Cohesive element is one of the most popular techniques for modelling crack propagations. However, it suffers from a stringent constrain on its mesh density - multiple elements are needed within the Cohesive Zone to be able to capture the correct stress profile and hence predict the correct fracture initiation and propagation. The dimension of the cohesive zone in carbon-fibre composite laminates can be smaller than 1 mm, which means that the cohesive element size must be smaller than 0.5 mm. Imagine modelling a wing of Boeing 787 with less than 0.5-mm elements!

The objective of this research is to develop new cohesive element formulations which overcome this cohesive zone limit and enable the use of much larger elements in FE models with cohesive elements.

Adaptively-partitioned cohesive element

A simple technique is to use the Floating Node Method to form elements with internal Degrees of Freedom (DoF) to allow partitioning of the cohesive element when the cohesive zone is passing through. After the cohesive zone has passed, the internal DoFs will be simply removed to revert back to the original element size. 

With this technique, elements larger than cohesive zone can be used and CPU time reduction can be more than 80%.

Reference: Adaptive FNM cohesive element

Structural cohesive elements with higher-order integration

A new class of cohesive element formulation, here termed structural cohesive element, has been developed to overcome the cohesive zone limit in delamination modelling. The core idea is derived from a simple question: how could the analytical solutions of composite delamination tests, namely Double-Cantilever Beam, End-Notch Flexure and Mixed-Mode Bending, be largely independent of the cohesive zone length, while their finite element modelling counterparts suffer so much constraint from it? A related question to ask would be: whether aspects of the analytical solutions or solution approaches can be incorporated into the finite element formulation for such problems so that the finite element models could also be relieved from the cohesive zone limit?

It turns out that the analytical solutions are based on Euler-Bernoulli beam (2D) and classical plate (3D) theories, which would require C1 continuous finite elements to properly model the deflection and slope continuities.  Such elements exist for beams, plates, and shells, but not previously for their interfaces. We therefore developed a class of cohesive elements which conform to C1 beam, plate and shell ply elements. We call them "structural" cohesive elements as they must be used in combination with the aforementioned structural ply elements. 

The structural cohesive element approach allows the use of elements 10 times larger than the cohesive zone and achieves 98% reduction on CPU time (see the reference papers below).  

Reference: Adaptively-integrated Euler beam-based structural cohesive element; Classical plate-based structural cohesive element for 3D Mode I delamination; Shell-based structural cohesive element for 3D general delamination

Adaptive higher-order integration without changing D.o.F.

With the use of large elements through the structural CE approach, we developed an algorithm to adaptively change the integration scheme, without changing the element interpolation or the D.o.F.. A finer integration scheme with more integration points is used when the cohesive zone is passing through the element domain, as the stress profile at this moment exhibits high gradients and kinks which cannot be accurately evaluated with standard integration schemes. The substrate elements must be higher-order in case the substrates are beams or shells. The reason that it is deemed not necessary to change the element interpolation function is that beams and shells have continuous gradients even under point loads, as long as they don't fracture.

Reference: Adaptively-integrated Euler beam-based structural cohesive element