Three-Dimensional CA-LBM Model of Silicon Facet Formation during Directional Solidification

A new 3D cellular automata-lattice Boltzmann method (CA-LBM) coupling model is proposed to simulate the formation of facet and facet dendrites in directional solidification. In this model, the CA method is used to simulate the crystal growth process and the LBM method is used to simulate the physical field in the calculation area. A new three-dimensional anisotropic function is introduced, and the model is modified by interpolation and neighborhood restriction. We add the remelting calculation model. The interaction between interface energy anisotropy and dynamic anisotropy is solved reasonably. The growth process and morphology of small plane and small plane dendrites were simulated.

Extension of mathematical background for Nearest Neighbour Analysis in three-dimensional space

Proceeding deals with development and testing of the module for GRASS GIS [1], based on Nearest Neighbour Analysis. This method can be useful for assessing whether points located in area of interest are distributed randomly, in clusters or separately. The main principle of the method consists of comparing observed average distance between the nearest neighbours r A to average distance between the nearest neighbours r E that is expected in case of randomly distributed points. The result should be statistically tested. The method for two- or three-dimensional space differs in way how to compute r E . Proceeding also describes extension of mathematical background deriving standard deviation of r E , needed in statistical test of analysis result. As disposition of phenomena (e.g. distribution of birds’ nests or plant species) and test results suggest, anisotropic function would repre- sent relationships between points in three-dimensional space better than isotropic function that was used in this work.

Homogenized Elastic-Viscoplastic Behavior of Anisotropic Open-Porous Bodies

This lecture presents constitutive modeling of the homogenized elastic-viscoplastic behavior of pore-pressurized anisotropic open-porous bodies. The base solids are assumed to be metallic materials at small strains and rotations. First, by describing micro-macro relations relevant to periodic unit cells of anisotropic open-porous bodies with pore pressure, constitutive features are discussed for the viscoplastic macrostrain rate in steady states. Second, on the basis of the constitutive features found, the viscoplastic macrostrain rate is represented as an anisotropic function of Terzaghi’s effective stress. Third, the resulting viscoplastic equation is used to simulate the homogenized elastic-viscoplastic behavior of an ultrafine plate-fin structure and a thick perforated plate subjected to macroscopic loading in the absence and presence of pore pressure. The corresponding FE homogenization analysis is performed for comparison to validate the developed viscoplastic equation.