Modified virtual internal bond model based on deformable Voronoi particles  

作　　者：Oleg Konovalov Shunying Ji Michael Zhuravkov 

机构地区：[1]Research Laboratory of Information Technologies and Computer Graphics,Belarusian State University,Minsk 220030,Belarus [2]DUT-BSU Joint Institute,Dalian University of Technology,Dalian 116023,China [3]State Key Laboratory of Structural Analysis for Industrial Equipment,Dalian University of Technology,Dalian 116023,China [4]Department of Theoretical and Applied Mechanics,Belarusian State University,Minsk 220030,Belarus

出　　处：《Theoretical & Applied Mechanics Letters》2020年第2期87-91,共5页力学快报（英文版）

摘　　要：In last time,the series of virtual internal bond model was proposed for solving rock mechanics problems.In these models,the rock continuum is considered as a structure of discrete particles connected by normal and shear springs(bonds).It is well announced that the normal springs structure corresponds to a linear elastic solid with a fixed Poisson ratio,namely,0.25 for threedimensional cases.So the shear springs used to represent the diversity of the Poisson ratio.However,the shearing force calculation is not rotationally invariant and it produce difficulties in application of these models for rock mechanics problems with sufficient displacements.In this letter,we proposed the approach to support the diversity of the Poisson ratio that based on usage of deformable Voronoi cells as set of particles.The edges of dual Delaunay tetrahedralization are considered as structure of normal springs(bonds).The movements of particle’s centers lead to deformation of tetrahedrals and as result to deformation of Voronoi cells.For each bond,there are the corresponded dual face of some Voronoi cell.We can consider the normal bond as some beam and in this case,the appropriate face of Voronoi cell will be a cross section of this beam.If during deformation the Voronoi face was expand,then,according Poisson effect,the length of bond should be decrees.The above mechanism was numerically investigated and we shown that it is acceptable for simulation of elastic behavior in 0.1–0.3 interval of Poisson ratio.Unexpected surprise is that proposed approach give possibility to simulate auxetic materials with negative Poisson’s ratio in interval from–0.5 to–0.1.

关 键 词：Discrete element method Real multi-dimensional INTERNAL bond VORONOI TESSELLATION MICROMECHANICAL poisson ratio Barycentric COORDINATES AUXETIC effects 

分 类 号：O29[理学—应用数学] TU45[理学—数学]