Open AccessPolygonal finite elements for three-dimensional Voronoi-cell-based discretisations
Author(s) -
K. Jayabal,
Andreas Menzel
Publication year - 2012
Publication title -
european journal of computational mechanics
Language(s) - English
Resource type - Journals
eISSN - 2642-2085
pISSN - 2642-2050
DOI - 10.13052/17797179.2012.702432
Subject(s) - voronoi diagram , hexahedron , finite element method , discretization , stiffness matrix , tetrahedron , mathematics , mixed finite element method , stiffness , matrix (chemical analysis) , geometry , mathematical analysis , structural engineering , engineering , materials science , composite material
Hybrid finite element formulations in combination with Voronoi-cell-based discretisation methods can efficiently be used to model the behaviour of polycrystalline materials. Randomly generated three-dimensional Voronoi polygonal elements with varying numbers of surfaces and corners in general better approximate the geometry of polycrystalline microor rather grain-structures than the standard tetrahedral and hexahedral finite elements. In this work, the application of a polygonal finite element formulation to three-dimensional elastomechanical problems is elaborated with special emphasis on the numerical implementation of the method and the construction of the element stiffness matrix. A specific property of Voronoi-based discretisations in combination with a hybrid finite element approach is investigated. The applicability of the framework established is demonstrated by means of representative numerical examples.