A cracked zone clustering method for discrete fracture with minimal enhanced degrees of freedom

Abstract

Many state-of-the-art approaches for predicting discrete fracture within the finite element framework were designed by enhancing the continuous displacement field with a discontinuous part. Broadly categorised into elemental and nodal enrichment approaches, they provided unprecedented versatility in discretising domains with prescribed and evolving boundaries. However, there can be an additional computational burden when global tracking schemes are used to enforce the continuity of tractions/jumps along crack paths. Many current approaches also entail involved integration procedures over cut subdomains, which pose challenges of efficiency and accuracy. In addition, although cracks do not need to conform to the geometry of the mesh, the discretisation of cracks is still linked to that of the underlying elements, which can lead to the inaccurate representation of traction profiles along stiff interfaces. Aiming at overcoming these issues, the present work introduces a new formulation with minimal enhanced degrees of freedom. This is achieved by decoupling the discretisation of bulk and cracks, a feature that is enabled by a novel clustered rigid body definition of enhancement field in the set of the variational equations. A new method, termed Cracked Zone Clustering Method (CZCM), is then proposed for discrete fracture propagation by deploying only one rotational degree of freedom per set of cracked elements within the same zone. The stability of the method is first studied using element examples. The method is also shown to resolve the issue of traction oscillations over stiff interfaces. The accuracy and efficiency of the independent discretisation strategy are studied using several known crack propagation benchmarks. Results are compared with the Extended/Generalised Finite Element Method (XFEM/GFEM) and the Discrete Strong Discontinuity Approach (DSDA). In summary, it is shown that the cracked zones can encompass a multitude of elements, thus significantly decreasing the required number of enhancement degrees of freedom by orders of magnitude and without compromising accuracy.