Ericksen-Landau Modular Strain Energies for Reconstructive Phase Transformations in 2D crystals

By using modular functions on the upper complex half-plane, we study a class of strain energies for crystalline materials whose global invariance originates from the full symmetry group of the underlying lattice. This follows Ericksen's suggestion which aimed at extending the Landau-type theori...

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Bibliographic Details
Published in:arXiv.org 2022-11
Main Authors: Arbib, Edoardo, Biscari, Paolo, Patriarca, Clara, Zanzotto, Giovanni
Format: Article
Language:English
Subjects:
Crystal defects
Hexagonal phase
Micromechanics
Microstructure
Nucleation
Phase change
Phase transitions
Shearing
Stress relaxation
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Summary:By using modular functions on the upper complex half-plane, we study a class of strain energies for crystalline materials whose global invariance originates from the full symmetry group of the underlying lattice. This follows Ericksen's suggestion which aimed at extending the Landau-type theories to encompass the behavior of crystals undergoing structural phase transformation, with twinning, microstructure formation, and possibly associated plasticity effects. Here we investigate such Ericksen-Landau strain energies for the modelling of reconstructive transformations, focusing on the prototypical case of the square-hexagonal phase change in 2D crystals. We study the bifurcation and valley-floor network of these potentials, and use one in the simulation of a quasi-static shearing test. We observe typical effects associated with the micro-mechanics of phase transformation in crystals, in particular, the bursty progression of the structural phase change, characterized by intermittent stress-relaxation through microstructure formation, mediated, in this reconstructive case, by defect nucleation and movement in the lattice.
ISSN:2331-8422