In this study, based on the pressure blister test technique, a theoretical study on the synchronous characterization of surface and interfacial mechanical properties of thin-film/substrate systems with residual stress was presented, where the problem of axisymmetric deformation of a blistering film with initial stress was analytically solved and its closed-form solution was presented. The expressions to determine Poisson's ratios, Young's modulus, and residual stress of surface thin films were derived; the work done by the applied external load and the elastic energy stored in the blistering thin film were analyzed in detail and their expressions were derived; and the interfacial adhesion energy released per unit delamination area of thin-film/substrate (i.e., energy release rate) was finally presented. The synchronous characterization technique presented here has theoretically made a big step forward, due to the consideration for the residual stress in surface thin films.

https://www.mdpi.com/2073-4360/10/1/49/pdf

Theoretical Study on Synchronous Characterization of Surface and Interfacial Mechanical Properties of Thin-Film/Substrate Systems with Residual Stress Based on Pressure Blister Test Technique

In this paper, the problem of large pure bending deformations of membrane is considered. The membrane is a sector of torus with a closed cross-section. This membrane is called a curved tube for short. We consider the homogenous, incompressible, isotropic and hyperelastic material. The external load is a constant pressure and bending couples acting at the edges. The equilibrium equations reduce to ordinary differential equations. As an example, the membrane with a constant thickness and with a circular cross-section is investigated.

http://am.ippt.pan.pl/am/article/viewFile/422/pdf

Large bending deformations of pressurized curved tubes

The problem of the inflation of a curved tube for large elastic strains using a nonlinear membrane theory is investigated. This problem is the special case of a pure bending. The boundary-value problem reduces to a system of ordinary differential equations with periodical boundary conditions. Tubes with an elliptical cross-section are considered. To describe mechanical properties of tubes a neo-Hookean incompressible material model is used. The dependence between the pressure and the curvature of the deformed curved tube is obtained. The influence of the cross-section on this dependence is analyzed.

The finite inflation of a curved elastic tube

The problem of axisymmetric deformation of a peripherally fixed and uniformly loaded circular membrane under deflection restrictions (by a frictionless horizontal rigid plate) was analytically solved, where the assumption of constant membrane stress adopted in the existing work was given up, and a closed-form solution of this problem was presented for the first time. The numerical analysis shows that the closed-form solution presented here has higher calculation accuracy than the existing approximate solution.

/pdf/closed-form-solution-of-a-peripherally-fixed-circular-22qbxl7qch.pdf

Closed-Form Solution of a Peripherally Fixed Circular Membrane under Uniformly Distributed Transverse Loads and Deflection Restrictions

https://elib.bsu.by/bitstream/123456789/56552/1/131-133.pdf

Aspiration of a nonlinear elastic spherical membrane

We consider the large bending of a thin-walled cylinder made of a rubberlike material. It is loaded by internal pressure and bending moments at the ends. The exact formulation of the problem is given within the framework of the nonlinear membrane theory taking into account large strains of the cylinder. Using the special substitution describing the pure bending of the cylinder, the problem is reduced to the system of nonlinear ordinary differential equations. The latter is solved numerically. We establish that there exists the limit value of the bending moment, which depends essentially upon the internal pressure. As an example, the Mooney-Rivlin material is considered. On the base of the calculations we propose the approximate formulae describing the bending moment dependence on the axis curvature of the cylinder and the ultimate bending moment dependence on the internal pressure.

Large bending deformations of a cylindrical membrane with internal pressure

In this work the effect of the unbending of a curved tube under a uniform normal pressure is investigated. The problem is considered within the framework of the nonlinear membrane theory. It is shown that the inflation of a curved tube is the special case of pure bending. The tube with a circular cross section made of a Mooney-Rivlin material is studied numerically. The dependencies between the curvature of the centerline of deformed curved tube and the internal pressure are obtained. It is found that there are the maximum pressures for the considered materials.

Alexei M. Kolesnikov

Papers

Large bending deformations of a cylindrical membrane with internal pressure

Unbending of Curved Tube by Internal Pressure