Mixtures of binary spheres are numerically simulated using a relaxation algorithm to investigate the effects of volume fraction and size ratio, A complete profile of the packing properties of binary spheres is given. The density curve with respect to the volume fraction has a triangular shape with a peak at 70% large spheres. The density of the mixture increases with the size ratio, but the growth becomes slow in the case of a large size disparity, The volume fraction and size ratio effects are reflected in the height and movement, respectively, of specific peaks in the radial distribution functions. The structure of the mixture is further analyzed in terms of contact types, and the mean coordination number is demonstrated to be primarily affected by ＂large-small＂ contacts. A novel method for estimating the average relative excluded volume for binary spheres by weighting the percentages of contact types is proposed and extended to polydisperse packings of certain size distributions. The method can be applied to explain the density trends of polydisperse mixtures in disordered sphere systems,
Sphericity, as one of the most important shape parameter for non-spherical objects, is extensively applied in evaluating the porosity or packing density of particles. In this paper, the sphericities of common non- spherical objects are deduced and investigated. Maximum sphericities and optimum shapes of these objects are presented as well. A decreasing order of sphericity from sphere （1.0） to regular tetrahedron （0.671） for objects with constant sphericity is given. Similar trends are found in most sphericity-aspect ratio relationships, which exhibit single Peak and the sphericity increases with the growth of aspect ratio before the peak point and decreases afterward. The peak loci of aspect ratio are all around 1.0 which makes the shape approaching to a sphere. The information in the paper could be useful as literature for general application.
Teng Li Shuixiang Li Jian Zhao Peng Lu Lingyi Meng
Random packings of binary mixtures of spheres and spherocylinders with the same volume and the same diameter were simulated by a sphere assembly model and relaxation algorithm. Simulation results show that, independently of the component volume fraction, the mixture packing density increases and then decreases with the growth of the aspect ratio of spherocylinders, and the packing density reaches its maximum at the aspect ratio of 0.35. With the same volume particles, results show that the dependence of the mixture packing density on the volume fraction of spherocylinders is approximately linear. With the same diameter particles, the relationship between the mixture packing density and component volume fraction is also roughly linear for short spherocylinders, but when the aspect ratio of spherocylinders is greater than 1.6, the curves turn convex which means the packing of the mixture can be denser than either the sphere or spherocylinder packing alone. To validate the sphere assembly model and relaxation algorithm, binary mixtures of spheres and random packings of spherocylinders were also simulated. Simulation results show the packing densities of sphere mixtures agree with previous prediction models and the results of spherocylinders correspond with the simulation results in literature.
LU Peng, LI ShuiXiang , ZHAO Jian & MENG LingYi State Key Laboratory for Turbulence and Complex Systems, Department of Mechanics & Aerospace Engineering, College of Engineering, Peking University, Beijing 100871, China
A novel hybrid-stress finite element method is proposed for constructing simple 4-node quadrilateral plane elements, and the new element is denoted as HH4-3fl here. Firstly, the theoretical basis of the traditional hybrid-stress elements, i.e., the Hellinger-Reissner variational principle, is replaced by the Hamilton variational principle, in which the number of the stress variables is reduced from 3 to 2. Secondly, three stress parameters and corresponding trial functions are introduced into the system equations. Thirdly, the displacement fields of the conventional bilinear isoparametric element are employed in the new models. Finally, from the stationary condition, the stress parameters can be expressed in terms of the displacement parameters, and thus the new element stiffness matrices can be obtained. Since the required number of stress variables in the Hamilton variational principle is less than that in the Hellinger-Reissner variational principle, and no additional incompatible displacement modes are considered, the new hybrid-stress element is simpler than the traditional ones. Furthermore, in order to improve the accuracy of the stress solutions, two enhanced post-processing schemes are also proposed for element HH4-3β. Numerical examples show that the proposed model exhibits great improvements in both displacement and stress solutions, implying that the proposed technique is an effective way for developing simple finite element models with high performance.
Song CenTao ZhangChen-Feng LiXiang-Rong FuYu-Qiu Long
To simulate the nonlinear behavior of ferroelectric structures and devices under non-uniform electromechanical loadings,a domain-switching embedded electromechanical finite element method is developed in this paper.Following continuum assumption,the electromechanical behavior of each representative material point can be obtained by averaging the behavior of the local corresponding microstructure,e.g.42 domains used in this work.A new Double Gibbs free energy criterion for domain-switching is proposed to ensure the convergence and stability of the simulations on ferroelectrics under non-uniform field.Several computational examples are given to demonstrate that this nonlinear finite element method can yield reasonable and stable simulation results which can be used to explain some experimental results and assist the design of ferroelectric devices.
