of different yield criteria and Poisson’s ratio on the two critical bending moments, the radii of the interfaces between the elastic and plastic regions and the radial displacements of the points at the symmetrical plane of the curved beam are significant. Once the value of bis obtained by experiments, the yield criterion and the corresponding solution for the materials of interest are then determined.

Calibration of anisotropic yield function by introducing plane strain test instead of equi-biaxial tensile test

The equi-biaxial tensile test is often required for parameter identification of anisotropic yield function and it demands thespecial testing technique or device. Instead of the equi-biaxial tensile test, the plane strain test carried out with the traditional uniaxialtesting machine is suggested to provide the experimental data for calibration of anisotropic yield function. This simplified method byusing plane strain test was adopted to identify the parameters of Yld2000-2d yield function for 5xxx aluminum alloy and AlMgSialloy sheets. The predicted results of yield stresses, anisotropic coefficients and yield loci by the proposed method were very similarwith the experimental data and those by the equi-biaxial tensile test. It is validated that the plane strain test is effective to provideexperimental data instead of equi-biaxial tensile test for calibration of Yld2000-2d yield function.

Plane strain consolidation of soil layer with anisotropic permeability

This paper presents an alternative analytical technique to study a plane strain consolidation of a poroelastic soil by taking into account the anisotropy of permeability. From the governing equations of a saturated poroelastic soil, the relationship of basic variables for a point of a soil layer is established between the ground surface （z=0） and the depth z in the Laplace-Fourier transform domain. Combined with the boundary conditions, an exact solution is derived for plane strain Biot＇s consolidation of a finite soil layer with anisotropic permeability in the transform domain. Numerical inversions of the Laplace transform and the Fourier transform are adopted to obtain the actual solution in the physical domain. Numerical results of plane strain Biot＇s consolidation for a single soil layer show that the anisotropic of permeability has a great influence on the consolidation behavior of the soils.

ELASTIC-PLASTIC CRACK GROWTH ON PLANE STRAIN BIMATERIAL INTERFACE

Finite element computations are carried out to simulate plane strain crack growth on a bimaterial interface under the assumption of small scale yielding.The modified Guron constitutive equation and the element vanish technique introduced by Tvergaard et al.are used to model the final formation of an open crack.It is found from the calculation that the critical fracture toughness for crack growth is much low- er in bimaterials than that in homogeneous material.The critical fracture toughness is strongly dependent on material properties of the bimaterial pair and the mixed mode of remote loads.The interface crack grows in the more compliant(lower hardening)material or in the weaker(lower yield strength)material.In Mode-Ⅰ loading,the crack grows zigzag along the interface.

RECRYSTALLIZATION BEHAVIOR AND PRIOR AUSTENITE GRAIN BOUNDARY CORROSION IN THE PLANE STRAIN COMPRESSION CONDITION FOR A LOW CARBON X70 PIPELINE STEEL

Recrystallization behavior of a low carbon X70 pipeline steel was studied in the plane strain compression condition. It was found that the dynamic recovery but no dynamic recrystal- lization occurred in the current experimental condition. A method for examining the prior austenite grain boundary corrosion was supposed.

A generalized plane strain theory for transversely isotropic piezoelectric plates

Study of generalized plane strain has so far been limited to elasticity. The present is aimed at parallel development of transversely isotropic piezoelasticity. By assuming that the along depth distribution of electric potential is linear, and that com- monly used Kane-Mindlin kinematical assumption is valid, two dimensional solution systems were deduced, for which, explicit solutions of the out-of-plane constraint factor, as well as the stress resultant concentration factor around a circular hole in a transversely isotropic piezoelectric plate subjected to remote biaxial tension are obtained. Comparisons of these formulas with their counterparts for elastic case yielded suggestions that whether the piezoelectric effect exacerbates or mitigates the stress resultant concentration greatly depends on material properties, particularly, the piezoelectric coefficients; the effect of plate thickness was extensively investigated.

AN APPROACH TO THE ELASTIC-PLASTIC ANALYSIS OF THE PLANE STRAIN MODE-I CRACK

This paper presents an approach to the solution of the approximate elastic-plastic analysis for the plane strain mode-1 crack.

