Finite element analysis of anchor plates using non-coaxial models

The non-coaxial model simulating the non-coincidence between the principal stresses and the principal plastic strain rates is employed within the framework of finite element method（FEM） to predict the behaviors of anchors embedded in granular material.The non-coaxial model is developed based on the non-coaxial yield vertex theory,and the elastic and conventional coaxial plastic deformations are simulated by using elasto-perfectly plastic Drucker-Prager yield function according to the original yield vertex theory.Both the horizontal and vertical anchors with various embedment depths are considered.Different anchor shapes and soil friction and dilation angles are also taken into account.The predictions indicate that the use of non-coaxial models leads to softer responses,compared with those using conventional coaxial models.Besides,the predicted ultimate pulling capacities are the same for both coaxial and non-coaxial models.The non-coaxial influences increase with the increasing embedment depths,and circular anchors lead to larger non-coaxial influences than strip anchors.In view of the fact that the design of anchors is mainly determined by their displacements,ignoring the non-coaxiality in finite element numerical analysis can lead to unsafe results.

Modelling of Non-coaxial Viscoplastic Deformation in Geodynamics

The formation of shear bands for time and length scales appropriate for deformation processes in the upper Lithosphere is investigated in plane strain finite element simulations under predominantly uniaxial extension and compression, respectively. The direction of gravity is assumed orthogonal to the extension/compression axis. Mathematically, the formation of shear zones may be explained as a consequence of changes in the type of the governing model equations. Such changes or bifurcations depend strongly on the details of the constitutive relationships such as strain softening, thermal or chemical effects, associated or non-associated--coaxial or non-coaxial flow rules. Here we focus on strain softening and coaxial and non-coaxial flow rules. In the simulations, we consider an initially rectangular domain with the dimensions Lo, Ho in the horizontal, vertical directions, respectively. The domain is extended or compressed by prescribing a uniform, horizontal velocity field along one of the vertical boundaries while keeping the opposite boundary fixed. An important global descriptor of the deformation process is the relationship between the horizontal stress resultant （average horizontal stress） and the strain ln（L/Lo）, where L is the deformed length of the domain. The main goal of this paper is to investigate key factors influencing the phenomenology of the localization process such as flow rule, coaxial, non-coaxial and strain softening. Different origins of the mesh sensitivity of deformations involving localization are also investigated.

Effects of core position of locally resonant scatterers on low-frequency acoustic absorption in viscoelastic panel

Locally resonant sonic materials, due to their ability to control the propagation of low-frequency elastic waves, have become a promising option for underwater sound absorption materials. In this paper, the finite element method is used to investigate the absorption characteristics of a viscoelastic panel periodically embedded with a type of infinite-long noncoaxially cylindrical locally resonant scatterers(LRSs). The effect of the core position in the coating layer of the LRS on the low-frequency(500 Hz–3000 Hz) sound absorption property is investigated. With increasing the longitudinal core eccentricity e, there occur few changes in the absorptance at the frequencies below 1500 Hz, however, the absorptance above 1500 Hz becomes gradually better and the valid absorption(with absorptance above 0.8) frequency band(VAFB)of the viscoelastic panel becomes accordingly broader. The absorption mechanism is revealed by using the displacement field maps of the viscoelastic panel and the steel slab. The results show two typical resonance modes. One is the overall resonance mode(ORM) caused by steel backing, and the other is the core resonance mode(CRM) caused by LRS. The absorptance of the viscoelastic panel by ORM is induced mainly by the vibration of the steel slab and affected little by core position. On the contrary, with increasing the core eccentricity, the CRM shifts toward high frequency band and decouples with the ORM, leading to two separate absorption peaks and the broadened VAFB of the panel.

