# Numerical methods for The Modelling Of Debonding In Composites

• R. de Borst
Chapter
Part of the Solid Mechanics And Its Applications book series (SMIA, volume 154)

This monograph starts with a discussion of various phenomena in laminated composite structures that can lead to failure: matrix cracking, delamination between plies, and debonding and subsequent pull-out between fibres and the matrix material. Next, the different scales are discussed at which the effect of these nonlinearities can be analysed and the ways to couple analyses at these different length scales. From these scales—the macro, meso and micro-levels — the meso-level is normally used for the analysis of delamination, which is the focus of this monograph. At this level, the plies are modelled as continua and interface elements between them conventionally serve as the framework to model delami-nation and debonding. After a brief discussion of the cohesive—zone concept and its importance for the analysis of delamination, a particular finite element model for the plies is elaborated: the solid—like shell. This is followed by a derivation of interface elements. In the second part of this monograph more recent methods to numerically model delamination are discussed: meshfree methods, methods that exploits the partition—of—unity property of finite element shape functions, and discontinuous Galerkin methods. These approaches offer advantages over the more traditional approach that uses interface elements, as will be discussed in detail. From these more modern discretisation concepts the partition-of-unity approach seems the most promising for modelling debonding in composite structures, one advantage being that it can rather straightforwardly be incorporated in solid-like shell elements, thus enabling large-scale analyses of layered composite structures that take into account the possibility of debonding.

## Keywords

multiscale analysis debonding delamination finite element methods interface elements meshfree methods partition-of-unity approach solid-like shell elements discontinuous Galerkin methods

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