Incremental-Secant Modulus Iteration Scheme and Stress Recovery for Simulating Cracking Process in Quasi-Brittle Materials Using XFEM

In this paper, an incremental-secant modulus iteration scheme using the extended/generalized finite element method (XFEM) is proposed for the simulation of cracking process in quasi-brittle materials described by cohesive crack models whose softening law is composed of linear segments. The leading term of the displacement asymptotic field at the tip of a cohesive crack (which ensures a displacement discontinuity normal to the cohesive crack face) is used as the enrichment function in the XFEM. The opening component of the same field is also used as the initial guess opening profile of a newly extended cohesive segment in the simulation of cohesive crack propagation. A statically admissible stress recovery (SAR) technique is extended to cohesive cracks with special treatment of non-homogeneous boundary tractions. The application of locally normalized co-ordinates to eliminate possible ill-conditioning of SAR, and the influence of different weight functions on SAR are also studied. Several mode I cracking problems in quasi-brittle materials with linear and bilinear softening laws are analysed to demonstrate the usefulness of the proposed scheme, as well as the characteristics of global responses and local fields obtained numerically by the XFEM