Computational Methods for Debonding in Composites

1 Computational Methods for Debonding in Composites 5
6.4 [µm]
Fig. 1.3 Layer which is unidirectionally reinforced with long fibres (above) and finite element
discretisations for three different levels of refinement of a representative volume element composed
of a quarter of a fibre, the surrounding epoxy matrix and the interface between fibre and epoxy [21]
modelled via interface elements, equipped with cohesive-zone models, quite similar
to models for delamination. An example is given in Fig. 1.3, which shows an epoxy
layer, which has been reinforced uniaxially by long fibres, together with three levels
of mesh refinement for a Representative Volume Element of the layer.
1.3 Zero-Thickness Interface Elements
The classical way to represent discontinuities in solids is to introduce zero-thickness
interface elements between two neighbouring (solid) finite elements, e.g. Fig. 1.2 for
a planar interface element. The governing kinematic quantities in interfaces are relative
displacements: vn,vs,vt for the normal and the two sliding modes, respectively.
When collecting these relative displacements in a relative displacement vector v,
they can be related to the displacements at the upper (+) and lower sides (−) of the
interface, u − n ,u + n ,u − s ,u + s ,u − t ,u + t ,by
with u T =(u − n ,...........,u+ t ) and L an operator matrix:
⎡
⎢
L = ⎢
⎣
v = Lu (1.1)
−1 0 0
+1 0 0
0 −1 0
0 +1 0
0 0 −1
0 0 +1
⎤
⎥
⎦
θ
(1.2)