Anisotropic characteristics of granular materials under simple shear

The discrete element method was used to investigate the microscopic characteristics of granular materials under simple shear loading conditions. A series of simple tests on photo-elastic materials were used as a benchmark. With respect to the original experimental observations, average micro-variables such as the shear stress, shear strain and the volumetric dilatancy were extracted to illustrate the performance of the DEM simulation. The change of anisotropic density distributions of contact normals and contact forces was demonstrated during the course of simple shear. On the basis of microscopic characteristics, an analytical approach was further used to explore the macroscopic behaviors involving anisotropic shear strength and anisotropic stress-dilatancy. This results show that under simple shear loading, anisotropic shear strength arises primarily due to the difference between principal directions of the stress and the fabric. In addition, non-coaxiality, referring to the difference between principal directions of the strain rate and the stress, generates less stress-dilatancy. In particular, the anisotropic hardening and anisotropic stress-dilatancy will reduce to the isotropic hardening and the classical Taylor’s stress-dilatancy under proportional loading.

A DEM investigation on simple shear behavior of dense granular assemblies

A micromechanical investigation on simple shear behavior of dense granular assemblies was carried out by discrete element method.Three series of numerical tests were performed to examine the effects of initial porosity,vertical stress and particle shape on simple shear behavior of the samples,respectively.It was found that during simple shear the directions of principal stress and principal strain increment rotate differently with shear strain level.The non-coaxiality between the two directions decreases with strain level and may greatly affect the shear behavior of the assemblies,especially their peak friction angles.The numerical modelling also reveals that the rotation of the principal direction of fabric anisotropy lags behind that of the major principal stress direction during simple shear,which is described as fabric hyteresis effect.The degrees of fabric and interparticle contact force anisotropies increase as particle angularity increases,whereas the orientations of these anisotropies have not been significantly influenced by particle shape.An extended stress–dilatancy relationship based on ROWE-DAVIS framework was proposed to consider the non-coaxiality effect under principal stress rotation.The model was validated by present numerical results as well as some published physical test and numerical modelled data.

Numerical Analysis and Centrifuge Modeling of Shallow Foundations

The influence of non-coaxial constitutive model on predictions of dense sand behavior is investigated in this paper. The non-coaxial model with strain softening plasticity is applied into finite-element program ABAQUS, which is first used to predict the stress-strain behavior and the non-coaxial characteristic between the orientations of the principal stress and principal plastic strain rate in simple shear tests. The model is also used to predict load settlement responses and bearing capacity factors of shallow foundations. A series of centrifuge tests for shallow foundations on saturated dense sand are performed under drained conditions and the test results are compared with the corresponding numerical results. Various footing dimensions, depths of embedment, and footing shapes are considered in these tests. In view of the load settlement relationships, the stiffness of the load-displacement curves is significantly affected by the non-coaxial model compared with those predicted by the coaxial model, and a lower value of non-coaxial modulus gives a softer response. Considering the soil behavior at failure, the coaxial model predictions of bearing capacity factors are more advanced than those of centrifuge test results and the non-coaxial model results;besides, the non-coaxial model gives better predictions. The non-coaxial model predictions are closer to those of the centrifuge results when a proper non-coaxial plastic modulus is chosen.

MHD UNSTEADY FLOWS DUE TO NON—COAXIAL ROTATIONS OF A DISK AND A FLUID AT INFINITY

Exact analytical solution for flows of an electrically conducting fluid over an infinite oscillatory disk in the presence of a uniform transverse magnetic field is constructed. Both the disk and the fluid are in a state of non-coaxial rotation. Such a flow model has a great significance not only due to its own theoretical interest, but also due to applications to geophysics and engineering. The resulting initial value problem has been solved analytically by applying the Laplace transform technique and the explicit expressions for the velocity for steady and unsteady cases have been established. The analysis of the obtained results shows that the flow field is appreciably influenced by the applied magnetic field, the frequency and rotation parameters.

