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UBC Theses and Dissertations

Mathematical models of an elastomeric material for non-uniform and multiaxial deformation conditions Li, Dan


The goal of this research project is to develop mathematical constitutive models to predict the stable mechanical behaviour of elastomeric materials for non-uniform and/or multiaxial deformation conditions at low or medium strain (<100%) and with a low strain rate. This study required a series of characterization tests for elastomers in standard deformations modes. These experimental data were used to fit the standard Mooney- Rivlin strain energy function. A series of characterization tests for a silicone elastomer were completed at UBC and correlated to material characterization data provided by Ballard Power Systems, Inc. The experimental data showed that material response changes with the maximum strain experienced and deformation mode. The material constants in the Mooney-Rivlin strain energy function were fitted by regression analysis according to the results of the characterization tests. For each individual strain level and deformation mode, the resulting material constants are unique. A constitutive model was developed by applying the standard Mooney-Rivlin constitutive model with novel techniques incorporating the maximum strain experienced and the deformation mode. The techniques are a non-uniform strain and a strain partitioning technique. The non-uniform strain technique was expected to give better results for a component experiencing non-uniform strain conditions. The strain partitioning technique eliminates the need of determining the deformation mode before an analysis. Together, these techniques were expected to provide more realistic deformation predictions for elastomeric materials experiencing non-uniform and multiaxial deformation. Two mechanical tests were designed to provide the data necessary to validate the non-uniform strain and strain partitioning techniques. The first test, a tapered dogbone sample, exhibited varying amounts of uniaxial tension deformation within the gauge-length area, when stretched. The second test, a cross sample, exhibited varying multiaxial deformations when loaded in two perpendicular directions with different amounts of displacements. The predictions from the mechanical models incorporating the proposed constitutive models as an input agree with experimental data in these two tests, which validates the applicability of the proposed techniques. These techniques will aid in understanding the stable response of elastomeric materials used for seals in fuel cells. Developing an improved understanding of the deformation response will help in predicting seal integrity and improve the overall reliability of PEM fuel cells.

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