We present a partition of unity finite element method for simulating non-linear debonding and matrix failure in thin fibre composites. Fibres are superimposed on a background mesh without meshing them. The constitutive behaviour of the matrix material, the fibre material and the fibre–matrix bond can be independently defined. A concise derivation of the discrete governing equations is given for two classes of continuum damage models describing the matrix material. A non-linear bond-slip law including debonding and fibre pull-out behaviour is used. Several examples illustrate the potential of the proposed approach. Copyright © 2010 John Wiley & Sons, Ltd.
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