Plain Strain Problem Research Articles

Complex potentials solutions for isotropic Cosserat bodies with voids

This paper aims to obtain solutions in terms of the complex potential structure for the plain strain problem of an elastic micropolar and isotropic body with pores. The constitutive equations on which the method is applied and is useful are the well-known equations of the elasticity theory for the above-mentioned body. We intend to solve the Kirch problem using the procedure of complex variables.

Finite Element Modeling of the Soil-Nailing Process in Nailed-Soil Slopes

The finite element technique has been accepted as a tool for modeling geotechnical complex processes. In this study, finite element (FE) modeling of various stages of the soil-nailing process, i.e., construction stages and overburden pressure stages, is carried out considering different soil parameters, simulating with in-house developed laboratory models. The soil-nailing process built in laboratory models is idealized as a plain strain problem and modeled in PLAXIS software. The laboratory models of the soil-nailing process consist of a Perspex sheet box containing a sandy soil slope, a Perspex sheet facing, steel bars as reinforcement and a steel plate as foundation. The stress–strain relationship of the sand is represented by a Hardening-Soil model. The interface at the soil and nail is described by the Coulomb friction model. The behavior of the soil-nailing process, during the construction stage and under varying overburden pressure and varying soil density, are investigated in terms of displacements of slope and stress conditions in slope soil mass. The slope displacements and stress conditions in slope soil mass are all well presented by the FE modeling and compared with laboratory model test data. The sensitivity analysis of the laboratory models’ dimensions is carried out by three-dimensional modeling of the nailed-soil slope. It can be concluded that the developed finite element model has the potential to simulate the performance of a field nailed-soil slope during construction and working stages and could provide guidance for the construction/maintenance of soil-nailed cut slopes in granular soils/weathered rocks.

Singularity of subsonic and transonic crack propagations along interfaces of magnetoelectroelastic bimaterials

The unified method for addressing the propagation of subsonic and transonic cracks along the interfaces of anisotropic bimaterials in Shen and Nishioka (2000) is applied in this paper for the plain strain problem of subsonic and transonic crack propagation along the interfaces of anisotropic magnetoelectroelastic (MEE) bimaterials. Using a modified Eshelby–Stroh formalism and analytic continuation, the problem here leads to a Riemann–Hilbert problem. After solving the Riemann–Hilbert equation, near-tip asymptotic fields are obtained, which shows the properties of the subsonic and transonic crack propagation in an MEE bimaterial system. Finally, the numerical results related to different singularity powers of the crack-tip are presented and discussed for barium titanate-cobalt ferrite (BaTiO3CoFe2O4) composites. The effects of piezoelectricity and piezomagnetics are also examined.

Response Due To Impulsive Force In Generalized Thermomicrostretch Elastic Solid

A two dimensional Cartesian model of a generalized thermo-microstretch elastic solid subjected to impulsive force has been studied. The eigen value approach is employed after applying the Laplace and Fourier transforms on the field equations for L-S and G-L model of the plain strain problem. The integral transforms have been inverted into physical domain numerically and components of normal displacement, normal force stress, couple stress and microstress have been illustrated graphically.

An Elastic-Viscoplastic Model for Time-Dependent Behavior of Soft Clay and Its Application on Rheological Consolidation

To describe the time-dependent behavior of soft clay, this paper extended one-dimensional Nishihara model to three-dimensional stress state based on the framework of Perzyna’s overstress theory and modified cam-clay model. The yield criterion of modified cam-clay model was used to describe the plastic properties of soft clay, and the overstress theory was used to describe the strain rate effect. Triaxial rheological tests were carried out on Ningbo soft clay and the rheological characteristics were studied. Based on laboratory results, the parameters of proposed model were determined by curve fitting, which show that this model is suitable for the rheological characteristics of Ningbo soft clay. The analysis of parameters shows that, the value of parameters changes slightly with different deviatoric stress when the confining pressure was constant, but changes notably with the increase of confining pressure. A user material subroutine of the proposed constitutive mode was coded on the platform of the FEM software ABAQUS and verified by triaxial compression of soil column. A plain strain problem was computed to analyze the rheological consolidation properties of soft clay, in which the rheological effect and the finite strain effect were considered.

Modeling of coupled heat, moisture transfer and mechanical deformations of wood during drying process

PurposeThe purpose of this paper is to present a numerical model of coupled heat, moisture transfer and their effects on the mechanical deformations of wood during the drying process.Design/methodology/approachCoupling among heat, moisture, and mechanical deformations is solved consecutively by use of sparse solver of MATLAB. The weighted residual of the equilibrium equations of drying process of wood, based on finite element method, is investigated. The stress and plastic strain increments can be solved with Newton's method.FindingsThe numerical model is applied to a plain strain problem of a long wood board taken from the outer region of the wood log. Numerical simulation reveals the stress reversal during the drying process. The mechanical deformations and the principle stresses of a three‐dimensional wood board in consideration of the orthotropic properties are presented.Originality/valuePlane strain and plane stress are analysed. The tangential modulus is derived. The transformation of the stress and strain tensors between the local coordinate system resulting from the cylindrical properties of wood and the global one is evaluated. Selection of element type for temperature, moisture content and displacement is discussed.

추가성토에 의한 성토체 하부에서의 연직응력 산정

The needs for enlargement of width of existing embankment have been increasing due to heavy traffic and large amount of transporting goods. In this study, it was intended to derive formula for estimating vertical stress induced by additional embankment. Theoretical background for handling plain strain problem was investigated. It can be seen that stress function considered in the analysis was justifiable for compatibility and boundary condition. Notes for using derived formula were also considered.

