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In this work, a micromechanical finite element analysis is developed in order to determine the debonding evolution in periodic fibre reinforced composites. The cohesive-zone model developed by Alfano and Crisfield (2001) is used to schematize the fibre-matrix interface: the model has a linear softening, considers irreversible damage of the interface and takes into account the mixed mode of debonding by satisfying an interaction criterion. The overall behaviour of the composite is determined with a homogenization analysis, where a representative volume element of the composite is subjected to suitable boundary conditions. The periodic microstructure and the central symmetry of the composites under consideration enable the use of a very small representative volume element, which contains just one fibre or a portion of it, reducing significantly the CPU time. Composites with central symmetry are worth of interest and are frequently used in engineering applications: in the homogenization analysis of orthotropic composites with periodic microstructures, the microdisplacement field has central symmetry (Ohno et al. 2001) and the resulting damage configuration can also exhibit this symmetry. The overall behaviour depends on the load condition prescribed to the composite.
In the most homogenization analysis, the load condition is a prescribed average strain and this can be considered sufficient for the characterization of the overall behaviour in time independent analysis (e.g. elastoplasticity).
In time dependent analysis (e.g. visco-elasticity and visco-plasticity), it is useful to prescribe a precise rate of the average stress as well as a precise rate of the average strain in order to characterize the overall behaviour (Caporale and Luciano 2010). These kinds of load conditions are prescribed in the proposed homogenization technique by imposing suitable boundary conditions. With respect to other existing methods able to prescribe the rate of macrostrain or macrostress, the proposed procedure results easy to use in commercial codes: it simply requires the imposition of conditions on the boundary of the finite element model of a suitable representative volume element, namely half of a unit cell, and it does not require the modification of parts of the source code that are usually not accessible to the user, e.g. the routines for the formation of the equations solving the problem. In fact, in the commercial FEM software the boundary conditions are imposed by assigning given displacements or forces to selected nodes of the finite element mesh, without entering in the system of equations solving the problem. The damage process in composites is very sensitive to the parameters that define the microstructure of the material, i.e. dimensions, shape, orientation of the heterogeneities, their volume fraction and space distribution. The proposed finite element simulations analyse the fibre-matrix debonding evolution for different types of periodic microstructures: specifically, it is evaluated how and how much the fibre volume fraction, the spatial distribution of the fibres and the load conditions affect the overall behaviour in presence of fibre-matrix debonding evolution.