Application of Local Approaches to Crack Development in Structural Materials

The scientific community and engineers are interested in simulating and analysing the behaviour of individual components and complex structures. This review article highlights progress in the area of modelling of structural materials based on the use of the finite element method. In addition to being described deterministically, the situation ahead of a possible stress concentrator is also defined using modern statistical techniques, and the behaviour simulation is explained in terms of length scales. Crack development and generation in the component are the main uses of the description of the impact of local microstructure on macrostructure. There are two predominant types of multiscale analysis: hierarchical and concurrent. Hybrid types also exist, but these are beyond the scope of this paper. Mainly, two-scale hierarchic simulations are illustrated hereafter. The modelling is dedicated to the following groups of materials: (i) crack initiation around inclusions, carbides at grain boundaries, and natural or artificial stress concentrators; (ii) composites with short or long fibres and pronounced interfaces; and (iii) combinations of (i) and (ii) in the case where the grain structure behaves like a short fibre. The authors draw on many years of experience in the field of numerical methods and, in particular, the modified finite element method.