Modeling shear localization along granular soil–structure interfaces using elasto-plastic Cosserat continuum

The current study presents finite element simulations of shear localization along the interface between cohesionless granular soil and bounding structure under large shearing movement. Micro-polar (Cosserat) continuum approach is applied in the framework of elasto-plasticity in order to overcome the numerical problems of localization modeling seen in the conventional continuum mechanics. The effects of different micro-polar kinematic boundary conditions, along the interface, on the evolution and location of shear band are shown by the numerical results. Furthermore, shear band thickness is also investigated for its dependence on the initial void ratio, vertical pressure and mean grain size. Here, the distribution and evolution of static and kinematic quantities are the main focuses regarding infinite layer of micro-polar material during plane shearing, especially with advanced large movement of bounding structure. The influence of such movement has not been investigated yet in the literature. Based on the results obtained from this study, shear localization appears parallel to the direction of shearing. It occurs either in the middle of granular layer or near boundaries, regarding the assumed micro-polar kinematic boundary conditions at the bottom and top surfaces of granular soil layer. Narrower shear band is observed in lower rotation resistance of soil particles along the interface. It is emphasized that the displacement magnitude of bounding structure has significant effect on the distribution and evolution of state variables and polar quantities in the granular soil layer. However, continuous displacement has no meaningful effect on the thickness of shear band. Here, smooth distributions of void ratio and shear stress components are obtained within the shear band, what the other previous numerical investigations did not receive. Despite indirect linking of Lade’s model to the critical state soil mechanics, state variables tend towards asymptotical stationary condition in large shear deformation.     

Quantification of large and localized deformation in granular materials

Quantifying large deformation in granular assemblies using concepts originating from continuum mechanics is a challenging task because of (1) the discontinuous nature of granular displacement, which does not allow the definition of a continuum measure of deformation, and (2) the almost inevitable shear band localization. These problems exist in both real-world granular materials and their numerical idealizations using particle-based simulations. In this work a new method is developed in order to address these issues. Instead of creating a meshed equivalent continuum for quantifying small engineering strains, the new method performs independent random queries on the velocity gradient characteristics of arbitrary sub-domains in the assembly through the novel concept of overlapping reference triangles, thus, enabling rigorous handling of large deformations which are usually associated with localization. The proposed method is illustrated and validated by discrete element method (DEM) simulation of a biaxial compressive test, in which apparent shear banding takes place. The homogenized deformation quantifications based on the new method match the estimations from the imposed boundary conditions. The numerical examples are also applied to (1) quantifying the heterogeneous distribution of deformation over the specimen, (2) visualizing the nucleation process of shear bands, and (3) characterizing shear flow patterns in shear bands. An investigation on the effects of the reference triangle sizes yields some inspiring and practically significant results.     

基于涡旋识别方法的高速列车尾涡结构的讨论

利用改进型延迟分离涡模拟方法对缩尺比例1:30的高速列车简化模型的绕流流场进行数值计算,主要针对近尾流区的涡旋结构展开具体讨论. 通过不同的涡旋识别方法,发现在尾涡结构中,高涡量的强涡旋主要聚集于尾车附近,而涡量较低但处于相对稳定状态的涡旋分布在大部分尾流空间中. 对此,主要基于最新提出的涡旋定义及其物理意义认为,由于边界层在尾部发生的流动分离,剪切变形以及高涡量的扩散对强涡旋的形成发挥着重要的作用,而涡旋会被较强的剪切旋转拉伸,使得局部复杂的流动表现出突出的湍流特性;另一方面,尽管涡强度明显下降,但是在强剪切应变迅速衰减的情况下,流向涡核中的涡旋涡量是主要的,此时,在较接近地面的情况下,流体微团以涡核为中心的旋转运动使得涡旋与地面之间的相互作用成为主导的流动机制. 虽然涡强度会相对缓慢地衰减,但是从湍流能量产生的角度,该机制对涡旋的自维持发挥重要的作用,从而使尾涡结构能够相对稳定地存在于尾流流动中.      

Turbulence measurements around a body in a re-circulating water channel by a hot film probe

Measurements were made in the stern boundary layers and near wakes of an elliptic cylinder and a slender ship model. Turbulence intensities, Reynolds stresses, kinematic eddy viscosities and mixing lengths are presented. For the elliptic cylinder, furthermore, auto-correlation and power spectrum are obtained. It is shown that the separation from the cylinder increases the turbulence intensities, and the Kármán vortices enhance the turbulence power at the vortex frequency. All distributions of Reynolds stresses in the thick boundary layer and wake of the ship model show a secondary low peak at about half the thickness.     

