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.
Highlights
In quasi-brittle materials, such as geomaterials and concrete, the fracture behavior is quite different from that of brittle materials
The assumption of linear elastic fracture mechanics (LEFM) is quite restrictive for certain types of failure, where the nonlinear zone ahead of the crack tip is negligible in comparison with the dimension of the crack
We focus on investigating the accuracy and convergence properties of different enrichment schemes for cohesive crack simulation
Summary
In quasi-brittle materials, such as geomaterials and concrete, the fracture behavior is quite different from that of brittle materials. As far as convergence rates are concerned, when numerically simulating traction-free crack by the XFEM, the factors that influence the convergence rate include the enrichment zone size [21], the shape function polynomial order [24], the special treatment of the blending elements, and the choice of enrichment functions. Gupta et al [34] studied the influence of enrichment zone size on convergence rate and found that, for traction-free crack simulation, the convergence rate is controlled by the stress gradient outside the enrichment zone and the error is caused by the blending element When it comes to the cohesive crack problem, the smoother stress gradient and the nonlinearity of the governing equation make the accuracy and convergence properties new problems that require study.
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