Accounting for shape factor effects in Ogden-Hill elastomeric foam model

Abstract

Abstract A framework for the determination of shape-factor dependent parameters in the constitutive models of elastomeric foams, to account for the shape factor effect in quasi-static pressure-strain response of elastomeric foam isolators, is presented. The methodology is an empirical-based method which is applied to the Ogden-Hill foam model. There is no information or model in the literature to account for the shape factor effect on mechanical behaviour of elastomeric foams. Also, none of the existing models of elastomeric foam including Ogden-Hill model are able to predict accurately the pressure-strain response of vibrational isolation systems designed with elastomeric foam isolator pads/strips of different sizes or shape factors. The reason is that all the parameters in such models are a function of material intrinsic property alone which have constant values irrespective of the size of the pads/strips. Therefore, the aim of this study is to derive a set of empirical shape factor dependent parametric functions μ ( s ) and β ( s ) , and to apply them instead of constant parameters μ and β in Ogden-Hill model. This will enable the model to take the shape factor (s) of the pads/strips into account when predicting the pressure-strain response of an elastomeric foam-based system. The study involved testing of polyurethane (PU) pads/strip samples of different sizes and densities (160, 270 and 385 kg/m 3 ) at a displacement rate of 5 mm/min up to 30% compressive strain. Analysis of the measured data showed that the static stiffness of an elastomeric foam-based system increases under a constant compressive load when the shape factor of the pads/strips increases. This implies that the compression modulus of such systems should be a function of both intrinsic material property and shape factor. The test results show that μ ( s ) and β ( s ) are nonlinear functions of the shape factor. The predictions using the derived shape factor-dependent parameters in Ogden-Hill model show good agreement with the measured pressure-strain response of the tested pads/strips. They show that the accuracy of the predicted pressure at, for example, 15% strain is higher than 90% for most of the samples. • Shape factor independent parameters μ and β in Ogden-Hill model give large errors. • Errors minimised by use of shape factor dependent material parameters μ ( s ) and β ( s ) • Derivation of μ ( s ) and β ( s ) from compression stress-strain data of different samples. • Polyurethane pads of different shape factors and densities tested up to 30% strain. • Prediction errors of Ogden-Hill model using μ ( s ) and β ( s ) mostly less than 10%.