The damage in composites is generally represented by several modes: matrix cracking, matrix crushing, fibre kinking, fibre rupture or breakage. From a modelling point of view, one may find in the literature different choices of mixed modes of damage in composites. Hashin (1980) considered in his stress criteria four modes:
• matrix failure in tension and compression represented by a criterion that includes transverse-to-fibres stress and a combination of shear stresses.
• fibre-matrix disbonding as a function of the longitudinal stress and shear stresses.
• fibre failure in compression or tension, depending upon the limit values of the axial stresses.
Similar mixed modes criteria were used by Chang and Lessard (1991) which were coded by Ambur et al. (2004) as an Abaqus user subroutine for the reader interested in this type of computer implementations. They modelled the progression of the damage modes proposed by Hashin (1980) and applied it to the simulation of composite shells. No implementations to 3D solid elements were shown. Some authors, for example Curiel Sosa et al. (2008a); Curiel Sosa (2008b); Matzenmiller et al. (1995), take into account the following damage modes for modelling:
Composite Materials – Ecodesign and Analysis
• fibre rupture.
• fibre kinking.
• matrix cracking.
• matrix crushing.
In the progressive damage model presented in Section 3 a three dimensional element is used rather than shells and, hence, a general description of the modes is more appropriate under these premises. Delamination is in an upper material scale and is implicitly implemented in the general flow of the procedure as matrix cracking may eventually result in delamination. In this manner, inelasticity is integrated straightforward within the model. It is well-known from experimental evidence that the idealisation of composite behaviour as linear elastic is inadequate (Chang and Lessard, 1991; Xu, 1994) as inelastic deformations evolve not only due to micro-cracks at the micro-scale but also due to complex damage modes occurring at the macroscale, leading, eventually, to the total failure. Contrary to purely brittle materials, the fibre-reinforced composite material exhibits at some extent a softening behaviour preceding the total failure. This phenomenon, from a strictly thermodynamical point of view, is related to the dissipative (irreversible) process that rearranges the distribution of material properties due to the presence of damage.