Mathematical modeling of viscoelastic material under impact load

A linear physics-based model is developed to investigate the one-dimensional impact on a viscoelastic material. A generalized model with three Maxwell elements is considered to describe the viscoelastic behavior. An analytical method based on Laplace transformation is used to solve the impact problem. To have a comprehensive understanding of viscoelastic material response, drop-weight impact is also considered in this study. For both linear impact and drop-weight cases, a maximum reduction of 15% of the impact force as well as 32% higher energy absorption can be achieved with the increase in tan δ from 0.01 to 0.8 of viscoelastic material. In addition, for linear impact, impact force decreases by 20% when tan δ？=？1. With the increase in tan δ, storage modulus decreases by around 57% for maintaining a predetermined deformation. Moreover, for almost constant maximum displacement, materials with a higher storage modulus absorb more impact energy and experience higher impact force as compared to materials with a lower storage modulus