Existence theorems in intrinsic nonlinear elasticity

Existence theorems in intrinsic nonlinear elasticity

We first show how the displacement-traction problem of nonlinear three-dimensional elasticity can be recast either as a boundary value problem or as a minimization problem over a Banach manifold, where the unknown is the Cauchy-Green strain tensor instead of the deformation as is customary. We then consider the pure displacement problem, and we show that, under appropriate smoothness assumption...

Existence Theorems for a Class of Problems in Nonlinear Elasticity: Equilibrium of Incompressible Hyperelastic Bodies

Existence of Minimizers and Microstructure in Nonlinear Elasticity

In this paper, the existence of a solution in the form of a minimizer or microstructure is established for the boundary value problems of nonlinear elasticity with certain nonconvex stored energy functions such as those of St. Venant-Kirchhoff type materials. Necessary and sufficient conditions for minimizing sequences of the potential energy to converge to a minimizer or to microstructure are ...

Existence Theorems for a Class of Problems in Nonlinear Elasticity Ii. Analysis of a Model Problem of Finite Plane Strain

Mechanical Interpretation of Existence Theorems in a Nonlinear Dirichlet Problem

The existence of radial solutions of a nonlinear Dirichlet problem in a ball is translated to the language of Mechanics, i.e. to requirements on the time of motion of a particle in an external potential and under the action of a viscosity force. This approach reproduces existing theorems and, in principle, provides a method for the analysis of the general case. Examples of new theorems are give...