engleski

Mixed-mode rate-dependent delamination in geometrically non-linear multi-layer beam finite elements

Layered structures are widely used in different engineering applications as well as in nature due to their optimised functional and structural performance. Delamination, which occurs when a crack initiates and/or propagates along the interface between two layers, is one of the most prevalent and severe failure modes in these types of structures. In this work, cohesive-zone models (CZMs), which assume discontinuous displacement field and a nonlinear traction-separation law on the considered interface, are used to study delamination [1]. In case of a significantly rate dependent fracture process, the traditional fracture-mechanics based approaches can only characterise the phenomenological dependence of the fracture energy on the crack speed. Instead, the recently developed rate- dependent CZM [2], where the different dissipation mechanisms occurring during fracture are separated out, is less phenomenological and better linked to the underlying physics. It has also been recently shown that beam elements can be used with very good accuracy to model delamination in layered structures both in geometrically linear and non- linear analysis [3]. In a geometrically linear analysis, Reissner’s theory corresponds to the well-known Timoshenko theory, while in a geometrically non-linear setting, it makes the basis for the development of extremely robust finite elements capable of handling finite displacements and rotations. Most importantly, beam elements make use of a smaller number of degrees of freedom, which significantly reduces the overall computational burden. Building on the earlier work discussed above [1-3], in this work, a multi-layer beam finite element consisting of rate-dependent mixed-mode interface elements and of two- or three-noded beam finite elements is presented. The model is verified against experimental results for mode I delamination (DCB test) and numerical results from models which use plane-strain 2D finite elements for the bulk material. Improved computational efficiency and accuracy of the results of the new model is demonstrated, which will become a framework for a novel method of determining the material properties of the interconnection of layered structures used in conjunction with experimental measurements (e.g. force-displacement diagram for a DCB test).

delamination, rate-dependent, mixed-mode delamination, geometrically non-linear beams, finite element analysis

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