Asymmetric Low-Velocity Impact of a Finite Layer

The dynamic indentation of structural elements such as beams and plates continues to be an intriguing problem, especially for scenarios where large area contacts can occur. Standard methods of indentation analysis typically use a dynamic beam theory solution to obtain an overall load-displacement relationship and then a Hertzian contact solution to determine local stresses under the impactor. However, previous static and dynamic modeling efforts have shown that the stress distribution in the contact region will differ significantly from a Hertzian one when the contact length exceeds the thickness of the beam. In such cases point contact can no longer be assumed and Hertzian relationships are no longer valid. The dynamic indentation model presented herein is a first effort to model the asymmetric (i.e., off-center) low-velocity impact problem for elastically supported beams. Numerical results obtained are compared with elementary beam theory solutions for model validation.