Two-dimensional elastoplastic analysis of a long, cylindrical cavity under non-hydrostatic loading

By applying the series expansion technique in the complex variable method established by Muskhelishvili, the plane elasticity problem for the stress and displacement field around a lined circular tunnel in conjunction with the consideration of misfit and interaction between the liner and the surrounding geomaterial is dealt with. The tunnel is assumed to be driven in a homogeneous and isotropic geomaterial. The coefficients in the Laurent series expansion of the stress functions are determined. The complex potentials in the liner and the surrounding geomaterial are explicitly derived, respectively. As an example, the case of a lined circular tunnel located in an isotropic initial stress field but subjected to uniform internal pressure is numerically considered. Numerical results indicate that the installation of tunnel liner can reduce the influences of the tunnel excavation on the in situ displacement and stress fields. However, the relative thickness and rigidity of the liner should be in an appropriate range. In addition, the effect of the tunnel excavation upon the displacement field is more significant than that upon the stress field. As far as the stress field in the surrounding geomaterial is concerned, when the ratio between the cover depth of tunnel and the tunnel radius is larger than 5, the results for the stress field in the paper are applicable. When the ratio between the tunnel depth and the tunnel radius is larger than 20, the results are applicable for the displacement field. Copyright © 2008 John Wiley & Sons, Ltd.

Evaluation of crack tip stress and strain fields under nonproportional loading in a viscoelastic material

A study of effects of the Earth's radial anisotropy on the tidal stress field

Optimal design of anchor cables for slope reinforcement based on stress and displacement fields

The stress field near the apex of two-phase materials formed from two isotropic homogeneous wedges with arbitrary angles under surface traction has been obtained by Bogy. The singularity in the stress field is investigated using Dundurs' composite parameters α and β. The stress singularity depends on the values of α and β, and is represented by the order O(r-s-2) for α(α-2β)>0, O(log r) for α(α-2β)=0, and O(1) for α(α-2β)<0. However, the order in the displacement field has not yet been clarified. In this paper, equations of the stress field and displacement field near the apex in bonded quarter-planes of dissimilar materials under surface traction are derived for α(α-2β)<0, α(α-2β)=0 and α(α-2β)>0. It is shown that the limiting behavior r→0 for the r-direction and θ-direction displacement differs from each other.

In-situ monitoring platform and preliminary analysis of monitoring data of Majiagou landslide with stabilizing piles

A simple technique for constructing the full stress and displacement fields in elastic plates with multiple cracks

Many rock fractures are entirely driven open by fluids such as ground water, geothermal water, gas, oil, and magma. These are a subset of extension fractures (mode I cracks; e.g., dikes, mineral veins and joints) referred to as hydrofractures. Field measurements show that many hydrofractures have great variations in aperture. However, most analytical solutions for fracture displacement and stress fields assume the loading to be either constant or with a linear variation. While these solutions have been widely used, it is clear that a fracture hosted by heterogeneous and anisotropic rock is normally subject to loading that is neither constant nor with a linear variation. Here we present new general solutions for the displacement and stress fields around hydrofractures, modelled as two-dimensional elastic cracks, opened by irregular overpressure variations given by the Fourier cosine series. Each solution has two terms. The first term gives the displacement and stress fields due to the average overpressure acting inside the crack; it is given by the initial term of the Fourier coefficients expressing the overpressure variation. The second term gives the displacement and stress fields caused by the overpressure variation; it is given by general terms of the Fourier coefficients and solved through numerical integration. Our numerical examples show that the crack aperture variation closely reflects the overpressure variation. Also, that the general displacement and stress fields close to the crack follow the overpressure variation but tend to be more uniform far from the crack. The present solutions can be used to estimate the displacement and stress fields around any fluid-driven crack, that is, any hydrofracture, as well as its aperture, provided the variation in overpressure can be described by Fourier series. The solutions add to our understanding of local stresses, displacements, and fluid transport associated with hydrofractures in the crust.

Nondimensional parameters that are needed to describe the stress field in an anisotropic bimaterial with tractions prescribed on its boundary are investigated. Two real matrices, which play an important role in representing the stress field, are proposed. They are shown to be an extension of the Dundurs parameters to the anisotropic bimaterial. A general solution of the stress and displacement fields in an anisotropic bimaterial with a straight interface is also obtained by using the complex function theory. In particular, a complete solution for the stress and displacement fields in the vicinity of the tip of an interfacial crack, between two dissimilar anisotropic elastic media, is also derived.

