Semi-analytical solution to elastic–plastic contact-impact between a 316 stainless steel rod with truncated cone nose and rigid flat

When subjected to impacts, rods suffer local large deformation and global vibrational deformation along with abrupt kinematic and mechanical response changes. Studies on the responses during impact are beneficial to structural health monitoring. In this study, both kinds of deformation of rods with truncated-cone noses were investigated. A semi-analytical solution describing the vibrational responses of the rod was obtained based on the plastic contact model of the truncated-cone nose against a rigid flat and the one-dimension hypothesis of the rod. The theoretically predicted results agreed well with those calculated by finite element model (FEM), and the scaling law in rod response was theoretically derived and verified by FEM. Besides, the compression degree of the rod with three truncated-cone noses was considered, and the rod nose of lower contact stiffness presented better buffering effects. Finally, the applicability map of the semi-analytical solution was depicted according to the scope of the contact model.