  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.
