A consistently compressible Mooney‐Rivlin model for the vulcanized rubber based on the Penn's experimental data

Based on the Penn's experimental data, a consistently compressible Mooney‐Rivlin model is developed for the vulcanized rubber. First, the Penn's experimental data are re‐analyzed, which show the near incompressibility. Next, the incompressible Mooney‐Rivlin model and three conventional types of compressible model are studied for the vulcanized rubber, which exhibit an apparent inconsistence with the incompressible model due to the dissimilar initial shear modulus. Finally, a consistently compressible model with extra constants is proposed, which obeys the normalization conditions and the consistent conditions, and a procedure to identify model constants is suggested, and then applied to the Penn's experimental data. The consistently compressible Mooney model is eventually established for the vulcanized rubber, and then compared with other four hyper‐elastic models.