engleski

A finite element formulation for a 2D geometrically exact multi-layer beam with interconnection allowing for mixed-mode delamination

In this work we present a planar geometrically exact finite element model for a multi-layer beam with interconnection allowing for mixed- mode delamination. A general formulation, for an arbitrary number of layers, which are modelled as geometrically exact Reissner’s beams and made of linear elastic material, is proposed. Mixed-mode delamination at the interconnection is determined as a combination of individual modes I and II which are modelled using a bi-linear constitutive law with cohesive zone model embedded. The proposed model can be simplified to a geometrically linear analysis, but since the material behaviour at the interconnection is always non- linear, the solution is still obtained iteratively using the Newton-Raphson procedure. In both cases the problems are characterised by sharp snap-backs in the load-displacement diagram and in order to overcome the path- tracing problems the modified arc-length method has been utilised. Numerical examples show that the present model in geometrically linear analysis, in comparison with similar models from the literature which use 2D plane-strain finite elements for the layers, not only gives excellent accuracy, but also uses considerably less degrees of freedom. Examples with pure modes I and II, as well as examples with single or dual mixed-mode delamination have been presented and analysed. It has been also shown the geometrically exact analysis, in comparison with the geometrically linear one, can give considerable differences in the results, especially in cases when the displacements and rotations can no longer be described as small. The geometrically exact formulation allows us to solve problems that are genuinely geometrically non-liner, e.g. buckling of a layered beam is also presented, where again an improvement may be observed in tracing the post-critical behaviour of the buckled structure due to the full geometrical non- linearity implemented.

multi-layer beam; mixed-mode delamination; arc-length method; damage; composites; geometrically exact formulation

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