Waves in elastic bars under axial constant velocity loading

Abstract

Elastic bars serve as primary mechanical members, spanning from atomic to macroscopic scales. The development of theoretical frameworks for elastic bars is crucial for guiding a wide array of industrial and everyday applications. In this study, we comprehensively investigate wave propagation in elastic bars subjected to tension and compression under constant velocity loading conditions. First, axial waves were studied by analytically solving the axial wave equation with damping. Subsequently, we employed this theoretical framework in atomistic simulations to measure loading-rate effects and thus determine the conditions for distinguishing quasi-static and dynamic loading. Given the coupled compressive axial waves, deflection waves were analyzed to predict dynamic instability. Our findings revealed that a continuous increase in impact velocity may not necessarily result in a larger impact force. This study offers fresh insights into the mechanical theory on the dynamic behaviour of bars across diverse scales (atomic to macroscopic). These insights are invaluable for determining suitable loadings in atomistic simulations, and provide guidelines for engineering impact applications.