Embedded discontinuity finite element method for modeling of localized failure in heterogeneous materials with structured mesh: an alternative to extended finite element method

Abstract

In this work we discuss the finite element model using the embedded discontinuity of the strain and displacement field, for dealing with a problem of localized failure in heterogeneous materials by using a structured finite element mesh. On the chosen 1D model problem we develop all the pertinent details of such a finite element approximation. We demonstrate the presented model capabilities for representing not only failure states typical of a slender structure, with crack-induced failure in an elastic structure, but also the failure state of a massive structure, with combined diffuse (process zone) and localized cracking. A robust operator split solution procedure is developed for the present model taking into account the subtle difference between the types of discontinuities, where the strain discontinuity iteration is handled within global loop for computing the nodal displacement, while the displacement discontinuity iteration is carried out within a local, element-wise computation, carried out in parallel with the Gauss-point computations of the plastic strains and hardening variables. The robust performance of the proposed solution procedure is illustrated by a couple of numerical examples. Concluding remarks are stated regarding the class of problems where embedded discontinuity finite element method (ED-FEM) can be used as a favorite choice with respect to extended FEM (X-FEM).

Modelling of reinforced‐concrete structures providing crack‐spacing based on X‐FEM, ED‐FEM and novel operator split solution procedure

“…This is in sharp contrast with the standard parametrization of interface discontinuities (e.g. see Belytschko et al [15] or Jirasek and Belytschko [18]), which (as noted by Ibrahimbegovic and Melnyk [19]) would not allow the use of the same operator split procedure.…”

An Accurate and Efficient Augmented Finite Element Method for Arbitrary Crack Interactions

“…This method follows the earlier research in smeared localization models [26][27][28] and it has been extended to account for discrete discontinuities by several research groups [29][30][31][32][33][34]. This approach seeks to enrich the elemental strain field by introducing displacement jumps with certain defonnation modes (constant and/or linear mode) in addition to the normal continuous displacement field.…”

Performance Based Earthquake-Resistant Design: Migrating Towards Nonlinear Models and Probabilistic Framework

“…However, it is only since recent times that we have acquired the modelling capabilities; e.g. see (Benkemoun et al 2010;Dominguez et al 2005;Ibrahimbegovic and Brancherie 2003;Ibrahimbegovic and Delaplace 2003;Ibrahimbegovic and Markovic 2003;Ibrahimbegovic and Melnyk 2007;Ibrahimbegovic 2009;Ibrahimbegovic et al 2008Ibrahimbegovic et al , 2010Jehel et al 2010;Markovic and Ibrahimbegovic 2004) to provide a more refined interpretation of the local failure mechanisms rather than the global, push-over-type models. We have also very well advanced in the long process, from early works (Ibrahimbegovic andWilson 1990, 1992) to more recent works (Ibrahimbegovic and Markovic 2003) or (Ibrahimbegovic et al 2008) in development of the robust computational procedure that is able to isolate the most severely damaged zone and deliver the corresponding scenario on the interplay of different local mechanisms in building the global failure mechanisms for structures and systems of any complexity.…”