Comparative study of numerical explicit schemes for impact problems

Abstract

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 nondissipative 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 has been 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.

Reducing spurious oscillations in discontinuous wave propagation simulation using high-order finite elements

“…The idea goes back to a similar modification applied in the TW method [18]. The CD method being the reference non-dissipative method [48], the difference between the internal forces of the proposed method and the CD scheme for the free undamped system defines the numerical damping. For the first sub-step, the numerical damping Table 1 The algorithms of NB, CD, TW and proposed methods [21].…”

Time-Integration Schemes for the Finite Element Dynamic Signorini Problem

“…There exist also explicit schemes with high-frequency dissipation, such as the ChungHulbert or Tchamwa-Wielgosz schemes (see [30] and references therein). Downloaded 11/18/14 to 155.33.120.209.…”

On the use of some numerical damping methods of spurious oscillations in the case of elastic wave propagation

“…The evolutions of the spectral radius and the errors in the numerical damping ratio and the relative period have been studied by Nsiampa et al (2008).…”

“…Fewer studies have dealt, however, with the use of explicit time integration methods, and the main dissipative schemes of this kind available to our knowledge are those developed by Newmark (1959), Chung and Lee (1994), Zhai (1996), Hulbert and Chung (1996), and Tchamwa (1997). The latter one has been the subject of recent research works which showed its efficiency in damping spurious oscillations in the case of low velocity impact (Nsiampa et al, 2008) and under instantaneous loading conditions (Mahéo et al, 2009).…”

“…Using viscous or plastic dissipative behavioral laws, as done by Nsiampa with the TW scheme (Nsiampa et al, 2008), naturally results in a "filtering" process, which causes the highest frequencies in particular to disappear. To prevent the occurence of this "natural filtering" process, which might make it difficult to assess the efficiency of the TW scheme, a linear elastic conservative law was adopted in the present study.…”