Experimental study on wake flow structures of screen cylinders using PIV

Experiments were conducted in a water flume using Particle Image Velocimetry (PIV) to study the evolution of the vortical structures in the wakes of four types of screen cylinders at a Reynolds number of about 3200. The results were compared with that of a bare cylinder. The screen cylinders were made of stainless steel screen meshes of various porosities (37%, 48%, 61% and 67%) rolled into cylindrical shapes. Smoke wire flow visualisations in a wind tunnel were also conducted in support of the PIV tests. Depending on the porosity of the screen mesh, two vortex formation mechanisms for the screen cylinder wakes were identified. One was associated with wake instability and the other was associated with shear-layer (Kelvin-Helmholtz) convective instability which involved merging through pairing and tripling of small-scale vortices within the shear layers. The former was responsible for the formation of large-scale vortices in the bare cylinder and the screen cylinder wakes with 37% and 48% porosities, while the latter was responsible for the screen cylinder wakes with 61% and 67% porosities. The results also showed that with increasing porosity, the vortex formation region was extended farther downstream and the Reynolds shear stress, the Turbulent Kinetic Energy (TKE) and vortex intensity were decreased constantly.     

Grain- and macro-scale kinematics for granular micromechanics based small deformation micromorphic continuum model

Macro-scale deformation of granular solids comprising large number of grains (>10⁶) are most efficiently described within the framework of continuum mechanics. It is notable, however that the micro-scale deformations in these materials are concentrated at the grain-boundaries or grain-contacts. Thus, the deformation energies in these systems must be modeled by considering the deformations concentrated in the neighborhood of the grain-boundaries or grain-contacts. To address this issue, grain-interactions has been widely described in the Hertzian sense by considering the relative movement of points on either side of a grain boundary or contact treated as an imperfect interface. This communication introduces the relevant kinematic variables given in the terms of the grain displacements, spins and size that can be used to estimate the relative movement of a grain boundary or contact. The macro-scale kinematic variables useful for continuum modeling are then identified with the grain-scale kinematic variables. The deformation energy density of the granular solid can thus be expressed both in terms of the grain-scale as well as the macro-scale kinematic variables providing the necessary pathway for micro-macro identification which can lead to non-classical micromorphic continuum models that incorporate grain-scale representation.     

A simulation based on the cosserat continuum model of the vortex structure in granular materials

Displacement fluctuation is the difference between the real displacement and the affine displacement in deforming granular materials. The discrete element method(DEM) is widely used along with experimental approaches to investigate whether the displacement fluctuation represents the vortex structure. Current research suggests that the vortex structure is caused by the cooperative motion of particle groups on meso-scales, which results in strain localization in granular materials. In this brief article, we investigate the vortex structure using the finite element method(FEM) based on the Cosserat continuum model. The numerical example focuses on the relationship between the vortex structure and the shear bands under two conditions:(a) uniform granular materials;(b) granular materials with inclusions. When compared with distributions of the effective strain and the vortex structure, we find that the vortex structure coexists with the strain localization and originates from the stiffness cooperation of different locations in granular materials at the macro level.     

Experimental study on wheel-soil interaction mechanics using in-wheel sensor and particle image velocimetry part II. Analysis and modeling of shear stress of lightweight wheeled vehicle

Wheeled vehicle mobility on loose sand is highly subject to shear deformation of sand around the wheel because the shear stress generates traction force of the wheel. The main contribution of this paper is to improve a shear stress model for a lightweight wheeled vehicle on dry sand. This work exploits two experimental approaches, an in-wheel sensor and a particle image velocimetry that precisely measure the shear stress and shear deformation generated at the interaction boundary. Further, the paper improves a shear stress model. The model proposed in this paper considers a force chain generated inside the granular media, boundary friction between the wheel surface and sand, and velocity dependency of the friction. The proposed model is experimentally validated, and its usefulness is confirmed through numerical simulation of the wheel traction force. The simulation result confirmed that the proposed model calculated the traction force with an accuracy about 70%, whereas the conventional one overestimated the force, and its accuracy was 13% at the best.     

Topology of the vorticity field in three-dimensional shear layers and wakes

An experimental and numerical study of the three-dimensional transition of plane wakes and shear layers behind a flat plate is presented. Flow visualization techniques are used to monitor the response of laminar flows at moderate Reynolds numbers (≈100) to perturbations periodically distributed along the span. In this way, the formation and evolution of streamwise vortex tubes and their interaction with the spanwise vortices are analyzed. The flow was studied numerically by means of three-dimensional inviscid vortex dynamics. Assuming periodicity in the spanwise and the streamwise direction, we discretize the vorticity field into two layers of vortex filaments with finite core diameter. Comparison between experiment and visualization indicates that important features of the three-dimensional evolution can be reproduced by inviscid vortex dynamics. Vortex stretching in the strain field of the spanwise rollers appears to be the primary mechanism for the three-dimensional transition in this type of flows.     

