An explicit dynamics extended finite element method. Part 1: Mass lumping for arbitrary enrichment functions

Abstract

This paper presents a general mass lumping technique for explicit dynamics simulations using the eXtended Finite Element Method with arbitrary enrichment functions. The proposed mass lumping technique is a generalization of previously published results for cracks and holes. Time step estimates are studied for crack singular enrichment functions and for hole enrichment. In both cases, we show that the critical time step does not tend to zero and is of the same order as that of the same unenriched element. The performance of the method is demonstrated on several numerical examples that compare well with classical finite elements and previously published X-FEM results.

An XFEM/Spectral element method for dynamic crack propagation

“…9a, one can notice that apparent numerical oscillations appear in the stress intensity factor for element SE1. This was also observed in the same simulations carried out by the other researchers using low-order element (Elguedj et al 2009;Menouillard et al 2006. However, for element SE2 and SE3, the stress intensity factors vary smoothly when the tensile wave and the reflected wave approach the crack tip, and the results are quite similar to the analytical results.…”

“…The small oscillations in element SE2 and SE3 correspond to the crack tip passing from one element to the next. This error was also apparent in the time-dependent tip enrichment technique in References Elguedj et al (2009), Réthoré et al (2005.…”

Time dependent crack tip enrichment for dynamic crack propagation

“…The enrichment does not decrease this error significantly. This error was also strongly apparent in the multi-enrichment technique of Réthoré et al (2005), Elguedj et al (2009).…”

“…Whereas the 4-node linear element is not a constant strain element, the latter relation holds approximately because this element as been used with one quadrature point and hourglass control Flanagan and Belytschko (1981), Koh and Kikuchi (1987); so it becomes like a constant strain element Liu et al (1994). The critical time step due to the XFEM formulation and more particularly to the tip enrichment function was studied by Elguedj et al (2009), using the same approach as the one used with the discontinuous enrichment in Menouillard (2008), applied to the tip enrichment √ r sin (θ/2). The development of the lumped mass matrix is based on the conservation of the discretized kinetic energy.…”

Explicit dynamics with a non‐local damage model using the thick level set approach

“…in [37,38], a damage model is used until strain localization occurs, then a cohesive crack model is introduced; in [39][40][41], brittle materials are considered, modeling is not focused on strain localization aspects but on efficient and accurate strategy to use the X-FEM in explicit dynamics. It focuses on schemes, enrichment, and lumping strategy; A projectile is launched at velocity v 0 on an edge of a rectangular l 2l steel plate as depicted in Figure 10.…”