Mixed stabilized finite element methods in nonlinear solid mechanics. Part III: Compressible and incompressible plasticity

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

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.

Evaluating stress and strain fields in anatomical structures is a way to test hypotheses that relate specific features of facial and skeletal morphology to mechanical loading. Engineering techniques such as finite element analysis are now commonly used to calculate stress and strain fields, but if we are to fully accept these methods we must be confident that the applied loading regimens are reasonable. Multibody dynamics analysis (MDA) is a relatively new three dimensional computer modeling technique that can be used to apply varying muscle forces to predict joint and bite forces during static and dynamic motions. The method ensures that equilibrium of the structure is maintained at all times, even for complex statically indeterminate problems, eliminating nonphysiological constraint conditions often seen with other approaches. This study describes the novel use of MDA to investigate the influence of different muscle representations on a macaque skull model (Macaca fascicularis), where muscle groups were represented by either a single, multiple, or wrapped muscle fibers. The impact of varying muscle representation on stress fields was assessed through additional finite element simulations. The MDA models highlighted that muscle forces varied with gape and that forces within individual muscle groups also varied; for example, the anterior strands of the superficial masseter were loaded to a greater extent than the posterior strands. The direction of the muscle force was altered when temporalis muscle wrapping was modeled, and was coupled with compressive contact forces applied to the frontal, parietal and temporal bones of the cranium during biting.

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.

Nurrent calculation analysis approaches to the fracture resistance assessment for main equipment elements of the WWER NPP primary circuit are considered. It is noted that the solution of the problems of justifying safe operation, assessment of the integrity and extension of the lifetime of the reactor pressure vessel is essentially dependent on the results of calculations of the kinetics of the stress strain state, a proper consideration of the residual welding stress and strain fields, reliable evaluation of non-linear fracture mechanics parameters. A general methodology is developed for a calculated analysis of the fracture resistance of WWER reactor pressure vessels in the simulation of emergency cooling conditions. The main statements in the elastoplastic calculation of the kinetics of the stress strain state for reactor pressure vessels are formulated with consideration of the residual welding stress and strain fields, and the calculation procedure for determining the fracture parameters of the postulated crack is presented. Using the calculation methods and software product developed, a significant influence of such factors as consideration of the thermomechanical loading history and elastoplastic deformation of the metal in the vicinity of the postulated crack front, different ways of taking into consideration the residual welding stress level, the regularity and density of the finite element mesh in the vicinity of the calculated crack front, the procedure for calculating the elastoplastic fracture parameters in discrete finite element method models on the calculated fracture resistance assessment of WWER-1000 reactor pressure vessels is shown. It is found that the neglect of the loading history and residual stress level after heat treatment results in a non-conservative assessment of the fracture resistance for the collector-to-nozzle welded joint in the PGV-1000 steam generator in the simulation of the operating cycle of loading.

A continuous vibration theory for rotors with an open edge crack

Deformation of thin straight pipes under concentrated forces or prescribed edge displacements

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.

A complete experimental determination of the stress and strain fields in an arbitrary deformed structure is generally unavailable. However, for two dimensional elasticity problems, such determinations are possible since in those cases one needs only to solve for three stresses (two normal and one shear). In fact, such determinations have been conducted quite often. By using isochromatic and isoclinic photoelastic data, the shear difference and numerical iteration techniques (1) and the least squares techniques (2) have been successfully used for complete stress field determinations of two dimensional elasticity problems. Though the shear difference technique can be particularly sensitive to cumulative errors resulting from numerical integration, the least squares technique is not affected by this and appears to yield better accuracy. The methods just cited use both experimental data and one or more mechanics conditions(e.g., the equations of equilibrium) to determine the stress field. However, the stress field can also be obtained from experimental data alone for planar elasticity problems, if there is enough of it to solve for the three stresses. For example, the Moire* technique or the combination of isochromatic, isoclinic, and isopachic data (for transparent models) can be used for such determinations. Further, with the marriage of advanced image processing equipment to computers, such analyses using this type of data can be conveniently conducted. It is even possible that such analyses could be more accurate than those using the combined experimental/numerical techniques cited above. The purposes of this report are two fold: i) to describe a single apparatus for obtaining isochromatic, isopachic, and isoclinic results for complete stress field determinations of two dimensional transparent models, and ii) to compare experimental and theoretical stress field values for an antisymmetrically loaded beam obtained using that apparatus.© (1987) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.

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

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