Stochastic Structural Model of Rock and Soil Aggregates by Continuum-Based Discrete Element Method

This paper first presents a stochastic structural model to describe the random geometrical features of rock and soil aggregates. The stochastic structural model uses mixture ratio, rock size and rock shape to construct the microstructures of aggregates,and introduces two types of structural elements (block element and jointed element) and three types of material elements (rock element, soil element, and weaker jointed element)for this microstructure. Then, continuum-based discrete element method is used to study the deformation and failure mechanism of rock and soil aggregate through a series of loading tests. It is found that the stress-strain curve of rock and soil aggregates is nonlinear, and the failure is usually initialized from weaker jointed elements. Finally, some factors such as mixture ratio, rock size and rock shape are studied in detail. The numerical results are in good agreement with in situ test. Therefore, current model is effective for simulating the mechanical behaviors of rock and soil aggregates.

Embedded cell model of three-dimensional two-phase composites

An embedded cell model is presented to obtain the effective elastic moduli and the elastic-plastic stress-strain relations of three-dimensional two-phase particulate composites. Each cell consists of an ellipsoidal inclusion surrounded by a finite ellipsoidal matrix that embedded in an infinite matrix. When both matrix and particle are elastic, the effective elastic moduli are derived which is an exact analytic formula without any simplified approximation that can be expressed in an explicit form. Further, the elastic-plastic stress-strain relations are obtained for spherical cells and oblate spheroid cells, in which the matrix is elastic and the particle is elastic-plastic. In addition, the macroscopic elastic-plastic constitutive relation of particle reinforced composites (PRC) is investigated by a systematic approach [1] in which the matrix is elastic-plastic and the particle is elastic.

Generalized Maugis-Dugdale Model of an Elastic Cylinder in Non-Slipping Adhesive Contact with a Stretched Substrate

We have recently developed a generalized JKR model for non-slipping adhesive contact between an elastic cylinder and a stretched substrate where both tangential and normal tractions are transmitted across the contact interface. Here we extend this model to a generalized Maugis-Dugdale model by adopting a Dugdale-type adhesive interaction law to eliminate the stress singularity near the edge of the contact zone. The non-slipping Maugis-Dugdale model is expected to have a broader range of validity in comparison with the non-slipping JKR model. The solution shares a number of common features with experimentally observed behaviors of cell reorientation on a cyclically stretched substrate.

Two-Dimensional Kinematic Wave Model of Overland-Flow

A two-dimensional kinematic wave model was developed for simulating runoff generation and flow concentration on an experimental infiltrating hillslope receiving artificial rainfall. Experimental observations on runoff generation and flow concentration on irregular hillslopes showed that the topography of the slope surface controlled the direction and flow lines of overland flow. The model-simulated results satisfactorily compared with experimental observations. The erosive ability of the concentrated flow was found to mainly depend on the ratio of the width and depth of confluent grooves.

Equivalent Model Of Expansion Of Cement Mortar Under Sulphate Erosion

The expansion property of cement mortar under the attack of sulfate ions is studied by experimental and theoretical methods. First, cement mortars are fabricated with the ratio of water to cement of 0.4, 0.6, and 0.8. Secondly, the expansion of specimen immerged in sulphate solution is measured at different times. Thirdly, a theoretical model of expansion of cement mortar under sulphate erosion is suggested by virtue of represent volume element method. In this model, the damage evolution due to the interaction between delayed ettringite and cement mortar is taken into account. Finally, the numerical calculation is performed. The numerical and experimental results indicate that the model perfectly describes the expansion of the cement mortar.

Threshold diversity and trans-scales sensitivity in a finite nonlinear evolution model of materials failure

We present a slice-sampling method and study the ensemble evolution of a large finite nonlinear system in order to model materials failure. There is a transitional region of failure probability. Its size effect is expressed by a slowly decaying scaling law. In a meso-macroscopic range (similar to 10(5)) in realistic failure, the diversity cannot be ignored. Sensitivity to mesoscopic details governs the phenomena. (C) 1997 Published by Elsevier Science B.V.

A micromechanical model of influence of particle fracture and particle cluster on mechanical properties of metal matrix composites

A general analytical model for a composite with an isotropic matrix and two populations of spherical inclusions is proposed. The method is based on the second order moment of stress for evaluating the homogenised effective stress in the matrix and on the secant moduli concept for the plastic deformation. With Webull's statistical law for the strength of SiCp particles, the model can quantitatively predict the influence of particle fracture on the mechanical properties of PMMCs. Application of the proposed model to the particle cluster shows that the particle cluster has neglected influence on the strain and stress curves of the composite. (C) 1998 Elsevier Science B.V.

Investigation on a simulation model of floating half zone convection .2. Experiment

A simulation model of floating half zone with non-uniform temperature distribution at the upper rod and uniform temperature distribution at lower rod was discussed by numerical investigation in a previous paper. In the present paper, the experimental investigation of the simulation model is given generally. The results of the present model show that the temperature profile is quite different and the critical applied temperature difference is lower than the one of usual model with same geometrical parameters in most cases. The features of critical Marangoni number depending on the liquid bridge volume are also different from the ones of usual model.