Testing the intraplate origin of mega-earthquakes at subduction margins

The disastrous Mw 9.3 （seismic moment 1.0 × 10^30 dyn/cm） earthquake that struck northwest Sumatra on 26 December 2004 and triggered -30 m high tsunami has rejuvenated the quest for identi- fying the forcing behind subduction related earthquakes around the world. Studies reveal that the stron- gest part （elastic core） of the oceanic lithosphere lie between 20 and 60 km depth beneath the upper （- 7 km thick） crustal layer, and compressive stress of GPa order is required to fail the rock-layers within the core zone. Here we present evidences in favor of an intraplate origin of mega-earthquakes right within the strong core part （at the interface of semi-brittle and brittle zone）, and propose an alternate model exploring the flexing zone of the descending lithosphere as the nodal area for major stress accumulation. We believe that at high confining pressure and elevated temperature, unidirectional cyclic compressive stress loading in the flexing zone results in an increase of material yield strength through strain hardening, which transforms the rheology of the layer from semi-brittle to near-brittle state. The increased compres- sive stress field coupled with upward migration of the neutral surface （of zero stress fields） under non- coaxial deformation triggers shear crack. The growth of the shear crack is initially confined in the near-brittle domain, and propagates later through the more brittle crustal part of the descending oceanic lithosphere in the form of cataclastic failure,

The Pendulum of Dynamic Interactions

In this paper, we present evidence to show that the dynamics of rigid solid bodies is not a closed discipline, particularly in the field of rotational dynamics. From the observation of bodies with intrinsic rotation in our universe, our research group proposes new dynamic hypotheses that explain the behaviour observed when these bodies are subject to new simultaneous non-coaxial rotations. A new gyroscopic conical pendulum was designed for this purpose. Experimental tests initially conducted with this new gyroscopic conical pendulum were repeated for their recording on video, which accompanied this paper for better understanding thereof. These experimental tests positively confirm the new Theory of Dynamic Interactions, and its dynamic laws, which help us to understand the behaviour of this pendulum and, in general, that of the baryonic mass when it is subject to non-coaxial simultaneous rotations. It thus provides a better understanding of the nature and the dynamic behaviour of our universe.

Numerical Solution for Variable Accelerated Flow Subject to Slip Effect

In this paper, we examine the unsteady magneto hydrodynamic (MHD) flow generated by a disc that is making non-coaxial rotations with a third grade fluid at infinity and moving with a variable acceleration. The fluid is assumed to satisfy slip boundary condition on the disc. The governing equations are three dimensional and highly non-linear in nature. The assumed slip boundary condition is non-linear as well. The governing equations are transformed to a nonlinear boundary value problem which is solved numerically. Comparison of this generalized problem with uniformly accelerated disk satisfying no slip condition is made. Variations of the characterizing dimensionless parameters such as slip parameter λ, acceleration parameter c, unsteady parameter τ, third grade parameter β, suction parameter S, and magnetic parameter N on the flow field are discussed and analyzed graphically.

On Motion, Its Relativity and the Equivalence Principle

The Equivalence Principle put forward by Albert Einstein is currently undergoing comprehensive revision to determine its degree of accuracy. Notwithstanding, this principle refers to a very specific circumstance, as free-fall;thus in our opinion it cannot be generalised to any other movement in space. This paper refers to the dynamic hypotheses of moving rigid bodies and a particular, structured theory that would establish how such bodies behave when subject to different actions that oblige them to make successive, non-coaxial spins. With respect to bodies subject to acceleration by rotation, we understand that there are indications to identify the prior dynamic state of the moving object and that examples of a violation of the aforementioned Equivalence Principle can be deduced thereof. Based on the findings of this paper and the theory put forward herein, we suggest that an observer can identify the prior situation of absolute rest or absolute non-rotation of a body, thus leading to the conclusion that movement does not necessarily have to be a relative concept. The foregoing leads us to propose that the Equivalence Principle is fully valid for the situation put forward by Albert Einstein, but cannot be generalised to any dynamic situation.

Dynamic Interactions in the Atmosphere

Even today, with the great progress that has been made in the scientific, technological and computational fields, we are still stunned by the devastating effects brought about by atmospheric phenomena. This paper aims to propose new hypotheses in the field of dynamics to enhance our understanding of the behaviour of atmospheric disturbances caused by rotating winds. I believe that the criteria of classical dynamics that are applied to vortex systems in the atmosphere should be rigorously reviewed. I propose to establish new hypotheses in the field of dynamics, in order to better interpret rotation in nature. These hypotheses have been structured into a new theory that has been tested experimentally by both ourselves and third parties, with positive results. I propose to use the Theory of Dynamic Interactions (TDI) to interpret the behaviour of systems undergoing successive rotations around different axes—which we will refer to as non-coaxial rotations. I hold that this theory applies to air masses and groups of particles in suspension that are accelerated by rotations. Accordingly, it should be used to interpret the behaviour of tornadoes, cyclones and hurricanes. I believe that this proposal could enhance our understanding of these atmospheric phenomena and improve predictions about them.

