Dynamic fracture analysis in quasi-brittle materials via a finite element approach based on the combination of the ALE formulation and M−integral method

This work proposes an efficient FE-based approach for reproducing dynamic crack propagation phenomena in quasi-brittle materials. The proposed model uses a Moving Mesh technique based on the Arbitrary Lagrangian-Eulerian formulation (ALE) to adapt the computational mesh consistently to the geometry variations caused by dynamically growing cracks. Specifically, the motion of mesh nodes occurs according to Fracture Mechanics criteria, which provide suitable conditions regarding the direction and velocity of a growing crack tip. These conditions usually depend on the Dynamic Stress Intensity Factors (DSIFs) at the crack front. For extracting the DIFSs at a moving crack tip, this work introduces the ALE formulation of the dynamic M−integral as a key novelty. This strategy offers the key advantage of performing numerical integration procedures on deforming finite elements without losing accuracy. The validity of the proposed method has been assessed through comparisons with experimental and numerical data reported in the literature.