Computational Mechanics of Failure in Composites at Multiple Scales

Abstract

The contribution 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 non-linearities 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 chapter. At this level, the plies are modelled as continua and interface elements between them conventionally serve as the framework to model delamination and debonding. After a brief discussion of the cohesive-zone concept and its importance for the analysis of delamination, various finite element models for the plies are elaborated: three-dimensional, generalised plane-strain and solid-like shell models. This is followed by a derivation of interface elements and a discussion of advanced techniques for solving the nonlinear equations that ensue after discretisation. In the last part of this chapter a new, recent method to numerically model delamination is discussed. It exploits the partition-of-unity property of finite element shape functions. The approach offers advantages, since interfaces — and more generally, discontinuities — can be inserted at the onset of delamination only and not a priori, as in the conventional approach. As a consequence, artificial elastic compliance of the interface prior to onset of delamination, spurious traction oscillations ahead of the delamination front, and spurious wave reflections because of the presence of a high stiffness value are avoided. Moreover, unstructured meshes can be employed.