Session: 07-23-01: 100th Anniversary of the Timoshenko-Ehrenfest Beam Model

Paper Number: 97083

97083 - Transverse Impact of Fibers by a High Velocity Projectile in Elastic and Elastic-Plastic Contact Regimes 

High velocity impact of rigid projectiles has been used to investigate energy absorption behavior new fiber material formulations such as CNT bundles. Interaction of the fiber with the projectile can be modeled by using the finite element (FE) method to determine material properties based on experimental results, but this approach comes with a heavy computational burden. In this work, we study the transverse impact between a spherical projectile and a long deformable fiber, theoretically. This approach yields faster solutions as compared to a dynamic contact analysis conducted by using a commercially available FE package, and also provides an indepth physical interpretation. The projectile is treated as a rigid particle, and the slender fiber is assumed to be elastic, homogeneous, and isotropic with both ends fixed. Three models of the dynamics of the fiber are compared: tensioned-string model, and Euler-Bernoulli and Timoshenko beam models. Timoshenko himself presented an analytical solution for a similar problem by treating the impact as a quasistatic Hertzian contact. His general approach is adopted in this work in modified form. This approach requires a high number of modes for a fully converged solution to this impact problem. A numerically stable solution to solve the dispersion relation is presented, which allows improving the fidelity of high-frequency content of the solution. The present work considers both elastic and the elastic-plastic contact cases, thus allows for relatively higher impact velocities. An elastic-perfectly-plastic (EPP) contact is presented by using a contact model that considers the effects of sink-in, pile-up, and the variation of contact pressure in different plastic regimes. This model is tested against existing similar EPP contact models. The transient response of the impacting bodies, the wave propagation after impact, and the reflected waves from the boundaries using different models are investigated in detail. Time history of contact force and transverse deflection show that depending on the parameters, the projectile can make single or multiple impacts with the string. The coefficient of restitution (COR), defined as the ratio between the particle velocity after permanent separation and the impact velocity, is studied by using various pairs of structure and contact models. Plotted against the mass ratio, the COR displays distinct characteristics in single- and multiple-contact regimes. The effects of material-model on this behavior is presented. The result of the analysis can be used to determine material properties of novel fiber materials and also can shed light on the interpretation of experimental results. 

Presenting Author: Sinan Muftu Northeastern University

Presenting Author Biography: Sinan Muftu is a Professor of Mechanical Engineering at Northeastern University in Boston, MA

Authors:

Sinan Muftu Northeastern University
Runyang Zhang Northeastern University