A new constitutive model, which is a modification from Gao's second constitutive model, has been introduced by using the finite deformation theory. The new model fulfils the condition that strain energy becomes zero under no deformation. For incompressible polymer rubber materials, when n=1 and a=0, the new constitutive relation may be simplified to the Mooney-Rivlin model; when n=1 and α=1, the new constitutive relation may be simplified to the Neo-Hookean model. The discussions of basic finite deformation examples illustrate how the new constitutive model reasonably describes the deformation properties of polymer rubber materials, and how the applied range of polymer rubber materials have been broadened by using the new constitutive model.
Rubber tubes under pressure can undergo large deformations and exhibit a particular nonlinear elastic behavior. In order to reveal mechanical properties of rubber tubes subjected to internal pressure, large deformation analysis and stability analysis have been proposed in this paper by utilizing a modified Gent's strain energy function. Based on the nonlinear elastic theory, by establishing the theoretical model of a rubber tube under internal pressure, the relationship between the internal pressure and circumferential principal stretch has been deduced. Meanwhile stability analysis of the rubber tube has also been proposed and the relationship between the internal pressure and the internal volume ratio has been achieved. The effects on the deformation by different parameters and the failure reasons of the rubber tube have been discussed, which provided a reasonable reference for the design of rubber tubes.
Polymer membrane structures with voids can be fractured due to larger deformation and stress concentration with the effect of an externally applied load, which can lead to failure localization and crack propagation. With the modified constitutive model from Gao, finite deformation analysis of a polymer membrane containing a void has been researched. By deducing the basic governing equation for solving the problem, the paper figures out the stress distribution of different constitutive parameters and discusses the effects on membrane deformation by different parameters and the reasons for the failure of the membrane. The results show that the constitutive parameter n has a major impact on the mechanical properties of a polymer membrane with a void, which provides a reference for the design of polymer membranes.
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