Finite Element Analysis of Progressive Degradation versus Failure Stress Criteria on Composite Damage Mechanics

It is well known that the engineering applications using composite materials is in constant growth, mainly because of the large strength/weight ratio that they provide. The modelling of these materials has been of interest for a long time, due to the experimental costs that can be saved by means of computer simulations. However, the mixed mode of failure in composite materials makes it a complicated task to deal with, resulting often in sophisticated damage models. There have been numerous techniques proposed for the simulation or prediction of the failure of composites. Many of these techniques were integrated on analytical methods that were subsequently implemented on major simulation software packages or in-house finite element method programs. This is the case in failure models based on stress quadratic functionals, such as those by Tsai & Wu (1971), and implemented within ANSYS (Swanson, 2007) or by Hoffman (1967) and included within ABAQUS (Hibbit et al., 2007). Such functionals imply the disappearing of bearing capability to outstanding loads once the stress criteria are satisfied. From a strict numerical point of view, a finite element satisfying the criteria may potentially be removed from the mesh as it does not experience further loading. This possibility is available in major software packages such as LS-DYNA. The removal of a finite element frequently causes certain numerical oscillations when using explicit solvers. This may degenerate into instabilities and, hence, in divergence of the numerical procedure. A significant number of these criteria have been proposed in the last decades. For instance, the models by Tsai & Wu (1971), Hoffman (1967), Yamada and Sun (1978) or Puck and Schurmann (1998) amongst many others have been very popular. A worldwide assessment failure exercise (WWFE) of a number of these criteria is described in references (Hinton and Soden, 1998; Hinton et al., 2004). Also, Soden et al. (1998a) presented the result for fibre-reinforced composite laminates and their correlation to a set of shared-by-participants experimental data (Soden et al., 1998b). It is clear that considerable efforts have been done in the searching of a general criteria that may be applied in a wide range of problems. However, Daniel (2007) reveals discrepancies of up to 200-300% in the WWFE results shown by Soden et al. (1998a). Unawareness of the numerical consequences that carry the use of these criteria within a finite element method, such as instability and, finally, divergence of the numerical procedure , result in unrealistic solutions. On the other hand, different 19