Finite element modelling of rubber-like polymers based on chain statistics

Abstract

In this work finite element simulations are conducted based on the micro structure of polymers in order to transfer the information of the micro level to the macro level. The micro structure of polymers is characterized by chain-like macromolecules linked together at certain points. In this way an irregular three-dimensional network is formed. Many authors use the tool of statistical mechanics to describe the deformation behaviour of the entire network. Most of these concepts can be reformulated as traditional continuum mechanical formulations. They are, however, restricted to affine deformation, regular chain arrangements and purely elastic material behaviour. For this reason, in the present contribution, we propose a new finite element-based simulation method for polymer networks which enables us to include non-affinity and arbitrary chain configurations. It can be easily extended to include chain breakage and reconnection. The polymer structure to be investigated, e.g. a rubber boot or a seal, is discretized by means of tetrahedral elements. To each edge of a tetrahedral element one truss element is attached which models the force–stretch behaviour of a bundle of polymer chains. Each of these tetrahedral unit cells represents the micro mechanical material behaviour in a certain point of the network. The proposed method provides the possibility to observe how changes at the microscopic level influence the macroscopic material behaviour. Such information is especially valuable for the polymer industry.