By performing atomistic calculations with a tight-binding potential, we study the displacement field induced by a screw dislocation lying along a free $\ensuremath{\langle}011\ensuremath{\rangle}$ Cu cylindrical nanowire. For this anisotropic orientation that is often encountered experimentally, we show that the displacement field ${u}_{z}$ along the nanowire can be seen as the superposition of three different fields: the screw dislocation field in an infinite medium, the warping displacement field caused by the so-called Eshelby twist, and an additional image field induced by the free surfaces. A Fourier series analysis of this latter image displacement and stress fields is given. For a circular cross section of the wire, this image field corresponds mainly to an additional warping displacement ${u}_{z}\ensuremath{\propto}xy$. The dissociation mechanism of the dislocation into partials and the surface stress effects being also captured in our simulations, the present study enables one to quantify the various contributions to the formation of the x-ray diffractograms.

Displacement and stress fields in a functionally graded (FG) fiber-reinforced rotating annular disk with a non-uniform thickness profile, subjected to angular deceleration and a temperature profile were investigated. Unidirectional fibers were considered to be circumferentially distributed within the disk with fiber volume fraction changing radially. The governing equations for displacement, stress, and temperature fields were solved using finite difference method. The results indicated that thermal induced stresses were more dominate than the rotational induced stresses. Disks which were fiber rich at the inner radius, the fibers made negligible difference on the displacement and stress fields when compared to a homogenous disk made from the matrix material. In addition, it was found that the deceleration magnitude had no effect on the radial and hoop stresses, nor the temperature on the developed shear stress. The shear stress was only affected by the disk deceleration. Tsai-Wu failure criterion was applied for decelerating disks to ascertain their failure behavior. The results show that Tsai-Wu failure index is dominated by the thermal stresses.

It is customary to use a displacement-based formulation to seek solutions to boundary value problems for its computational efficacy. In displacement-based formulations, it is convenient to prescribe the constitutive relation for stress as an explicit function of displacement gradient. However, from a general theoretical point of view, the stress and displacement gradient could be related by an implicit function. This study develops techniques to solve boundary value problems when linearized strain and stress are related by an implicit function. Here both the stresses and the displacement are taken as unknowns. The stress field is constructed such that it satisfies the equilibrium equations identically within the element and the traction continuity requirements between the elements. A continuously differentiable displacement field is constructed, and the linearized strain is computed from this displacement field. Then, the unknown parameters in the stress and displacement field are estimated such that the constitutive relation holds in weak integral sense. Though in this procedure the number of unknowns has increased in comparison with the displacement formulation, both the strength and serviceability condition can be checked directly without any post-processing. Also, in this procedure, both the equilibrium equations and continuity of displacement are met exactly. The equation that is not satisfied exactly is the constitutive relation, which is an approximation anyway. The efficacy and accuracy of this method are benchmarked by studying some standard problems. Planar and three-dimensional truss elements have been developed and benchmarked. Then, a rectangular plane element is implemented and its performance recorded.

A quality of multi-parameter approximation of the stress and displacement fields around a crack tip in a non-brittle material test specimen is studied in the paper. The stress field approximation using Williams power series is intended to be utilized for estimation of the nonlinear zone extent which potentially plays a role within methods for determination of true values of fracture parameters of materials exhibiting nonlinear failure. Considering the fact that in the case of elastic-plastic and especially quasi-brittle materials the size of this zone is substantial in comparison to the specimen dimensions, it is necessary to take a large region around the crack tip into account for this task. An automatic utility created to determine the values of coefficients of the higher order terms of Williams power series by usage of over-deterministic method applied on results of finite element analysis of arbitrary mode I test geometry is one of the tested procedures. The second one provides a backward reconstruction of the crack-tip stress field analytically by means of truncated Williams expansion. The developed procedures are based on the support of Java programming language and considerably simplify analyses of the mechanical fields’ description in a farther distance from the crack-tip. The presented research is focused on optimization of selection of FE nodal results for improvement of accuracy of the approximation.

The elastic-plastic singular stress field near an interface edge of bounded linear hardening material is substantially as same as that of bonded elastic materials whose Young's modulus and Poisson ratio are substituted by equivalent values, respectively. Further investigation by the elasto-plastic boundary element method (BEM) on the stress field near the interface edge showed that the stress field there can be divided into three regions: the domain region of the elastic-plastic singular stress field, the transitional region and the elastic region. The domain region of the elastic-plastic singular stress becomes larger with the increasing of the linear hardening coefficient. When the linear hardening coefficient decreases to a certain value, the effective stress in most of the yield zone equals approximately the yield stress. The stress distribution in the elastic region under small-scale yielding condition was also investigated.

A continuous vibration theory for rotors with an open edge crack