Finite Deformation Analysis Of Hyperelastic Membranes Containing Imperfection

Rubberlike materials are a kind of polymer materials, which have a great amount of superior properties. Due to the ability of being subjected to large deformations, this kind of materials is irreplaceable in engineering. Rubberlike materials are widely used in daily routine, metallurgy, automobile, mechanical engineering, electrical engineering, architectural engineering, petrochemical, light industry, aeronautics, aviation, navigation and other fields. Therefore, the research of rubberlike materials has theoretical significance and engineering values.In the past fifty years, people attempt to find out an authentic description of these materials. Owing to the nonlinear features on physical and geometric properties inherently, the work of building an accurate constitutive model becomes very difficult. Thus, the invention and application of computer renders the solution of mechanical problem efficient by using computer program. The solution always depends on the description of materials'mechanical property. Hence, the introduction of appropriate constitutive model is a vital problem of theoretical research on solid mechanics.A new constitutive model which is modified from Gao's second constitutive model has been introduced by using the finite deformation theory. New model fulfill that strain energy under no deformation becomes zero. In the circumstance that material is incompressible, when n = 1andα= 0, the new constitutive relation may be simplified to Mooney-Rivlin model; when n = 1andα=1, the new constitutive relation may be simplified to Neo-Hookean model. The discussions of basic finite deformation examples illustrate remarkable features that new model describe the deformation property of hyperelastic materials reasonably. And it set to broaden the range of applications.Linking with the process of manufacturing, holes or rigid inclusions emerge in the molding process of hyperelastic membranes as a result of residual catalysts and impurities. These kinds of macro defects have a significant impact on the mechanical properties of membrane. The new constitutive relation has been utilized to resolve two kinds of problems.In the first case, the issue of incompressible membrane under axisymmetric stretch has been investigated. At that time, membrane contains a hole or a rigid inclusion. The governing equations have been obtained and numerical solutions illustrate how constitutive parameters affect the distribution of stress and deformation. In certain circumstances, the phenomenon of localized wrinkling is revealed near the inner edge of the hole.In another case, the issue of incompressible membrane under vertical pressure has been studied. As the result of symmetrical load and structure, the membrane is transformed into a rotating shell. The distribution of vertical displacement and stress are obtained under different constitutive parameters and external force.These conclusions may provide theoretical references to practical problems about rubberlike materials.