A simplified continuous–discontinuous approach to fracture based on decoupled localizing gradient damage method

Abstract

In this work, two fracture modelling methods i.e., extended FEM (XFEM) and localizing gradient damage method (LGDM), are combined to get the advantages of both methods while eliminating their limitations. The LGDM is a micromechanics-based method that avoids spurious damage growth and incorrect damage initiation observed in conventional gradient damage method (CGDM). However, in the LGDM, a cracked/discontinuous domain is not fully realized due to its continuous nature, even at high damage. This leads to numerous non-physical effects in LGDM like high strains, severe stress oscillations and incorrect representation of secondary variables. These shortcomings are rectified in the combined continuous–discontinuous (XFEM + LGDM) approach by introducing XFEM at the end of damage evolution to impose a discontinuous crack in the domain. To simplify the implementation, a fully coupled LGDM is converted to a decoupled LGDM using an operator-split (staggered) methodology. It is observed from numerical examples that the decoupling of LGDM leads to a reduction in the computational effort without compromising accuracy. Besides, the XFEM+LGDM approach avoids use of cohesive zone modelling necessary in existing XFEM+CGDM approaches. Moreover, the proposed method (combined XFEM + LGDM) is also investigated in the multi-physical framework of thermoelasticity. The numerical results reveal that the shortcomings mentioned earlier are rectified in a physically consistent manner under mode I and mixed-mode conditions.