*Article* **Convergence Investigation of XFEM Enrichment Schemes for Modeling Cohesive Cracks**

**Guangzhong Liu 1,\*, Jiamin Guo <sup>1</sup> and Yan Bao <sup>2</sup>**


**Abstract:** When simulating cohesive cracks in the XFEM framework, specific enrichment schemes are designed for the non-singular near-tip field and an iteration procedure is used to solve the nonlinearity problem. This paper focuses on convergence and accuracy analysis of XFEM enrichment schemes for cohesive cracks. Four different kinds of enrichment schemes were manufactured based on the development of XFEM. A double-cantilever beam specimen under an opening load was simulated by Matlab programming, assuming both linear and exponential constitutive models. The displacement and load factors were solved simultaneously by the Newton–Raphson iterative procedure. Finally, based on a linear or an exponential constitutive law, the influences of variations in these enrichment schemes, including (i) specialized tip branch functions and (ii) corrected approximations for blending elements, were determined and some conclusions were drawn.

**Keywords:** cohesive cracks; convergence rate; enrichment schemes; XFEM
