Dynamic Nonlinear Material Behaviour of Thin Shells in Finite Displacements and Rotations

A dynamic analysis of a thin shell finite element undergoing large displacements and rotations is here presented. The constitutive model adopted derives from the coupling of an hyperelastic basic model fulfilling a De Saint Venant-Kirchhoff criterion with a scalar damage function depending on the maximum value of a suitable strain measure attained through the deformation history; then plastic effects are included using an isotropic/kinematic hardening law. A conservative time integration scheme for the non-linear dynamics of the hyperelastic damaged-plastic thin shell is applied. The main characteristic of the scheme is to be conservative, since it allows for the time-discrete system to preserve the basic laws of continuum, namely the balance of the linear and angular momentum as well as the fulfilment of the second law of thermodynamics.