Dynamic Interaction Confinement

The importance of developing new technologies to obtain energy by means of nuclear fusion procedures is beyond question. There are several different and technically possible models for doing this, though to date none of these has been able to attain an industrial reactor with an end performance greater than unity. We still find ourselves at the initial phase, after many years, as a result of having failed as yet to come up with a commercially productive machine. Nuclear fusion research has defined a prototype reactor based on a fluid conductor, isolated materially in a physical container and confined by means of magnetic fields. In this fluid-plasma which interacts with magnetic fields, fusion reactions are caused that release energy, while at the same time a quantity of movement and angular momentum is moved or “rotated” and transported. However, turbulence is caused in these magnetic confinement fusion processes that reduces system efficiency and prevents the obtaining of sufficient net energy from the nuclear reactions. This paper aims to propose new dynamic hypotheses to enhance our understanding of the behaviour of the plasma in the reactor. In doing so, we put forward a profound revision of classical dynamics. After over thirty years studying rotational dynamics, we propose a new theory of dynamic interactions to better interpret nature in rotation. This new theory has been tested experimentally returning positive results, even by third parties. We suggest that these new dynamic hypotheses, which we hold applicable to particle systems accelerated by rotation, be used in the interpretation and design of fusion reactors. We believe that this proposal could, in addition to magnetic confinement, achieve confinement by simultaneous and compatible dynamic interaction. Accordingly, we are of the opinion that it would be possible to get better performance and results in the design of fusion reactors by way of simultaneous magnetic and dynamic interaction confinement.

Macro-micromechanical approaches for non-coaxiality of coarse grained soils

For coarse grained soils,their principal stress directions may change when the water level of embankment dam varies instantaneously.In this loading case,the principal directions of stress and strain rate will become non-coaxial.In an effort to model non-coaxial behavior,a modified three-dimensional non-coaxial model is developed in the context of vertex yield(tangent plasticity) theory.Discrete Element Method(PFC) incorporating user-defined interparticle contact models is also employed to gain an insight into microscopic mechanism of non-coaxiality.The analysis focuses on non-coaxial behaviors under simple shear condition.It has been shown that the proposed non-coaxial model gives good predictions for non-coaxiality with reference to microscopic observations while the classical coaxial model fails to simulate the non-coaxial behaviors.In general,non-coaxiality as a result of the rotation of principal stress,is large at a small shear strain,and inclined to become negligible with increasing shear strain.For coarse grained soils,their non-coaxiality tends to largely depend on the initial normal pressure,where a larger degree of non-coaxiality can be observed at a higher pressure.

Undrained anisotropy and non-coaxial behavior of clayey soil under principal stress rotation

In this study, a series of undrained tests were conducted on both intact and reconstituted clay using an automatic hollow cylinder apparatus. Monotonic shearing tests with fixed principal stress directions were carried out, pure and cyclic prin- cipal stress rotation tests were also performed. The non-coaxiality, defined as the non-coincidence of the principal plastic strain increment direction and the corresponding principal stress direction, of clayey soil was studied experimentally. The effects of the intermediate principal stress, shear stress level, and inherent anisotropy were highlighted. Clear non-coaxiality was observed during pure principal stress rotation, in both intact and reconstituted clay. The influence of the intermediate principal stress pa- rameter, shear stress level, and inherent anisotropy on the non-coaxial behavior of the clayey soil was found to be insignificant when compared with the sand. The non-coaxial behavior of the clayey soil depended more on the stress paths. Under undrained conditions, the contribution of elastic strain to the direction of the total principal strain increment cannot be ignored.