Premium
Simulation of particle filled polymer networks based on chain statistics under consideration of the Mullins effect
Author(s) -
Böl Markus,
Reese Stefanie
Publication year - 2004
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.200410102
Subject(s) - truss , materials science , stiffness , softening point , natural rubber , finite element method , composite material , polymer , particle (ecology) , elastomer , stiffness matrix , breakage , structural engineering , engineering , oceanography , geology
It is well‐known, that adding amounts of fine particular fillers, such as carbon black, to a polymer matrix can significantly influence the stiffness and the strength of the whole material. Many authors produced important contributions of trying to understand the mechanism of filled rubber. Maybe the most cited models is the Guth‐Gold model [2]. The above described phenomenon is investigated here using the tool of statistical mechanics. We propose in the present contribution a finite element approach which enables us to include for instance non‐affinity, (near‐)incompressibility, inelasticity, non‐Gaussian chain statistics as well as the material behaviour of filled polymers. Therefore special unit cells, consisting of one tetrahedron and six truss elements, have been used. Crucial point of this approach is the fact, that in the truss elements the micromechanical material behaviour of a single chain is implemented. The tetrahedron element provides for (near‐)incompressibility of the material, for more details see Böl & Reese [1]. Putting arbitrary configurations of such unit cells randomly together allows us to simulate complex structures of unfilled materials. To calculate systems consisting of filled materials, in the above described matrix material fine particular fillers in form of finite elements are included to take care for the increasing of the stiffness and the strength of the whole material. Rubber‐like materials and especially filled rubber‐like materials under cyclic loading are characterized through stress‐softening phenomenon, commonly known as the Mullins' effect. This effect is the consequence of chain breakage inside the material. Many models have been developed to simulate this material behaviour, e.g. the ones of Marckmann et al . [3] and Ogden & Roxburgh [5]. In the present proposal this softening effect is analyzed from the physical point of view. Direct comparisons with experimental data suggest that the new approach generates satisfying predictions, particularly for large strain deformations. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)