The dynamic behaviour of elastic-plastic structures is much more difficult to predict in comparison with the corresponding quasi-static one because of complicated loading conditions and the effect of inertia. By assuming that the quasi-static structural and interface behaviour of a structure is specified, its dynamic deformation mode is similar to the quasi-static one and the material is strain-rate insensitive, two mechanical models, namely the Stick Model and Non-Stick Model, are proposed in order to predict the dynamic behaviour of the structure under a rigid-body impact. Each model contains two lumped masses and two inelastic springs. While spring [circled 2] represents the highly non-linear and in-elastic mechanical property of the interface between the structure and the striker, s...[ Read more ]

The dynamic behaviour of elastic-plastic structures is much more difficult to predict in comparison with the corresponding quasi-static one because of complicated loading conditions and the effect of inertia. By assuming that the quasi-static structural and interface behaviour of a structure is specified, its dynamic deformation mode is similar to the quasi-static one and the material is strain-rate insensitive, two mechanical models, namely the Stick Model and Non-Stick Model, are proposed in order to predict the dynamic behaviour of the structure under a rigid-body impact. Each model contains two lumped masses and two inelastic springs. While spring [circled 2] represents the highly non-linear and in-elastic mechanical property of the interface between the structure and the striker, spring [circled 1] represents the elastic-plastic behaviour of the structure, no matter the latter displays hardening, perfectly plastic or softening in the plastic range. The inertial effect of the structure is represented by an equivalent mass in both models. With the complicated deformation history involving loading, unloading and reversed loading being taken into account, the large dynamic deformation process can be completely simulated and the final deformation can be predicted by these models. A number of numerical examples are given to demonstrate the effects of the mass ratio, energy ratio, structural stiffness/local rigidity and the hardening/softening factor on the maximum and final deformations of the mechanical models. Finally, to verify the validity of the mechanical models proposed for real structures, impact tests on simply supported beams and type II structures, which were structural hardening and softening respectively, were investigated. Good agreements between the theoretical and experimental results indicates that the Stick and Non-Stick Models are reasonable and successful.