Nonlinear Elastic Deformations

Nonlinear axisymmetric deformations of an elastic tube under external pressure

Nonlinear Electroelastic Deformations

Electro-sensitive (ES) elastomers form a class of smart materials whose mechanical properties can be changed rapidly by the application of an electric field. These materials have attracted considerable interest recently because of their potential for providing relatively cheap and light replacements for mechanical devices, such as actuators, and also for the development of artificial muscles. I...

Decomposition of the deformations of a thin shell. Nonlinear elastic models

We investigate the behavior of the deformations of a thin shell, whose thickness δ tends to zero, through a decomposition technique of these deformations. The terms of the decomposition of a deformation v are estimated in terms of the L-norm of the distance from ∇v to SO(3). This permits in particular to derive accurate nonlinear Korn’s inequalities for shells (or plates). Then we use this deco...

Localized and extended deformations of elastic shells.

The dried raisin, the crushed soda can, and the collapsed bicycle inner tube exemplify the nonlinear mechanical response of naturally curved elastic surfaces with different intrinsic curvatures to a variety of different external loads. To understand the formation and evolution of these features in a minimal setting, we consider a simple assay: the response of curved surfaces to point indentatio...

Nonlinear electroelastic deformations of dielectric elastomer composites_ II — Non-Gaussian elastic dielectrics

This paper presents an analytical framework to construct approximate homogenization solutions for the macroscopic elastic dielectric response — under finite deformations and finite electric fields — of dielectric elastomer composites with two-phase isotropic particulate microstructures. The central idea consists in employing the homogenization solution derived in Part I of this work for ideal e...