Dynamic inflation of non‐linear elastic and viscoelastic rubber‐like membranes

On Axisymmetrjc Deformations of Nonlinear Viscoelastic Membranes

In previous work it was shown that a class of axisymmetric viscoelastic membrane problems can be reduced to the numerical solution of a system of partial differential-Volterra integral equations. This general method has the disadvantage that a change in constitutive equation requires rederivation of specific details of the governing system. In this paper, a revised method is presented in which ...

Nonlinear analysis of oscillatory indentation in elastic and viscoelastic solids.

Determining the mechanical properties at micro- and nanometer length scales using nanoindentation or atomic force microscopy is important to many areas of science and engineering. Here we establish equations for obtaining storage and loss modulus from oscillatory indentations by performing a nonlinear analysis of conical and spherical indentation in elastic and viscoelastic solids. We show that...

Nonlinear Dynamic Analysis of Viscoelastic Membranes Described with Fractional Differential Models

The dynamic response of an initially flat viscoelastic membrane is investigated. The viscoelastic model is described with fractional order derivatives. The membrane is subjected to surface transverse and inplane dynamic loads. The governing equations are three coupled second order nonlinear partial FDEs (fractional differential equations) of hyperbolic type in terms of the displacement componen...

Some Optimization Problems for Nonlinear Elastic Membranes

These types of optimization problems have been considered in the literature due to many applications in science and engineering, specially in the linear case p = 2. See for instance [5]. In recent years, models involving the p−Laplacian operator with nonlinear boundary conditions have been used in the theory of quasiregular and quasiconformal mappings in Riemannian manifolds with boundary (see ...

Dynamic Deformation of Axially Symmetric Elastic Membranes