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

TL;DR

This paper develops a mathematical framework using modular functions to model strain energies in 2D crystals undergoing reconstructive phase transformations, capturing microstructure formation and defect dynamics.

Contribution

It introduces Ericksen-Landau strain energies based on symmetry principles for modeling reconstructive phase changes in 2D crystals, extending Landau theories.

Findings

Observed bursty phase transformation behavior.

Simulated microstructure formation during shear tests.

Identified defect nucleation and movement as key mechanisms.

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.