Multi-scale modelling of inelastic behavior

In this chapter we will briefly explore the multi-scale modelling of inelastic behavior, the topic of much interest for the current research (e.g. see [118] for the state-of-the-art contributions). With this kind of approach, the phenomenological models are replaced by refined models of inelastic behavior constructed at two scales: macro-scale that represents the homogenized behavior of material for computing the global structural response, and microscale that allows us to capture the fine details of microstructure for heterogeneous multi-phase materials. The latter provides the main advantage of this kind of approach in offering a more reliable interpretation of inelastic behavior mechanisms, failure and/or plasticity modes. In trying to keep our developments within the most general framework, we will again employ the finite element method at the level of micro-scale.