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arXiv · 2211.14894

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

Edoardo Arbib·Paolo Biscari·Clara Patriarca·Giovanni Zanzotto
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Abstract

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.

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Edoardo Arbib, Paolo Biscari, Clara Patriarca, Giovanni Zanzotto. 2022-11-27. Ericksen-Landau Modular Strain Energies for Reconstructive Phase Transformations in 2D crystals. https://arxiv.org/abs/2211.14894

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