COMPUTATIONAL MECHANICS, vol.50, no.3, pp.303-320, 2012 (SCI-Expanded)
A large number of methods to describe fracture mechanical features of structures on basis of computational algorithms have been developed in the past due to the importance of the topic. In this paper, current and promising numerical approaches for the characterization of fracture processes are presented. A fracture phenomenon can either be depicted by a continuum formulation or a discrete notch. Thus, starting point of the description is a micromechanically motivated formulation for the development of a local failure situation. A current, generalized method without any restriction to material modelling and loading situation in order to describe an existing crack in a structure is available through the material force approach. One possible strategy to simulate arbitrary crack growth is based on an adaptive implementation of cohesive elements in combination with the standard discretization of the body. In this case, crack growth criteria and the determination of the crack propagation direction in combination with the modification of the finite element mesh are required. The nonlinear structural behaviour of a fibre reinforced composite material is based on the heterogeneous microstructure. A two-scale simulation is therefore an appropriate and effective way to take into account the scale differences of macroscopic structures with microscopic elements. In addition, fracture mechanical structural properties are far from being sharp and deterministic. Moreover, a wide range of uncertainties influence the ultimate load bearing behaviour. Therefore, it is evident that the deterministic modelling has to be expanded by a characterization of the uncertainty in order to achieve a reliable and realistic simulation result. The employed methods are illustrated by numerical examples.