Mass lumping strategies for X‐FEM explicit dynamics: Application to crack propagation

By T. Menouillard, J. Réthoré, N. Moes, Alain Combescure, Harridh Bung. 2008

122 citations recorded by the source corpus.

This paper deals with the numerical modelling of cracks in the dynamic case using the extended finite element method. More precisely, we are interested in explicit algorithms. We prove that by using a specific lumping technique, the critical time step is exactly the same as if no crack were present. This somewhat improves a previous result for which the critical time step was reduced by a factor of square root of 2 from the case with no crack. The new lumping technique is obtained by using a lumping strategy initially developed to handle elements containing voids. To be precise, the results obtained are valid only when the crack is modelled by the Heaviside enrichment. Note also that the resulting lumped matrix is block diagonal (blocks of size 2 × 2). For constant strain elements (linear simplex elements) the critical time step is not modified when the element is cut. Thanks to the lumped mass matrix, the critical time step never tends to zero. Moreover, the lumping techniques conserve kinetic energy for rigid motions. In addition, tensile stress waves do not propagate through the discontinuity. Hence, the lumping techniques create neither error on kinetic energy conservation for rigid motions nor wave propagation through the crack. Both these techniques will be used in a numerical experiment. Copyright © 2007 John Wiley & Sons, Ltd.

Subfields: Civil and Structural Engineering, Computational Mechanics, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/464ab47ed95ec7e971b6845b05a6876a710d3297

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In Civil and Structural Engineering

In Computational Mechanics

In Mechanics of Materials

Citations in the corpus

On generation of lumped mass matrices in partition of unity based methods (2017, background): “[22, 23] have successfully addressed this problem by proposing appropriate mass lumping strategies for enrichment that produce non-zero critical time steps for dynamic crack propagation problems.”
Extended finite element method in computational fracture mechanics: a retrospective examination (2015, unknown): “Indeed, dynamic fracture has raised speciﬁc issues related to the X-FEM, including the need for appropriate mass lumping strategies and stable time integrators with near-tip enrichment (Menouillard et al. 2008).”
Cracking node method for dynamic fracture with finite elements (2009, unknown): “Several methods have been proposed to circumvent these difficulties: implicit (in cracked elements)– explicit (in continuum elements) time integration [12] and modified mass lumping schemes [39, 45, 46].”
Stable imposition of stiff constraints in explicit dynamics for embedded finite element methods (2012, methodology): “[29] generalized the mass lumping procedure previously developed by Rozycki et al.”
Element‐local level set method for three‐dimensional dynamic crack growth (2009, unknown): “[14].”
An explicit dynamics extended finite element method. Part 2: Element-by-element stable-explicit/explicit dynamic scheme (2009, methodology): “In order to limit such a dependency, it was first proposed by various authors to built specific mass lumping techniques in order to recover a non-zero value for the critical time step when a discontinuity or an interface reaches an element boundary (see, for example, [30, 35]).”