Numerical investigation on a simulation model of floating zone convection

A simulation model with adiabatic condition at the upper rod and constant temperature at the lower rod is studied numerically in this paper. The temperature distribution in a simulation model is closer to the one in the half part of a floating full zone in comparison with the one in a usual floating half zone model with constant temperature at both rods, because the temperature distribution of a floating full zone is symmetric for the middle plane in a microgravity environment. The results of the simulation model show that the temperature profiles and the how patterns are different from those of the usual floating half zone model. Another type of half zone model, with a special non-uniform temperature distribution at the upper rod and constant temperature at the lower rod, has been suggested by recent experiments. The temperature boundary condition of the upper rod has a maximum value in the center and a lower value near the free surface. This modified simulation model is also simulated numerically in the present paper. Copyright (C)1996 Elsevier Science Ltd.

A stochastic jump and deterministic dynamics model of impact failure evolution with rate effect

Motivated by the observation of the rate effect on material failure, a model of nonlinear and nonlocal evolution is developed, that includes both stochastic and dynamic effects. In phase space a transitional region prevails, which distinguishes the failure behavior from a globally stable one to that of catastrophic. Several probability functions are found to characterize the distinctive features of evolution due to different degrees of nucleation, growth and coalescence rates. The results may provide a better understanding of material failure.

A model of an isolated magnetic-flux tube in a stratified atmosphere

A two-dimensional model of a magnetic flux tube confined in a gravitational stratified atmosphere is discussed. The magnetic field in the flux tube is assumed to be force-free. By using the approximation of large scale height, the problem of a free boundary with nonlinear conditions may be reduced to one involving a fixed boundary. The two-dimensional features are obtained by applying the perturbation method and adopting the Luest-Schlueter model as the basic state. The results show that the configuration of a flux tube confined in a gravitational stratified atmosphere is divergent, and the more twisted the magnetic field, the more divergent is the flux tube.

A consistent model of isolated force-free magnetic arches

The magnetic flux tube concentrating strong magnetic field is the basic configuration of magneticfield in the solar atmosphere. In the present paper, the equilibrium of isolated magnetic flux tube inthe solar atmosphere is discussed. In the viewpoint of mathematics, the boundary condition is nonlinearand the position of boundary needs to be determined by the physical condition although the equation ofmagnetic potential is linear for the linear force-free field. Analytical solutions to the arches of bothuniform circular cross-section and non-uniform cross section have been obtained. The results show thatthe nonlinear problem may have or not have any solution according to different azimuthal components of the magnetic field; the number of solutions to the nonlinear problem is four at most, and two in some cases. In the present paper, the analytical solutions to the approximations of both fat and slender arches are given in detail, and the general features of magnetic arch structure are shown.

Numerical experiments on one-dimensional model of turbulence

The initial-value problem of a forced Burgers equation is numerically solved by the Fourier expansion method. It is found that its solutions finally reach a steady state of 'laminar flow' which has no randomness and is stable to disturbances. Hence, strictly speaking, the so-called Burgers turbulence is not a turbulence. A new one-dimensional model is proposed to simulate the Navier-Stokes turbulence. A series of numerical experiments on this one-dimensional turbulence is made and is successful in obtaining Kolmogorov's (1941) k exp(-5/3) inertial-range spectrum. The (one-dimensional) Kolmogorov constant ranges from 0.5 to 0.65.

The piston model of coronal transients

In the present paper, the piston model of the coronal transient (see Hu. 1983a, b is discssed in detail, and the quantitative results of unsteady gasdynamics are applied to the coronal transient processes. The piston model explains the major features of the transient observations, such as the density profile, the geometric configuration, the kinetic process and the classifications of the coronal transient. Based on the idea of piston model, the bright feature and the dark feature of the transient are the gasdynamical response of the dense plasma ejecting into the corona, and associate with the compressed and rarefied flows, respectively. The quantitative results show that the density increment in the compressed region and the density decrement in the rarefied region are one order of magnitude larger and smaller, respectively, to the density in the quiet corona, it agrees quantitatively with the observations, and both the bright feature and dark feature are explained at the same time.

The wave model of mesothermal plasma near wakes and Korteweg-de Vries equation

The stationary two-dimensional (x, z) near wakes behind a flat-based projectile which moves at a constant mesothermal speed (V∞) along a z-axis in a rarefied, fully ionized, plasma is studied using the wave model previously proposed by one of the authors (VCL). One-fluid theory is used to depict the free expansion of ambient plasma into the vacuum produced behind a fast-moving projectile. This nonstationary, one-dimensional (x, t) flow which is approximated by the K-dV equation can be transformed, through substitution, t=z/V∞, into a stationary two-dimensional (x, z) near wake flow seen by an observer moving with the body velocity (V∞). The initial value problem of the K-dV equation in (x, t) variables is solved by a specially devised numerical method. Comparisons of the present numerical solution for the asymptotically small and large times with available analytical solutions are made and found in satisfactory agreements.