Smooth static and dynamic indentation of a cantilever beam

The static and dynamic indentation of structural elements such as beams and plates continue to be intriguing problems, especially for scenarios where large area contacts are expected to occur. Standard methods of indentation analyses use a beam theory solution to obtain an overall load–displacement relationship and then a Hertzian contact solution to calculate local stresses under the indenter. However, these techniques are only applicable in a fairly limited class of problems: the stress distribution in the contact region will differ significantly from a Hertzian one when the contact length exceeds the thickness of the beam. The indentation models developed herein are improvements over existing GLOBAL/LOCAL models for static and dynamic indentation of cantilever beams. Maximum contact stresses, beam displacements, and contact force time histories are obtained and compared with the predictions of current static and dynamic indentation models. The validity of the solutions presented herein is further assessed by comparing the results obtained to the predictions of modified beam theory solutions