Necessary conditions for a minimum at a radial cavitating singularity in nonlinear elasticity
Neumann problem for one-dimensional nonlinear thermoelasticity
The global existence theorem of classical solutions for one-dimensional nonlinear thermoelasticity is proved for small and smooth initial data in the case of a bounded reference configuration for a homogeneous medium, considering the Neumann type boundary conditions: traction free and insulated. Moreover, the asymptotic behaviour of solutions is investigated.
Non-classical phase transitions at a sonic point.
Nonlinear flexural excitations and drill-string dynamics.
Non-polyconvexity of the stored energy function of a Saint Venant-Kirchhoff material
A direct proof of the non-polyconvexity of the stored energy function of a Saint Venant-Kirchhoff material is given by means of a simple counter-example.
Note on a mixed variational principle in finite elasticity
In the present context the variation is performed keeping the deformed configuration fixed while a suitable material stress tensor and the material coordinates are required to vary independently. The variational principle turns out to be equivalent to an equilibrium problem of placements and tractions prescribed at the boundary of a body of finite extent.
Numerical modelling of semi-coercive beam problem with unilateral elastic subsoil of Winkler's type
A non-linear semi-coercive beam problem is solved in this article. Suitable numerical methods are presented and their uniform convergence properties with respect to the finite element discretization parameter are proved here. The methods are based on the minimization of the total energy functional, where the descent directions of the functional are searched by solving the linear problems with a beam on bilateral elastic ``springs''. The influence of external loads on the convergence properties is...