Allport, John and Day, A. J. (1996) Statistical Mechanics Material Model for the Constitutive Modelling of Elastomeric Compounds. Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, 210 (6). pp. 575-585. ISSN 0954-4062

Material models for the finite element analysis (FEA) of polymeric and elastomeric compounds are only available in limited form in most commercial finite element (FE) packages. The most common are the phenomenological Mooney-Rivlin and the Ogden models, for which the constants bear no relationship to the physical or chemical characteristics of the rubber and their derivation is difficult. Both models are limited in their accuracy for filled rubbers used in combined states of tensile and compressive deformation, and since these are common operational conditions for engineering components such as drive couplings, engine mounts and torsional vibration dampers, their use in engineering analyses is restricted.
In this paper a statistical mechanics material modelling approach for synthetic, filled elastomeric compounds in FEA is presented. Using styrene-butadiene rubber (SBR) as an example, the theory and its application in the commercially available ABAQUS finite element analysis program is explained. FE models of tensile and compressive specimens in two and three dimensions are used to demonstrate the use of the model, and results are presented, discussed and compared with measured data. Good correlation in both tension and compression is demonstrated. A practical application of the model to the SBR blocks in a Holset torsional drive coupling is presented; this analysis involves complex issues of mesh design and contact modelling. The results show good agreement with measured performance, and clearly demonstrate how this type of material modelling approach can be effectively used in the computer aided engineering and design of engineering rubber components.

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