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 progress 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.

通过在上复半平面上​​使用模函数，我们研究了一类晶体材料的应变能，其全局不变性源于底层晶格的完全对称群。这遵循了埃里克森的建议，该建议旨在扩展朗道型理论，以涵盖经历结构相变的晶体的行为，包括孪生、微观结构形成以及可能相关的塑性效应。在这里，我们研究了用于重建变换建模的埃里克森-朗道应变能，重点关注二维晶体中方形六边形相变的典型情况。我们研究了这些势的分叉和谷底网络，并在准静态剪切试验的模拟中使用其中之一。