Phase transformations and compatibility in helical structures

Abstract

We systematically study phase transformations from one helical structure to another. Motivated in part by recent work that relates the presence of compatible interfaces with properties such as the hysteresis and reversibility of a phase transformation [35,33,12,28], we give necessary and sufficient conditions on the structural parameters of two helical phases such that they are compatible. We show that, locally, four types of compatible interface are possible: vertical, horizontal, helical and elliptical. We discuss the mobility of these interfaces and give examples of systems of interfaces that are mobile and could be used to fully transform a helical structure from one phase to another.These results provide a basis for the tuning of helical structural parameters so as to achieve compatibility of phases. In the case of transformations in crystals, this kind of tuning has led to materials with exceptionally low hysteresis and dramatically improved resistance to transformational fatigue. Compatible helical transformations with low hysteresis and fatigue resistance would exhibit an unusual shape memory effect involving both twist and extension, and may have potential applications as new artificial muscles and actuators.

Helical Miura origami

“…We now define precisely what it means for a structure to be HMO, and we discuss the implications of this definition as it relates to characterizing all such structures. The line of thinking here is based on a systematic and complete characterization of helical and rod symmetry that we developed for an analogous problem: describing all possible phases in nanotubes [29]. To avoid being redundant, we simply borrow (and state without proof) ideas from this work that are used in the constructions here.…”

“…Nevertheless, we show that reconfigurability can be achieved. Inspired by atomistic theory [29], we discuss two strategies for doing so: one involving motion by slip and the other involving phase transformation.…”

Evolving, complex topography from combining centers of Gaussian curvature

“…Moreover, we can employ the generalized versions of ( 5) and ( 6) to study curved interfaces, with t not a constant vector, but a local tangent to the reference curved interface. This generalization has been used to study the phase transformation and compatible interfaces between helical structures [23]. Specifically, suppose the reference interface is described as r(s).…”

Crystal elasto-plasticity on the Poincaré half-plane

“…Atomistictype modelling, on the other hand, while free from such drawbacks, concerns only short time scales, and is also not particularly efficient in elucidating how crystal symmetry and kinematics influence defect and microstructure formation and evolution in the distorted solids. For instance, the fundamental role of kinematic compatibility in the mechanical behavior of crystalline materials may be appreciated only through an in-depth analysis of the deformation-gradient map representing the lattice distortion (Song et al, 2013;Biscari et al, 2015;James, 2018;Feng et al, 2019).…”

“…GL-symmetry has also been used to study reconstructive structural transformations, in which strains may reach or overcome the EPN bundaries, producing lattice-defects and plasticity phenomena (Pitteri and Zanzotto, 2002;Conti and Zanzotto, 2004;Bhattacharya et al, 2004;Caspersen et al, 2004;Lew at al, 2006;Perez-Reche et al, 2007;Denoual et al, 2010;Vattré and Denoual, 2016;Perez-Reche et al, 2016;Perez-Reche, 2017). Full lattice invariance has furthermore been used in the study of twinning-mode proliferation in metals , or of slip and twinning in helical structures (Feng et al, 2019).…”