The Analysis On Finite Deformation Of The Rubber Cylindrical Tube And The Membrane Inflatable Tube

The rubber cylindrical tube and the membrane inflatable tube have received the attention of researchers at home and abroad because of their important theoretical significance and engineering background.In this paper, based on a kind of strain energy function proposed by Y. C. Gao and adopted an universal deformation model, an incompressible rubber cylindrical tube or cylinder subjected to all kinds of loads is theoretically analyzed firstly. The fact shows that the large shearing strain can't be gained only through a moment for the cylinder, and it must need a compressive force on the free surface, otherwise the cylinder will be stretched. As we all know, it is much different from the case of small deformation.In addition, an incompressible inflatable tube consisting of the isotropic material under expanding process is also studied according to the same strain energy function .The analytic relationships between internal pressure and the principal stretches are also obtained respectively and meanwhile ,the influences of constitutive parameter on the relationships are given. When the constitutive parameters a and n are equal toμ/2(whereμis the shear modulus) and 1 respectively, the results are the same as these in the reference. At the same time, a membrane inflatable tube which is under plane strain is considered as well.Thirdly, an compressible inflatable tube consisting of the isotropic material under plane strain is also examined. According to introducing the concept of Poisson function, a bulk controllable relationship of the inflatable tube is obtained, furthermore a explicit function relationship between internal pressure and the principal stretch is also acquired. When the Poisson's ratio is equal to 0.5, the incompressible case can be given. At the same time, the constitutive parameter n and Poisson's ratioγ₀ have important influences on the explicit functionrelationship.In the end, a membrane inflatable tube consisting of transversely isotropic material is also analyzed.The results in present paper may be helpful as a theoretical reference in the production and application of the rubber cylindrical tube and the membrane inflatable tube.