Highly Reversible Phase-transforming Materials
New phase transforming materials, even with strong first-order transformations, can be designed with low hysteresis and multimillion cycle reversibility.
Phase transforming materials have an abrupt change of crystal structure at the transformation temperature. This change can be quite drastic. So it can happen, for example, that one phase is a strong magnet and the other is non-magnetic. Such materials also are usually ferroelastic, meaning that they also change shape at the phase transformation. We call this "multiferroism by reversible phase transformation". Over the past 10 years we have been seeking the fundamental explanation of what causes some phase transforming materials to fail after a few transformation cycles, while others can go many millions of cycles. The Zn45Au30Cu45 alloy at left was discovered using a systematic theory-designed procedure. It is a big first-order phase transformation, exceedingly low hysteresis, and excellent reversibility. During heating and cooling it exhibits the delightful (and very unusual) non repeating microstructures shown. See [115], [116], [122], [141] and [161] for more details. We are collaborating closely with researchers from Kiel, Germany and Hong Kong in this work.
Origami structures
World population is growing approximately linearly at about 80 million per year. As time goes by, there is necessarily less space per person. Perhaps this is why the engineering community seems to be obsessed with folding things. Here is our approach.
We depart from the standard approach to origami design which could be termed Eulerian -- develop relations between kinematic objects in the deformed sheet -- by developing a Lagrangian approach (describe the folding process as a deformation) [171]. We have previously developed a mathematical approach to ''rigid folding'' based on the use of piecewise rigid isometric mappings. A group orbit method using discrete isometry groups enables the design of complex structures from simple calculations. Our ideas are inspired by the way atomistic structures form naturally. These ideas are explained in our paper, ''Origami and Materials Science'' [157]. There are also fascinating mathematical analogs to the way microstructures form, as above.
Most recently, we depart from rigid folding by allowing the tiles to deform isometrically; that is, they are allowed to bend but not stretch. This is the way a piece of paper or sheet metal deforms. The work on curved origami structures with exact isometric deformations of the tiles is shown in the paper [178] and the videos on the right. Famously, buildings designed by Frank Gehry often use isometric deformations and some have creases: a great example is the Walt Disney Concert Hall. Our designs are like the Frank Gehry designs but are foldable from a flat sheet! The group orbit method also can be extended to the isometric case [169].
A revealing example of former postdoc Paul Plucinsky (Assistant Professor, USC) gives a simple 16x16 crease pattern that can be folded 65,434 distinct ways (above and [157]). And this is only the piecewise rigid foldings. If we allow curved creases and curved tiles, there is even more freedom. So, as one can imagine, the energy landscape of isometrically deformed origami structures can be exceedingly complicated. In the case that the energy is elastic energy due to deforming tiles, there is a wonderfully accurate theory to calculate the energy (and forces, moments) of these deformed tiles called Kirchhoff's plate theory. It says that the energy of a deformed tile goes as its thickness cubed. With different tiles having different thicknesses, there is tremendous latitude to design origami structures. We are trying to understand and manipulate this energy landscape to bias the structure to desired configurations, in a collaboration with the Air Force Research Laboratory. We also see relevance of some of these designs to the mitigation of climate change, but more about that to come. Currently, besides AFRL, we are collaborating with researchers at Caltech, Carnegie Mellon, Princeton, and Robert J. Lang.