A comparative study on the modelling of discontinuous fracture by means of enriched nodal and element techniques and interface elements

In this paper, three different approaches used to model strong discontinuities are studied: a new strong embedded discontinuity technique, designated as the discrete strong embedded discontinuity approach (DSDA), introduced in Dias-da-Costa et al. (Eng Fract Mech 76(9):1176–1201, 2009); the generalized finite element method, (GFEM), developed by Duarte and Oden (Tech Rep 95-05, 1995) and Belytschko and Black (Int J Numer Methods Eng 45(5):601–620, 1999); and the use of interface elements (Hillerborg et al. in Cem Concr Res 6(6): 773–781, 1976). First, it is shown that all three descriptions are based on the same variational formulation. However, the main differences between these models lie in the way the discontinuity is represented in the finite element mesh, which is explained in the paper. Main focus is on the differences between the element enrichment technique, used in the DSDA and the nodal enrichment technique adopted in the GFEM. In both cases, global enhanced degrees of freedom are adopted. Next, the numerical integration of the discretised equations in the three methods is addressed and some important differences are discussed. Two types of numerical tests are presented: first, simple academic examples are used to emphasize the differences found in the formulations and next, some benchmark tests are computed.Design and ConstructionCivil Engineering and Geoscience