Discrete fracture analysis using locally refined T‐splines

Abstract

Summary Locally refined T‐splines are used to model discrete crack propagation without a predefined interface. The crack is introduced by meshline insertions in the locally refined T‐mesh, which yields discontinuous basis functions. To implement the method in existing finite element programs, Bézier extraction is used. A detailed description is given as to how the crack path is inserted and how the domain is reparameterized after insertion. The versatility and accuracy of the approach to model discrete crack propagation without the crack path being predefined is demonstrated by two examples, namely, an L‐shaped beam and a single‐edge notched beam. When the crack approaches the physical boundaries, limitations to reparameterization arise, as will be discussed at the hand of a double‐edge notched specimen.

Cohesive fracture analysis using Powell‐Sabin B‐splines

“…While the stress computation is more accurate when using Powell‐Sabin B‐splines, the direction of crack propagation is very sensitive, and the quality of the prediction of the direction of crack propagation can be improved further by an averaging procedure . An averaged stress tensor is computed using a Gaussian weight function with l is a smoothing length, typically taken around three times a representative element size, and r is the distance to the crack tip.…”

“…This example serves to demonstrate the improvements for discrete crack propagation, which the use of Powell‐Sabin B‐splines offers over NURBS or T‐splines . The Nooru‐Mohamed tension‐shear test is considered.…”

“…The cohesive zone model can be incorporated in the finite element method, and different approaches have been proposed, for instance, using interface elements, remeshing or extended finite element methods . More recently, isogeometric analysis has also been introduced in the context of crack propagation analysis …”

“…However, NURBS and T‐splines have some limitations when modelling (cohesive) fracture, and a proper discrete representation of a discontinuity may not be feasible in some situations. Experience shows that when using NURBS or T‐splines the initial mesh must be sufficiently aligned with the final crack path a priori, see Section 8 in a previous study . Furthermore, the higher‐order continuity of the basis functions in isogeometric analysis, which is so appealing and leads to vastly improved stress predictions, fails near crack tips and only ‐continuity remains.…”

Energy conservation during remeshing in the analysis of dynamic fracture

“…Isogeometric analysis has also been introduced in the context of crack propagation analysis . However, isogeometric analysis has some limitations to insert cracks at arbitrary locations as the initial mesh must be aligned sufficiently closely with the final crack path a priori . Another disadvantage is that the higher‐order continuity of the basis functions breaks down near crack tips and only ‐continuity remains, due to the insertion of lines in order to shield the discontinuity due to the crack from the rest of the domain .…”