A simple hybrid linear and non-linear interpolation finite element for adaptive cracking elements method

Cracking Elements Method (CEM) is a numerical tool to simulate quasi-brittle fractures, which does not need remeshing, nodal enrichment, or complicated crack tracking strategy. The cracking elements used in the CEM can be considered as a special type of finite element implemented in the standard finite element frameworks. One disadvantage of CEM is that it uses nonlinear interpolation of the displacement field (Q8 or T6 elements), introducing more nodes and consequent computing efforts than the cases with elements using linear interpolation of the displacement field. Aiming at solving this problem, we propose a simple hybrid linear and non-linear interpolation finite element for adaptive cracking elements method in this work. A simple strategy is proposed for treating the elements with $p$ edge nodes $p\in\left[0,n\right]$ and $n$ being the edge number of the element. Only a few codes are needed. Then, by only adding edge and center nodes on the elements experiencing cracking and keeping linear interpolation of the displacement field for the elements outside the cracking domain, the number of total nodes was reduced almost to half of the case using the conventional cracking elements. Numerical investigations prove that the new approach inherits all the advantages of CEM with greatly improved computing efficiency.