The dominating dimensionless numbers of an elastic-plastic thin plate under dynamic loading

The response of an elastic-plastic thin plate under dynamic loading cannot be solved theoretically since both geometrical and material nonlinearities are involved and also highly coupled. Obviously, the response will be affected by material properties, geometries, and loads, whose effects are usually studied separately. In order to avoid repeated investigations and save costs, identifying the combined dominant dimensionless number must be essential. For a plate under pressure loading, a dominating dimensionless number ξ (referred to as the loading intensity) is proposed based on energy conservation and dimensional analysis. As an input parameter, ξ whose physical meaning denotes the plastic to elastic share (energy ratio and deflection ratio), characterizes the combined effects of structure, material, and load. According to its value, responses could be classified into three cases: elastic deformation (0<ξ<1), elastic-plastic coupling deformation (1≤ξ≤100), and plastic dominating deformation (ξ>100). Furthermore, the dimensionless deflection of elastic-plastic plates could also be predicted, by combination of loading intensity ξ and relative stiffness β. In addition, for plates under other loading conditions, a series of dimensionless numbers are also given. Among them, some numbers have already been investigated by previous researchers, while others are still unconcerned. These numbers are then verified by FEM simulations, and their physical meanings are revealed. Employing these numbers, the analysis of experimental and simulation results will be in a normalized and comparable form. Particularly, it will provide scaling criteria for the dynamic scaling experiments.