Comparative study of numerical explicit schemes for impact problems

Explicit numerical schemes are used to integrate in time finite element discretization methods. Unfortunately, these numerical approaches can induce high-frequency numerical oscillations into the solution. To eliminate or to reduce these oscillations, numerical dissipation can be introduced. The paper deals with the comparison of three different explicit schemes: the central-difference scheme which is a non-dissipative method, the Hulbert-Chung dissipative explicit scheme and the Tchamwa-Wielgosz dissipative scheme. Particular attention is paid to the study of these algorithms' behavior in problems involving high-velocity impacts like Taylor anvil impact and bullet-target interactions. It is shown that Tchamwa-Wielgosz scheme is efficient in filtering the high-frequency oscillations and is more dissipative than Hulbert-Chung explicit scheme. Although its convergence rate is only first order, the loss of accuracy remains limited to acceptable values.