Finite Elements for Damage & Fracture

Floating Node Method (FNM)

The Floating Node Method (FNM) enriches the finite element definition with all its useful geometrical entities such as nodes, edges and surfaces. Degrees of freedom (DoF) can be allocated to these entities to represent their changes during analysis. It opens up a flexible way of forming "smart" elements - self-partitioning elements tailored for a particular material of interest.

FNM solid element general definition
FNM lamina element - definition and partitioning with respect to a crack
A laminate element formed by FNM

Damage and Failure Predictions for Composites

In-Plane Fracture

FNM can predict the competition between matrix cracking and delamination and the effect of ply thickness on matrix crack saturation density and delamination area (note: red dots are failed integration points).

FNM can predict the large and complex crack networks exhibited in open-hole composite laminates under in-plane loading, including the full-length matrix splits and full-scale delamination.

0-degree open-hole lamina: explosive splittings

Cross-ply open-hole laminate: dense matrix cracks

Delamination Migration

Delamination migration is a common fracture event in composite laminates under bending (such as in low-velocity impact). It is a challenging problem for modelling because the critical damage mechanism is matrix crack/delamination interaction. Here, the FNM elements nicely captured the multiple migration events in the laminate.

Overcoming the cohesive zone limit

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 based on FNM

A simple technique is to use FNM 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%.

Adaptively-integrated higher-order cohesive element

A much simpler adaptivity technique from the one above is to adaptively change the integration scheme, but NOT the element interpolation. 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.

This simple technique allows the use of elements 10 times larger than the cohesive zone and achieves 98% reduction on CPU time.