PIERLUIGI CESANA | Last modified date：2021.06.21 |

Associate Professor /
Australia Branch /
Institute of Mathematics for Industry

**Presentations**

1. | Pierluigi Cesana, Atomistic-to-continuum limits of planar disclinations, JSIAM, 2021.02. |

2. | Pierluigi Cesana, Gamma-convergence results for nematic bilayers: relaxation and actuation, ANZIAM, 2021.02. |

3. | Pierluigi Cesana, Mathematical models and ideas for disclinations, 2021.02. |

4. | Pierluigi Cesana, Mesoscale modeling of disclinations towards a theory for kink and materials strengthening, 2020.12. |

5. | Pierluigi Cesana, Mathematical models and ideas for disclinations , 2020.12. |

6. | Pierluigi Cesana, Mathematical models and ideas for disclinations , 2020.12. |

7. | Pierluigi Cesana, Reduced-dimension models for nematic elastomers foundations, JSIAM, 2020.09. |

8. | Pierluigi Cesana, Mathematical models and ideas for disclinations, 2020.04. |

9. | Pierluigi Cesana, Mathematical models and ideas for disclinations, 2020.04. |

10. | Pierluigi Cesana, Mesoscale modeling for disclinations toward a theory for kink and material strengthening , 2020.02. |

11. | Pierluigi Cesana, Mathematical models and ideas for disclinations and avalanches in elastic crystals, 2020.01. |

12. | Pierluigi Cesana, Variational modeling of wrinkle-free membranes, 2019.12. |

13. | Pierluigi Cesana, Mathematical models and ideas for disclinations, 2019.12, [URL]. |

14. | Pierluigi Cesana, Mathematical models and ideas for disclinations , 2019.11. |

15. | Pierluigi Cesana, Mathematical models and ideas for disclinations (Kyoto), 2019.10, The austenite-to-martensite phase-transformation is a first-order diffusionless transition occurring in elastic crystals and characterized by an abrupt change of shape of the underlying crystal lattice. It manifests itself to what in materials science is called a martensitic microstructure, an intricate highly inhomogeneous pattern populated by sharp interfaces that separate thin plates composed of mixtures of different martensitic phases (i.e., rotated copies of a low symmetry lattice) possibly rich in defects and lattice mismatches. In this talk, we review a series of separate results on the modeling of inter-connected phenomena observed in martensite, which are self-similarity (criticality) and disclinations. Inspired by Bak’s cellular automaton model for sand piles, we introduce a conceptual model for a martensitic phase transition and analyze the properties of the patterns obtained. Nucleation and evolution of martensitic variants is modeled as a fragmentation process in which the microstructure evolves via formation of thin plates of martensite embedded in a medium representing the austenite. While the orientation and direction of propagation of the interfaces separating the plates is determined by kinematic compatibility of the crystal phases, their nucleation sites are inevitably influenced by defects and disorder, which are encoded in the model by means of random variables. We investigate distribution of the lengths of the interfaces in the pattern and establish limit theorems for some of the asymptotics of the interface profile. We also discuss numerical aspects of determining the behavior of the density profile and power laws from simulations of the model and present comparisons with experimental data. Turning our attention on defects, we investigate wedge disclinations, high-energy rotational defects caused by an angular lattice mismatch that were predicted by Volterra in his celebrated 1907 paper. Unlike dislocations, which have received considerable attention since the 1930s, disclinations have received disproportionally less interest. However, disclinations are not uncommon as they accompany, as a relevant example, rotated and nested interfaces separating (almost) kinematically compatible variants as in martensitic avalanche experiments. Here we follow two modeling approaches. First, we introduce a few recent results on the modeling of planar wedge disclinations in a continuum, purely (non-linear) elastic model that describes disclinations as solutions of some differential inclusion. Secondly an atomistic model of nearest-neighbor interactions over a triangular lattice inspired by the literature on discrete models for dislocations. Some of these results are from a collaboration with J.M. Ball and B. Hambly (Oxford) and P. Van Meurs (Kanazawa).. |

16. | Pierluigi Cesana, Variational and stochastic models for martensite, 2019.08. |

17. | Pierluigi Cesana, Variational and stochastic models for martensite, 2019.05. |

18. | Pierluigi Cesana, Models for self-similarity and disclinations in martensite, 2019.03. |

19. | Pierluigi Cesana, A probabilistic model for martensitic interfaces , ANZIAM, 2019.02. |

20. | Pierluigi Cesana, Modeling and analysis of nematic elastomer membranes, AIMS Conference, 2018.07. |

21. | Pierluigi Cesana, Self-organization and criticality in martensite, AIMS Conference, 2018.07, [URL]. |

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