Lagzdiņš Aivars, Beverte Ilze, Skruls Vilis, Andersons Jānis
Institute for Mechanics of Materials, University of Latvia, 3 Jelgavas St., LV-1004 Riga, Latvia.
Polymers (Basel). 2025 Sep 8;17(17):2431. doi: 10.3390/polym17172431.
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/m, 55 kg/m, and 75 kg/m. 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.
硬质聚氨酯泡沫具有广泛的实际应用，其数学建模将受益于对对称聚氨酯泡沫独立弹性常数变体的更深入了解。因此，在本研究中，分析了硬质聚氨酯泡沫的各种对称元素与生产模具和技术特性的关系。考虑了广义胡克定律以及对某些对称类型有效的附加关系。确定了正交各向异性、具有旋转对称性的正交各向异性和各向同性聚氨酯泡沫的独立弹性常数变体。对于准各向异性聚氨酯泡沫，确定了九个独立弹性常数变体，并推导了响应应变张量分量的相应方程。然后，为了研究这九个变体提供的结果，对平均密度分别为34 kg/m、55 kg/m和75 kg/m的自由发泡、硬质和准各向异性聚氨酯泡沫进行了压缩和剪切实验，测定了12个弹性常数。基于对（a）测量不确定度和（b）准各向异性方程满足情况的分析，对实验测定的弹性常数与理想准各向异性材料常数的对应关系进行了评估。这使得能够识别出能确保计算应变与平均应变集之间最佳对应关系的独立常数变体。
