Simplified mode solutions for final plastic deformation of circular plates under localized impulsive loading

A general approach for constructing simplified mode solutions for final plastic deformation of circular plates under localized impulsive loading are derived. During construction, the initial modal velocity is calculated by the modal approximation technique. The average strain rate effect is considered by estimating the maximum strain rate field in a circular plate when one-half the initial modal kinetic energy has been dissipated. Once a deformation profile is given, the formula for calculating final plastic deformation considering strain rate effects will be obtained according to the conservation of energy. Firstly, the Bessel deformation profile is selected according to the field equation, the calculated results of the analytical solution are in good agreement with the experimental results. Then the influence of two commonly used parabolic and cosine deformation profiles on the final plastic deformation is discussed. According to the simplified mode solutions, three new dimensionless numbers are proposed, and effective fitting formulas for predicting the final dimensionless plastic deformation are established based on new dimensionless numbers according to a large amount of experimental data. Moreover, the new dimensionless numbers are compared with Nurick's dimensionless number in different loading scenarios to prove that the dimensionless number given in this paper is more reasonable. The research in this paper can provide some reference for the study and evaluation of the dynamic plastic response of circular plates under localized impulsive loading.