Correlativity between coal permeability and strain in quasi-plane strain state

To simulate the variety of big coal sample permeability during the rupture process under quasi-plane strain state, a series of experiments have been performed by a set of self-made coal-gas coupling test system. The test results indicate that the development trend between the permeability rate-strain curve and the stress-strain curve of big coal sample is almost consistent. The permeability rate-strain curve is general hysteretic to stress-strain curve, indicating the close relativity between the evolvement of damage and the development of permeability rate. However, there is time interval between them and the perme- ability rate peaks value when the sample reaches the softened stage after the peak stress. Based on the characteristics of per- meability rate-strain curve, three stages were plotted out： the stage before minimum permeability rate （/co）, the stage between minimum and maximum of permeability rate and the stage after the maximum permeability rate （kmax）. According to the three stages of permeability rate, the segmental curve equations of permeability rate-strain were fitted： the first stage can be fitted with negative exponential function; the second stage can be fitted with Boltzmann equation; and the last stage can be fitted with multinomial equation.

THE INTEGRAL AS A FUNCTION OF THE UPPER LIMIT AND AN ANALYTICAL SOLUTION TO PLANE STRAIN DRAWING AND EXTRUSION

A kinematically admissible velocity field which is different from Avitzur's is established in Cartesian Coordinates. An upper-bound analytical solution to strip drawing andextrusion is obtained by using the integral as a function of the upper limit in this paper.

Effects of Internal Relaxation under Inplane Strain on the Structural,Electronic and Optical Properties of Perovskite BaZrO3

We present the specific ab-initio calculations that detail the variations of perovskite BaZrO3 caused by in-plane strain. Specifically, the internal relaxation, which was not captured in the widely used biaxial strain model, was included in a complementary manner to lattice relaxation. Density functional theory as well as a hybrid functional method based on a plane wave basis set was employed to calculate the lattice structure, elastic constants, electronic properties and optical properties of perovskite BaZrO3. The lattice parameter c exhibited a clear linear dependence on the imposed in-plane strain, but the Poisson＇s ratio caused by internal relaxation was smaller than the elastic deformation, indicating an ＂inelastic＂ or ＂plastic＂ relaxation manner caused by the introduction of internal relaxation. As a result, the related electronic and optical properties of perovskite BaZrO3 were also strongly affected by the in-plane strain, which revealed an effective way to adjust the properties of perovskite BaZrO3 via internal relaxation.

In-plane Tensile Behaviors of Bi-axial Warp-Knitted Composites under Quasi-static and High Strain Rate Loading

The in-plane tensile behaviors of bi-axial warp-knitted(BWK) composites under quasi-static and high strain rates loading were experimentally analyzed in this article. The tensile tests were conducted along warp direction( 0°) and weft direction( 90°) at quasi-static rate of 0. 001 s^(-1) and high strain rates ranging from 1 450 to 2 540 s^(-1),respectively. It is found that the significant strain rate sensitivity can be observed in the stress-strain curves of BWK composites. The fracture morphologies of BWK composites demonstrate that the tensile failure modes are shear failure and fiber breakage under the quasi-static testing condition while interface failure and fibers pullout are at high strain rates.

Strain effects on optical polarisation properties in (11■2) plane GaN films

We present the theoretical results of the electronic band structure of wurtzite GaN films under biaxial strains in the （11^-22）-plane. The calculations are performed by the k.p perturbation theory approach through using the effectivemass Hamiltonian for an arbitrary direction. The results show that the transition energies decrease with the biaxial strains changing from -0.5% to 0.5%. For films of （11^-22）-plane, the strains are expected to be anisotropic in the growth plane. Such anisotropic strains give rise to valence band mixing which results in dramatic change in optical polarisation property. The strain can also result in optical polarisation switching phenomena. Finally, we discuss the applications of these properties to the （1132） plane GaN-based light-emitting diode and lase diode.

EFFECT OF THE POISSON RATIO ON THE PERFECTLY PLASTIC STRESS FIELD AT A STATIONARY PLANE-STRAIN CRACK TIP

Under the condition that all the perfectly plastic stress components at a crack tip are the functions of ? only, making use of equilibrium equations and Von-Mises yield condition containing Poisson ratio, in this paper, we derive the generally analytical expressions of perfectly plastic stress field at a stationary plane-strain crack tip. Applying these generally analytical expressions to the concrete cracks, the analytical expressions of perfectly plastic stress fields at the stationary tips of Mode I, Mode II and Mixed-Mode I-II plane-strain cracks are obtained. These analytical expressions contain Poisson ratio.

