A boundary element framework for polycrystalline micro-mechanics

The seminar will describe the development of a three-dimensional framework for micro- and multi-scale analysis of degradation and failure processes in polycrystalline materials. The framework is based on the employment of a boundary integral representation of the mechanics of individual crystals, whose numerical treatment is addressed by the boundary element method. On the other hand, intergranular processes, included damage evolution and cracking, are modelled using extrinsic cohesive laws, embodying an irreversible damage parameter whose evolution is captured through incremental/iterative solution algorithms. A peculiar feature of the formulation is the expression of the micro-structural problem in terms of intergranular variables only, namely displacements jumps and tractions, which: i) allows a certain simplification of the pre-processing stage of the analysis; ii) induces a reduction in the number of DoFs needed in the analysis; iii) allows a natural inclusion of the cohesive laws representing intergranular phenomena. Applications shown will include: computational homogenisation of polycrystalline aggregates; inter- and trans-granular progressive failure; crystal plasticity; hydrogen embrittlement; high-cycle fatigue; homogenisation and micro-cracking of piezoelectric aggregates; two-scale modelling of degradation and failure of polycrystalline components.