VarCrysDef · Variational coarse-graining of lattice energies for crystal defects: Applications to partial dislocations and stacking faults
Horizon Europe — Marie Skłodowska-Curie Actions
- Duration
- 2022-10-01 → 2024-09-30
- EU contribution
- €172,750
- Participants
- 1
- Scheme
- HORIZON-TMA-MSCA-PF-EF
Lines connect the coordinator with its partners.
Results in brief
Variational coarse-graining of lattice energies for crystal defects: Applications to partial dislocations and stacking faults
Understanding the emergence, interaction, and motion of crystal defects is crucial for the prediction of possible failure or, on the contrary, strengthening of crystalline materials. Such defects can roughly be described as a local irregularity in the typical crystalline structure. A prominent example of crystal defects are partial dislocations and stacking faults, which typically appear in closed-packed crystalline structures, for example in Hexagonal-closed-packed (HCP) or Face-centered-cubic (FCC) crystals. The main goal of the present action was to predict the emergence of those defects in a mathematically rigorous passage from microscopic/ atomistic models to macroscopic/ continuum models, thus providing a possible justification of phenomenological models used in continuum mechanics. Here our viewpoint was energetic and we employed tools from the Calculus of Variations and Geometric Measure Theory, in particular Gamma-convergence. The latter technique allows to derive effective limiting energies for atomistic energies when the interatomic distance vanishes. Such a procedure is often referred to as a variational coarse-graining.
Data: CORDIS, © European Union
Project objective
Defects are omnipresent in crystalline materials and the understanding of their emergence and interaction is essential for the prediction of the macroscopic material behaviour. Thus, there is a huge interest to pass in a rigorous mathematical way from atomistic models for crystal defects to macroscopic models, e.g., for crystal plasticity. From a variational viewpoint this can be addressed by deriving effective limiting energies from lattice energies when the lattice spacing vanishes. A powerful method to carry out such a variational coarse-graining procedure is Gamma-convergence. In this framework we address here the variational coarse graining of lattice energies which capture the formation and interaction of defects of different dimension, namely partial dislocations and stacking faults. The splitting of dislocations into partial dislocations resulting in a stacking fault is a typical phenomenon of closed-packed crystalline structures. Thus, on the one hand we aim at proposing and analysing a suitable discrete model for partial dislocations and stacking faults in HCP, on the other hand we will embed this result into a broader context by investigating in a general framework the emergence of fractional vortices and string defects in XY-model type energies. Eventually, we will characterise geometric properties of minimisers for the coarse-grained energies.
Original text from CORDIS.
Participants
- UNIVERSITA DEGLI STUDI DI ROMA LA SAPIENZA · RomaCoordinatorItaly
Links
- View on CORDIS
- DOI: 10.3030/101065771
- https://ec.europa.eu/research/participants/documents/downloadPublic?documentIds=080166e5013b6747&appId=PPGMS
- https://ec.europa.eu/research/participants/documents/downloadPublic?documentIds=080166e5fab8eeb6&appId=PPGMS
Data: CORDIS, © European Union