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Voronoi cell finite element model based on micropolar theory of thermoelasticity for heterogeneous materials
Author(s) -
Ghosh Somnath,
Liu Yunshan
Publication year - 1995
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.1620380808
Subject(s) - voronoi diagram , finite element method , discretization , thermoelastic damping , centroidal voronoi tessellation , mathematics , mixed finite element method , phase (matter) , extended finite element method , mathematical analysis , geometry , structural engineering , thermal , physics , engineering , thermodynamics , quantum mechanics
In this paper, a new ‘Voronoi cell finite element model’ is developed for solving steady‐state heat conduction and micropolar thermoelastic stress analysis problems in arbitrary heterogeneous materials. The method is based on the natural discretization of a multiple phase domain into basic structural elements by Dirichlet Tessellation . Tessellation process results in a network of polygons called Voronoi polygons. In this paper, formulations are developed for treating these polygons as elements in a finite element mesh. Furthermore, a composite Voronoi cell finite element model is developed to account for the presence of a second phase inclusion within a polygonal element. Various numerical examples are executed for validating the effectiveness of this model in the analysis of the temperature and stress fields for micropolar elastic materials. Effective material properties are derived for microstructures containing different distributions of second phase.