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An energy-conserving scheme for dynamic crack growth using the eXtended finite element method. (English) Zbl 1122.74519
Summary: 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.

MSC:
74S05 Finite element methods applied to problems in solid mechanics
74R10 Brittle fracture
74H35 Singularities, blow-up, stress concentrations for dynamical problems in solid mechanics
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