Analyse Of Finite Deformations On Hyperelastic Membranes

The research of hyperelastic material is always an important frontier subject in the research of solid mechanics and applied mathematics. Hyperelastic membrane has been received the attention of researchers home and abroad because of its important theoretical significance and engineering background.In this thesis, basic equations of finite deformation theory are introduced and the establishing of the hyperelastic constitutive equations are also discussed. Two basic theoretical framework of the hyperelastic constitutive model are described. According to two kinds of the strain energy function proposed by Gao and Gent respectively, a new strain energy function is proposed.Based on the finite deformation theory, the axisymmetric large deformation problems of hyperelastic membrane are discussed. The governing equation of the tensile hyperelastic membrane with a hole or a rigid inclusion is derived. This axisymmetric large deformation problem is reduced to the two-point boundary value problem differential equations. According to the strain energy function by Gao and the new strain energy function, the differential equations are solved by the shooting method. The numerical solution is obtained. The stress distribution and deformation characteristics of the hyperelastic membrane are also given. The affection of the material constants on the membrane deformation is discussed.The fixed boundary hyperelastic circular membrane is studied. When the membrane applying to symmetrical load in the vertical direction on its surface, membrane will be deformed as the rotation shell structure, which can be analyzed by the non-moment theory. According to the strain energy function given by Gao and the new strain energy function, the basic equations of the membrane in the vertical loads could be given. In order to obtain the value on the boundary of R=0, r=0, these equations would be translate into the form of no R(orr). The equations should be solved by the shooting method. The stress distribution and deformation characteristics of the hyperelastic circular membrane are given and the affection of the material constants is discussed on the membrane deformation.Through the research on the two problems, the new strain energy function is discussed and this strain energy function which has universality and practicability is proved. The results in present paper maybe helpful as a theoretical reference in the production and application of the hyperelastic membrane.