A theory of finite elastic consolidation

Presented in this paper is a general theory describing the consolidation of a porous elastic soil. The formulation allows for the occurrence of finite geometry changes and finite elastic strains during the consolidation process. The governing equations have been cast in a rate form and the laws which determine deformation and pore fluid flow, i.e. Hooke's law and Darcy's law, are presented in a frame indifferent manner. A numerical technique is described that provides an approximate solution to the governing equations. The theory and the solution technique are illustrated by several examples of practical interest.     

An analytical prediction of sliding motions along discontinuous boundary in non-smooth dynamical systems

This paper presents a method for the analytical prediction of sliding motions along discontinuous boundaries in non-smooth dynamical systems. The methodology is demonstrated through investigation of a periodically forced linear oscillator with dry friction. The switching conditions for sliding motions in non-smooth dynamical systems are given. The generic mappings for the friction-induced oscillator are introduced. From the generic mappings, the corresponding criteria for the sliding motions are presented through the force product conditions. The analytical prediction of the onset and vanishing of the sliding motions is illustrated. Finally, numerical simulations of sliding motions are carried out to verify the analytical prediction. This analytical prediction provides an accurate prediction of sliding motions in non-smooth dynamical systems. The switching conditions developed in this paper are expressed by the total force of the oscillator, and the nonlinearity and linearity of the spring and viscous damping forces in the oscillator cannot change such switching conditions. Therefore, the achieved force criteria can be applied to the other dynamical systems with nonlinear friction forces processing a C ⁰-discontinuity.     

The effect of non-uniform bending deformation on the stability of circumferential growth of through-wall cracks in brass tubes

Experimental results on the stability of circumferential growth of through-wall cracks in brass tubes, show that non-uniform bending can adversely affect the crack stability criterion. The results are relevant to the important technological problem of crack stability in 304 stainless steel pipes used in Boiling Water Reactors.     

Nonlinear wave motion in magnetoelasticity

Archive for Rational Mechanics and Analysis -     

Corneal studies by photoelasticity

Freshly enucleated andin vivo eyes of cats were analyzed to determine the detailed distribution of birefringence across the cornea and through its thickness, and to determine the change of birefringence with intraocular pressure. Scattered light and oblique-incidence photoelasticity were used. The experiments are summarized and special considerations are discussed. These include the necessity for a laser-light source; diffraction limitation in producing a narrow ribbon of light; rotation of the plane of polarization; inequalities in reflected components of polarized light.     

On multiple-path sonic anemometer measurement theory

In this paper, a model of the measuring process of sonic anemometers with more than one measuring path is presented. The main hypothesis of the work is that the time variation of the turbulent speed field during the sequence of pulses that produces a measure of the wind speed vector affects the measurement. Therefore, the previously considered frozen flow, or instantaneous averaging, condition is relaxed. This time variation, quantified by the mean Mach number of the flow and the time delay between consecutive pulses firings, in combination with both the full geometry of sensors (acoustic path location and orientation) and the incidence angles of the mean with speed vector, give rise to significant errors in the measurement of turbulence which are not considered by models based on the hypothesis of instantaneous line averaging. The additional corrections (relative to the ones proposed by instantaneous line-averaging models) are strongly dependent on the wave number component parallel to the mean wind speed, the time delay between consecutive pulses, the Mach number of the flow, the geometry of the sensor and the incidence angles of mean wind speed vector. Kaimal´s limit k_W1=1/l (where k_W1 is the wave number component parallel to mean wind speed and l is the path length) for the maximum wave numbers from which the sonic process affects the measurement of turbulence is here generalized as k_W1=C_l/l, where C_l is usually lesser than unity and depends on all the new parameters taken into account by the present model.     

Multi-Stage Upscaling: Selection of Suitable Methods

Reservoirs are often composed of an assortment of rock types giving rise to permeability heterogeneities at a variety of length-scales. To predict fluid flow at the full-field scale, it is necessary to be aware of these different types of heterogeneity, to recognise which are likely to have important effects on fluid flow, and to capture them by upscaling. In fact, we may require a series of stages of upscaling to go from small-scales (mm or cm) to a full-field model. When there are two (or more) phases present, we also need to know how these heterogeneities interact with fluid forces (capillary, viscous and gravity). We discuss how these effects may be taken into account by upscaling. This study focusses on the effects of steady-state upscaling for viscous-dominated floods and tests carried out on a range of 2D models are described. Upscaling errors are shown to be reduced slightly by the increase in numerical dispersion at the coarse scale. We select a combination of three different upscaling methods, and apply this approach to a model of a North Sea oil reservoir in a deep marine environment. Six different genetic units (rock types) were identified, including channel sandstone and inter-bedded sandstone and mudstone. These units were modelled using different approaches, depending on the nature of the heterogeneities. Our results show that the importance of small-scale heterogeneity depends on the large-scale distribution of the rock types. Upscaling may not be worthwhile in sparsely distributed genetic units. However, it is important in the dominant rock type, especially if there is good connectivity through the unit between the injector wells (or aquifer) and the producer wells.This revised version was published online in May 2005. In the previous version one of the authors name was missing.     

Dynamics of oblique detonations in ram accelerators

Time-accurate numerical simulations are used to study the dynamic development of oblique detonations on accelerating projectiles in ram accelerators. These simulations show that the oblique detonation can be stabilized on the projectile. The high pressure generated behind the detonation can result in accelerations up to 10⁶G and propel the projectile to velocities higher than 4.0 km/s. The detonation structure on the projectile is sensitive to the projectile geometry. A small change in the projectile shape is sufficient to alter the overall detonation structure and significantly affect the pressure distribution on the projectile. In order to maximize the thrust, an appropriate projectile shape has to be chosen to generate the detonation structure just behind the widest part of the projectile body. The projectile acceleration also has strong effects on the flow field and the detonation structure. During the acceleration, the location of the oblique detonation moves upstream from one reflected shock to another. However, one the detonation is stabilized behind the upstream shock, it remains at the new location until the transition to the next upstream shock occurs. In the simulations, the Non-Inertial-Source (NIS) technique was used to accurately represent of the projectile acceleration. Also, the Virtual-Cell-Embedding (VCE) method was employed to efficiently treat the complex projectile geometry on cartesian grids.