A moving boundary approach of capturing diffusants penetration into rubber: FEM approximation and comparison with laboratory measurements

TL;DR

This paper introduces a moving-boundary finite element model to simulate diffusant penetration into rubber, successfully matching experimental data for both dense and foamed EPDM rubber and analyzing the large-time behavior of diffusion.

Contribution

It presents a novel moving-boundary approach with FEM approximation for modeling diffusant penetration into rubber, including transformation techniques to handle unknown boundary motion.

Findings

Model accurately predicts diffusion depths within experimental range.

The approach is robust across different rubber types.

Numerical estimations of long-term diffusion behavior are provided.

Abstract

We propose a moving-boundary scenario to model the penetration of diffusants into dense and foamed rubbers. The presented modelling approach recovers experimental findings related to the diffusion of cyclohexane and the resulting swelling in a piece of material made of ethylene propylene diene monomer rubber (EPDM). The main challenge is to find out relatively simple model components which can mimic the mechanical behavior of the rubber. Such special structure is identified here so that the computed penetration depths of the diffusant concentration are within the range of experimental measurements. We investigate two cases: a dense rubber and a rubber foam, both made of the same matrix material. After a brief discussion of scaling arguments, we present a finite element approximation of the moving boundary problem. To overcome numerical difficulties due to the \textit{a priori} unknown motion of the diffusants penetration front, we transform the governing model equations from the physical domain with moving unknown boundary to a fixed fictitious domain. We then solve the transformed equations by the finite element method and explore the robustness of our approximations with respect to relevant model parameters. Finally, we discuss numerical estimations of the expected large-time behavior of the material.