Abstract
The transverse spherical impact on an elastic-plastic beam is formulated and investigated herein. Both semi-analytical procedure and finite element (FEM) solution are elaborated. The semi analytical solution combines a finite difference method with the Hertz contact theory. The transient response of impact beams is computed by considering the loaded and unloaded phases. The contact force calculation is based on the model proposed by Stronge. To validate our semi-analytical model, a 3D finite element model has been developed. The comparison between the predictions from the presented semi-analytical and those from the 3D finite element models shows that the semi analytical model achieves very accurate predictions at a marginal computational time.
Highlights
The elastic-plastic impact behavior investigation is a prominent research topic
For 15 to 20m/s of impact velocity with plastic deformation of less than 0.2% throughout the beam we found that the plastic peak is concentrated under the point of impact but it is presented with a value larger than 0. 2% on the other points of the beam
We presented a semi-analytical model combining finite difference method with the Hertz contact theory and the Stronge model
Summary
The elastic-plastic impact behavior investigation is a prominent research topic It is targeted by mechanical engineering researchers, in order to understand the relationship force-indentation of the contact. Zhang et al [10] presented a hybrid, numerical–analytical model for elastic–plastic beam impact system with consideration of global elastic plastic deformation of the beam applied to analyze the transient impact response for low impact velocity. They found that the impact force response is influenced by impact-induced wave propagation and that the model is especially suitable for studying impact-induced wave effects. A more general plasticity integration allowing to take into account the hardening is elaborated, The present model allows obtaining results of elastic plastic deformation especially equivalent plastic strain at integration point (PEEQ) in different zone, and the global deformation behavior of the beam according to low and high velocities
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