The response of viscoelastic-frictionless bodies under normal impact

This paper presents a computational finite element model capable of simulation of the impact response of viscoelastic-frictionless bodies. The variational method is developed to drive the equations of motion. The Lagrange multiplier method is exploited to impose the nonholmonic contact constraints and convert the problem form constraint problem to unconstraint one. The constitutive equations are expressed in integral form. and involving relaxation moduli are adopted to describe the nonaging simple material. Generalized Standard Linear Solid (Wiechert) model is adopted to simulate the internal damping (viscoelastic) behavior of the structure. Wiechert model is exploited in order to drive a recursive relationship and thereby eliminate storage problem. Newmark constant average acceleration is proposed to integrate the governing equation numerically and transfer the problem into a static one for each time increment.