Quasi-plane-hypothesis of strain coordination for RC beams seismically strengthened with externally-bonded or near-surface mounted fiber reinforced plastic

The application of fiber reinforced plastic（FRP）,including carbon FRP and glass FRP,for structural repair and strengthening has grown due to their numerous advantages over conventional materials such as externally bonded reinforcement（EBR） and near-surface mounted（NSM） strengthening techniques.This paper summarizes the results from 21 reinforced concrete beams strengthened with different methods,including externally-bonded and near-surface mounted FRP,to study the strain coordination of the FRP and steel rebar of the RC beam.Since there is relative slipping between the RC beam and the FRP,the strain of the FRP and steel rebar of the RC beam satisfy the quasi-plane-hypothesis;that is,the strain of the longitudinal fiber that parallels the neutral axis of the plated beam within the scope of the effective height（h 0） of the cross section is in direct proportion to the distance from the fiber to the neutral axis.The strain of the FRP and steel rebar satisfies the equation：ε FRP =βε steel,and the value of β is equal to 1.1-1.3 according to the test results.

不同初始状态下黄土的平面应变卸载力学特性

针对于黄土工程中的平面应变卸载问题,利用平面应变改造后的真三轴仪,开展了不同初始状态(原状、重塑和饱和)黄土在不同固结围压和含水率条件下的平面应变卸载试验,揭示了不同初始状态黄土的应力-应变演化关系、中主应力特性和强度特性。研究结果表明,不同初始状态黄土的应力-应变曲线在低含水率和低围压条件下呈现理想塑性,随着固结围压和含水率增大,从弱硬化型向强硬化型转变;黄土的不同初始状态对应力-应变关系演化特性影响较大,原状黄土曲线最高,重塑黄土次之,饱和黄土最低;固结围压越大、含水率越低,初始切线斜率越大,应力应变曲线越高,土的强度发挥越快。原状和饱和黄土的中主应力和中主应力参数均先减小后增大,衰减幅度大,增长幅度小,中主应力参数的增长幅度要大于中主应力;重塑黄土的中主应力和中主应力参数则先减小后基本保持稳定。平面应变卸载条件下不同初始状态黄土的黏聚力和内摩擦角均随含水率增大近似呈现线性减小;不同初始状态对土黏聚力的影响要明显大于内摩擦角。原状黄土在低围压和低含水率条件下沿着剪切带形成明显的侧向滑移破坏,其余条件下均发生测胀破坏。

平面拉伸下聚氨酯裂纹板的裂纹扩展研究

聚氨酯(PU)因具有优异的物理化学性能,常用于一般工业与民用建筑中的屋面、地下室、浴室、卫生间地面等防水工程,但在长期服役过程中,难免会产生裂纹或微孔等缺陷,裂纹地萌生与扩展将劣化材料的使用性能,降低材料构件的承载力,甚至导致结构失效或安全事故。本文通过平面拉伸试验,探究了不同拉伸速率下聚氨酯裂纹板的力学性能及其裂纹扩展规律,研究结果表明,拉伸速率对裂纹板的应力应变关系、断裂失效时间以及裂纹扩展规律均有一定影响。

砾粒土卸载-再加载力学特性大型平面应变试验研究

针对水利和交通工程中平面应变类工程重复加卸荷问题,利用压力室平面应变改造后的西安理工大学大型土工真三轴仪在不同围压条件下对两种砾粒土进行固结排水平面应变卸载-再加载试验,研究了砾粒土在平面应变状态下的应力-应变关系和卸载回弹应变和卸载-再加载回弹坡度等力学特性。结果表明:砾粒土的颗粒圆度、孔隙比、母岩强度和围压均会影响剪切峰值应力及剪胀特性,颗粒圆度好、孔隙比小的砾粒土峰值应力较低且更易表现出剪胀特性,母岩强度低会促进应变软化并降低峰值应力,围压增大可抑制剪胀并使峰值应力增大;体积应变和广义剪应变卸载回弹量与应力水平和围压有关;回弹坡度随应力水平增大先增后减,密实度较大时回弹坡度较大;卸载-再加载过程中出现主应力轴旋转现象,零应变方向的应力并非一直为中主应力;回弹坡度显著大于初始切线坡度,回弹坡度与初始切线坡度之比随围压增大快速减小。