Investigation of the Variants of Independent Elastic Constants of Rigid Polyurethane Foams with Symmetry Elements

Rigid PU foams have wide practical applications, and their mathematical modelling would benefit from deeper knowledge about the variants of independent elastic constants of symmetric PU foams. Therefore, in this study, various symmetry elements of rigid PU foams were analysed in relation to the characteristics of production moulds and technologies. The generalised Hooke's law was considered together with additional relationships valid for certain types of symmetry. Variants of independent elastic constants were determined for orthotropic, orthotropic with a rotational symmetry, and isotropic PU foams. For transtropic PU foams, nine variants of independent elastic constants were identified and corresponding equations for the components of response strain tensor were derived. Then, in order to investigate the results provided by the 9 variants, 12 elastic constants were determined experimentally in compression and shear for free-rise, rigid, and quasi-transtropic PU foams with average densities of 34 kg/m3, 55 kg/m3, and 75 kg/m3. Based on the analysis of (a) measurement uncertainties and (b) satisfying of the transtropy equations, an assessment was made of the correspondence of the experimentally determined elastic constants to the constants of a perfectly transtropic material. This made it possible to identify variants of independent constants that ensure the best correspondence between the calculated strains and the set of average strains.