Response of a wire rope strand to axial and torsional loads: Asymptotic modeling of the effect of interwire contact deformations

The refined discrete mathematical model of a simple helical wire rope strand is developed. The effect of the transverse contraction of the wire strand through Poisson’s ratio and also through local contact deformations (wire flattening) has been studied in detail. In order to express the interwire contact deformation in terms of the parameters describing the strand deformation, we formulate a two-dimensional model interwire contact problem. The interwire contact interaction is treated as a frictionless unilateral plain strain problem. The nonlinear model interwire contact problem has been solved by the method of matched asymptotic expansions. The constitutive equations for a helical wire rope strand, which take into account both the Poisson’s ratio effect and the effect of contact deformation, are obtained in a closed form.

Effect of Compression on the Water Management of a Proton Exchange Membrane Fuel Cell With Different Gas Diffusion Layers

The gas diffusion layer (GDL) plays an important role in maintaining suitable water management in a proton exchange membrane fuel cell. The properties of the gas diffusion layer, such as its porosity, permeability, wettability, and thickness, are affected by the shoulders of the bipolar plates due to the compression applied in the assembly process. Compression therefore influences the water management inside fuel cells. A two-phase fuel cell model was used to study the water management problem in a proton exchange membrane fuel cell with interdigitated flow channels. The effect of the compression on the fuel cell performance was numerically investigated for a variety of GDL parameters. This paper focuses on studying the water management of fuel cells under compression for various types of gas diffusion layers. First, the deformation of a gas diffusion layer due to compression applied from the shoulders of the bipolar plates was modeled as a plain-strain problem and was determined using finite element analysis (FEA). The porosity and the permeability of the gas diffusion layer were then recalculated based on the deformation results. Next, the deformed domain from the FEA model was coupled with a fuel cell model, and the effects of the compression during the assembly process on the water management and fuel cell performance were studied for gas diffusion layers with different thicknesses, porosities, and compressive moduli. It was found that the deformation of the GDL results in a low oxygen concentration at the reaction site. The saturation level of liquid water increases along the flow direction, and is higher when the compression effect is considered in the simulation.

Analysis of Pre-Fracture Zones for an Electrically Permeable Crack in an Interlayer Between Piezoelectric Materials

The method of determination of the pre-fracture zone length and the crack opening displacement for a plain strain problem of electrically permeable crack located in a thin interlayer between two identical piezoelectric materials is suggested. This method takes into account certain stress distribution appearing at the crack continuation. This distribution is related to interlayer yielding or damage and it can be found experimentally or theoretically.

Orthotropic elastic medium under the effect of initial and couple stresses

The eigenvalue approach has been employed to find the analytical expressions for displacements and stresses at any point of an infinite initially stressed orthotropic elastic medium with the effect of couple stress. A plain strain problem has been studied. New closed forms of displacement and stress components have been obtained. The variations of the displacements and stresses with horizontal distance have been shown graphically.

Analysis of factors influencing the solution of the consolidation problem by using an element-free Galerkin method

The meshless method is new type numerical method developed in recent years. There are no fewer than 20 variations published to-date, and some of them were successfully applied to solve Biot's consolidation problem. In the present paper, the system equations for the plain-strain consolidation problem using an element-free Galerkin method (EFGM) are presented on the basis of enforcing essential boundary conditions with a penalty method. Next, a large number of calculations and analyses of the displacement and excess pore-water pressure for nodes are carried out. It is shown that the accuracy of the calculations is influenced by many factors including the distribution mode of nodes, the shape and size of the domain of influence of nodes, the numerical integration scheme, and the adopted penalty factor. Some useful conclusions are drawn. The findings can be advantageous to improve the computational capability and accuracy of numerical solutions to the Biot's consolidation problem with EFGM.

Plane strain deformation of an initially stressed orthotropic elastic medium

The eigenvalue approach, using the Laplace and Fourier transforms, has been employed to find the analytical expressions for displacements and stresses at any point, as a result of an inclined line load, of an initially stressed orthotropic elastic medium. A plain strain problem has been studied. The results in the form of displacement and stress components have been obtained and discussed graphically for a particular model. In this paper it is shown that the displacement and stress components are affected by initial stresses in the medium.

A Simple Monte Carlo Method for Locating the Three‐dimensional Critical Slip Surface of a Slope

Abstract Based on the assumption of the plain‐strain problem, various optimization or random search methods have been developed for locating the critical slip surfaces in slope‐stability analysis, but none of such methods is applicable to the 3D case. In this paper, a simple Monte Carlo random simulation method is proposed to identify the 3D critical slip surface. Assuming the initial slip to be the lower part of a slip ellipsoid, the 3D critical slip surface is located by means of a minimized 3D safety factor. A column‐based 3D slope stability analysis model is used to calculate this factor. In this study, some practical cases of known minimum safety factors and critical slip surfaces in 2D analysis are extended to 3D slope problems to locate the critical slip surfaces. Compared with the 2D result, the resulting 3D critical slip surface has no apparent difference in terms of only cross section, but the associated 3D safety factor is definitely higher.

Plain strain problem of poroelasticity using eigenvalue approach

A plain strain problem of an isotropic elastic liquid-saturated porous medium in poroelasticity has been studied. The eigenvalue approach using the Laplace and Fourier transforms has been employed and these transforms have been inverted by using a numerical technique. An application of infinite space with concentrated force at the origin has been presented to illustrate the utility of the approach. The displacement and stress components in the physical domain are obtained numerically. The results are shown graphically and can be used for a broad class of problems related to liquid-saturated porous media.