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Finite element simulation of rubber‐like material behaviour under consideration of its microscopic structure
Author(s) -
Böl M.,
Reese S.
Publication year - 2003
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.200310400
Subject(s) - truss , tetrahedron , finite element method , macro , natural rubber , context (archaeology) , unit (ring theory) , element (criminal law) , computer science , mathematics , materials science , structural engineering , geometry , composite material , engineering , geology , paleontology , programming language , mathematics education , law , political science
The structure of rubber‐like materials is characterized through chain‐like macromolecules which are linked together at certain points. This special design leads to a completely random three‐dimensional network. There exist several ways to specify rubber‐like material behaviour. Many scientists use the tool of statistical mechanics to transfer the information from the micro level to the macro level. In this context, one should mention e.g. the work of Treolar & Riding [1979] (full network theory) or the eight‐chain model suggested by Arruda & Boyce [1]. In the present contribution, the step from the micro level to the macro level is done by means of the finite element method. For this purpose, we derive a unit cell consisting of one three‐dimensional tetrahedral finite element and six truss elements lying on every edge of the tetrahedron. The truss elements represent the material behaviour of a certain group of polymer chains, whereas the tetrahedral elements ensure incompressibility. So, using a finite element model with a sufficiently high number of unit cells, we are able to model the well‐known macro‐mechanical material behaviour of rubber‐like polymers.