Exotic vortex wakes—point vortex solutions

Von Kármán was the first to present a quantitative model of the “vortex street” wake as a double row of point vortices, to determine which configurations propagate in the direction of the rows, and to consider the linear stability theory for such states. In the early literature one works with infinite rows of vortices. The vortex street is assumed to continue to infinity both upstream and downstream. Another analytical approach is to use periodic boundary conditions in the direction of the wake. This representation was used by Domm in his analysis of the instability of the Kármán vortex street. Birkhoff and Fisher in 1959 were the first to treat vortices in a periodic strip as a dynamical system in its own right. We have used the periodic system to address problems of vortex wake patterns, in particular vortex wakes that are more complicated than the traditional two-vortices-per-strip configurations. We use the term “exotic” for such wakes. We submit that this approach can yield a number of insights, including results of direct relevance to experiments, in the same sense that von Kármán's analysis has been helpful to the understanding of the regular vortex street wake, and we present the results obtained to date following this program.     

Applications of 2D helical vortex dynamics

In the paper, we show how the assumption of helical symmetry in the context of 2D helical vortices can be exploited to analyse and to model various cases of rotating flows. From theory, examples of three basic applications of 2D dynamics of helical vortices embedded in flows with helical symmetry of the vorticity field are addressed. These included some of the problems related to vortex breakdown, instability of far wakes behind rotors and vortex theory of ideal rotors.     

Cross-Stream Vorticity Field Induced by Streamwise Vortices in Unbounded and Wall-Bounded Shear Flows

This computational study examines the unsteady cross-stream vorticity structures that form when one or more streamwise vortices are immersed in homogeneous and boundary-layer shear flows. A quasi-two-dimensional limit is considered in which the velocity and vorticity fields, while still possessing three nonzero components, have vanishing gradient in the streamwise direction. This idealization is suitable to applications such as streamwise vortices that occur along a ship hull or airplane fuselage and it can be used as an idealized representation of the quasi-streamwise vortices in the near-wall region of a turbulent boundary layer. In this quasi-two-dimensional idealization, the streamwise velocity has no effect on the cross-stream velocity associated with the vortex. However, the vortex acts to modify the cross-stream vorticity component, resulting in regions of the flow with strong deviations in streamwise velocity. This paper examines the complex structures that form as the cross-stream vorticity field is wrapped up by the vortex and the effect of these structures on the streamwise velocity field, first for vortices immersed in homogeneous shear flow and then for vortices immersed in a boundary layer along a flat wall. Received 2 January 2002 and accepted 13 August 2002 Published online 3 December 2002 RID="*" ID="*" This project was supported by the Office of Naval Research under Grant Number N00014-01-1-0015. Dr. Thomas Swain is the program manager. Communicated by T.B. Gatski     

TR-PIV measurement of the wake behind a grooved cylinder at low Reynolds number

A comparative study of the wakes behind cylinders with grooved and smooth surfaces was performed with a view to understand the wake characteristics associated with the adult Saguaro cacti. A low-speed recirculation water channel was established for the experiment; the Reynolds number, based on the free-stream velocity and cylinder diameter (D), was kept at Re_D=1500. State-of-the-art time-resolved particle image velocimetry (TR-PIV) was employed to measure a total of 20 480 realizations of the wake field at a frame rate of 250 Hz, enabling a comprehensive view of the time- and phase-averaged wake pattern. In comparison to the wake behind the smooth cylinder, the length of the recirculation zone behind the grooved cylinder was extended by nearly 18.2%, yet the longitudinal velocity fluctuation intensity was considerably weakened. A global view of the peaked spectrum of the longitudinal velocity component revealed that the intermediate region for the grooved cylinder, which approximately corresponds to the transition region where the shear layer vortices interact, merge and shed before the formation of the Karman-like vortex street, was much wider than that for the smooth one. The unsteady events near St=0.3-0.4 were detected in the intermediate region behind the grooved cylinder, but no such events were found in the smooth cylinder system. Although the formation of the Karman-like vortex street was delayed by about 0.6D downstream for the grooved cylinder, no prominent difference in the vortex street region was found in the far wake for both cylinders. The Proper Orthogonal Decomposition (POD) method was used extensively to decompose the vector and swirling strength fields, which gave a close-up view of the vortices in the near wake. The first two POD modes of the swirling strength clarified the spatio-temporal characteristics of the shear layer vortices behind the grooved cylinder. The small-scale vortices superimposed on the shear layers behind the grooved cylinder were found to be generated and convected downstream in the same phase, which would significantly reduce the fluctuating force on the cylinder surface.     

