Finite element modelling of traction-free cracks: Benchmarking the augmented finite element method (AFEM). (August 2021)

• Record Type: Journal Article
• Authors: Essongue, Simon; Couégnat, Guillaume; Martin, Eric
• Is Part Of: Engineering fracture mechanics. Volume 253(2021)
• Publication Date: 2021-08
• Subjects: Embedded discontinuities -- Embedded finite elements -- Strong discontinuities -- Augmented finite element method -- Phantom node method; Fracture mechanics -- Periodicals; Rupture, Mécanique de la -- Périodiques; Fracture mechanics; Periodicals; 620.112605
• DOI: 10.1016/j.engfracmech.2021.107873
• Languages: English
• ISSNs: 0013-7944

Abstract

Abstract: This paper investigates the accuracy and the convergence properties of the augmented finite element method (AFEM). The AFEM is here used to model strong discontinuities independently of the underlying mesh. One noticeable advantage of the AFEM over other partition of unity methods is that it does not introduce additional global unknowns to represent cracks. Numerical 2D experiments illustrate the performance of the method and draw comparisons with the element deletion method (EDM), the phantom node method (PNM), the finite element method (FEM) and the embedded finite element method (EFEM). The h-convergence in the energy norm of the AFEM is studied for the first time and it is shown to outperform the aforementioned numerical methods when cracks are loaded in Mode I. Highlights: The convergence rate of the AFEM is numerically evaluated. The singularity of AFEM stiffness matrices is dealt with. The accuracy of the AFEM is thoroughly benchmarked against popular numerical methods. The AFEM outperforms the other evaluated methods under Mode I loading of a crack.