An Explicit Dynamics eXtended Finite Element Method With Standard Critical Time Step

Thomas Elguedj (1) , Anthony Gravouil (1) , Hubert Maigre (1) , David Grégoire (1, 2)

1 LaMCoS - Laboratoire de Mécanique des Contacts et des Structures [Villeurbanne]
2 TEFC - Thermodynamique et Energétique des fluides complexes

We present a framework based on the eXtended Finite Element Method and explicit dynamics for the simulation of dynamic crack growth. First, a new mass lumping technique is proposed for arbitrary enrichment functions. We focus on the case of singular enrichment functions for cracks on piece-wise linear elements and on the case of free boundary and hole enrichment functions for quadrilateral and hexahedral elements. Based on a systematic study for these cases, we propose reasonable critical time step estimates. For singular enrichment, respectively hole enrichment, 50%, respectively 66%, of the standard finite element critical time step is sufficient for accurate explicit dynamics simulations. Second, we propose a partitioned element-by-element Stable-Explicit / Explicit time integrator. The element partitioning is based on the implicit-explicit element-by-element time integrator proposed by Hughes and Liu. For the non-enriched elements, we use the central difference explicit time integrator. For the enriched elements we use the explicit unconditionally stable time integrator proposed by Chang. The stability of the method is demonstrated by the energy method. It shows that the overall stability is conditional and governed by the explicit group. Combining the general mass lumping formula with this time integrator, and defining features such as cracks, holes and free boundaries using enrichment allows us to use a regular mesh with standard finite element critical time step. Moreover, the use of a regular mesh, without any constraint from the enrichment on the critical time step, allows us to minimize the computational time and maximize accuracy. Comparisons with previously published numerical simulations and experiments illustrate the performance of the method.

Domaines: Matériaux et structures en mécanique [physics.class-ph]; Matériaux et structures en mécanique [physics.class-ph]

Thomas Elguedj, Anthony Gravouil, Hubert Maigre, David Grégoire. An Explicit Dynamics eXtended Finite Element Method With Standard Critical Time Step. 2009 ASME International Mechanical Engineering Congress & Exposition, Nov 2009, Lake Buena Vista, United States. ⟨hal-00574326⟩