An energy‐conserving scheme for dynamic crack growth using the eXtended finite element method

TLDR

The study extends the eXtended finite element method to dynamic fracture and time‑dependent problems, providing a proof of numerical stability in the linear case. The authors analyze stability of Newmark‑type schemes for evolving discretizations and introduce a Lagrangian‑based method to estimate dynamic stress‑intensity factors for arbitrary 2D cracks. The enrichment strategy satisfies the stability conditions, conserves energy, allows crack propagation without instability, and yields accurate results for both stationary and moving cracks. © 2005 John Wiley & Sons, Ltd.

Abstract

Abstract This paper proposes a generalization of the eXtended finite element method (X‐FEM) to model dynamic fracture and time‐dependent problems from a more general point of view, and gives a proof of the stability of the numerical scheme in the linear case. First, we study the stability conditions of Newmark‐type schemes for problems with evolving discretizations. We prove that the proposed enrichment strategy satisfies these conditions and also ensures energy conservation. Using this approach, as the crack propagates, the enrichment can evolve with no occurrence of instability or uncontrolled energy transfer. Then, we present a technique based on Lagrangian conservation for the estimation of dynamic stress intensity factors for arbitrary 2D cracks. The results presented for several applications are accurate for stationary or moving cracks. Copyright © 2005 John Wiley & Sons, Ltd.