Spatial perturbation of a wing-tip vortex using pulsed span-wise jets

The separation distance required between transport aircraft to avoid wake vortices remains a limiting factor on airport capacity. The dissipation of the wake can be accelerated by perturbing co-operative instabilities between multiple pairs of vortices. This paper presents the results of a preliminary experimental investigation into the use of pulsed span-wise air jets in the wing tip to perturb a single tip vortex in the very near field. Velocity measurements were made using PIV and hot-wire anemometry. The results demonstrate that the vortex position can be modulated at frequencies up to 50 Hz and, as such, the method shows promise for forcing instability in multiple vortex wakes.     

求解矩形夹层板在集中载荷下的稳定问题

在考虑了横向切应力和横向正应力对夹层板稳定影响的情况下,给出了矩形夹层板结构屈曲失稳的控制方程、基本解以及边界条件。应用功的互等定理求解了在均布载荷作用下的矩形夹层板的屈曲失稳问题。     

Kinematic variables bridging discrete and continuum granular mechanics

It is known that there is wide, and at present, unbridgeable, gap between discrete and continuum granular mechanics. In this contribution, first, microscopic kinematic variables neglected in classical continuum granular mechanics are investigated based on the kinematics of discs in contact. Then, a kinematic variable called the averaged pure rotation rate (APR) is proposed for an assembly of circular discs of different sizes, which is then used to produce another two kinematic tensors with one equal to the deformation rate tensor and the other unifying the spin tensor and the APR. As an example, the kinematic variables are incorporated into the unified double-slip plasticity model. Finally, these theoretical analyses are verified using a two-dimensional discrete element method. The study shows that these kinematic variables can be used to bridge discrete and continuum granular mechanics.     

Elementary aspects of vortex motion

Several aspects of vortex motion are considered, with a special stress on the present status of idealization, such as point vortices or vortex filament. As an introduction, elements of vortices induced by the transient flow past an obstacle are considered and their role and development are stated.

Following this introduction, a general survey of the issues in this symposium is made sketchily. As an example, the motion of point vortices in the presence of an external flow or a boundary is discussed on the basis of the Hamiltonian formalism. The cases of linear flow and semicircular boundary are taken as examples of regular and chaotic motions. Secular behaviour of a pair of vortices in the flow is remarked.     

Multiresolution continuum modeling of micro-void assisted dynamic adiabatic shear band propagation

A thermal-mechanical multiresolution continuum theory is applied within a finite element framework to model the initiation and propagation of dynamic shear bands in a steel alloy. The shear instability and subsequent stress collapse, which are responsible for dynamic adiabatic shear band propagation, are captured by including the effects of shear driven microvoid damage in a single constitutive model. The shear band width during propagation is controlled via a combination of thermal conductance and an embedded evolving length scale parameter present in the multiresolution continuum formulation. In particular, as the material reaches a shear instability and begins to soften, the dominant length scale parameter (and hence shear band width) transitions from the alloy grain size to the spacing between micro-voids. Emphasis is placed on modeling stress collapse due to micro-void damage while simultaneously capturing the appropriate scale of inhomogeneous deformation. The goal is to assist in the microscale optimization of alloys which are susceptible to shear band failure.     

Micro-macro scale instability in 2D regular granular assemblies

Instability and stress–strain behavior were investigated for 2D regular assemblies of cylindrical particles. Biaxial shear experiments were performed on three sets of assemblies with regular, albeit increasingly defective structures. These experiments revealed unique instability behavior of these assemblies. Continuum models for the assemblies were then constructed using the granular micromechanics approach. In this approach, the constitutive equations governing the behavior of inter-particle contacts are written in local or microscopic level. The behavior of the RVE is then retrieved by using either kinematic constraint or least squares (static constraint) along with the principle of virtual work to equate the work done by microscopic force–displacement conjugates to that of the macroscopic stress and strain tensor conjugates. The ability of the two continuum approaches to describe the measured stress–strain behavior was evaluated. The continuum models and the local constitutive laws were used to perform instability analyses. The onset of instability and orientation of shear band was found to be well predicted by the instability analyses with the continuum models. Further, macro-scale instability was found to correlate with the instability of inter-particle contacts, although with some variations for the two modeling approaches.     

Iterative control of Görtler vortices via local wall deformations

Görtler vortices develop along concave walls as a result of the imbalance between the centrifugal force and radial pressure gradient. In this study, we introduce a simple control strategy aimed at reducing the growth rate of Görtler vortices by locally modifying the surface geometry in spanwise and streamwise directions. Such wall deformations are accounted in the boundary region equations by using a Prandtl transform of dependent and independent variables. The vortex energy is then controlled via a classical proportional control algorithm for which either the wall-normal velocity or the wall shear stress serves as the control variable. Our numerical results indicate that the control algorithm is quite effective in minimizing the wall shear stress.