MAE Special Seminar: Ryan Elliott (Minnesota)

A Framework for the Interpretation of Modulated Martensites in Shape Memory Alloys

Shape memory alloys (SMAs) are a class of materials with unusual properties that have been attributed to the material undergoing a Martensitic Phase Transformation (MPT). An MPT consists of the material’s crystal structure evolving in a coordinated fashion from a high symmetry austenite phase to a low symmetry martensite phase. Often in SMAs, the austenite is a B2 cubic configuration that transforms a Modulated Martensite (MM) phase. MMs are long-period stacking order structures consisting of [110]_cubic basal planes. First-principles computational results have shown that the minimum energy phase for these materials is not a MM, but a short-period structure called the Ground State Martensite. It is commonly argued that energy contributions associated with kinematic compatibility constraints at the austenite-martensite interface explain the experimental observation of meta-stable MMs, as opposed to the expected Ground State Martensite phase. A general approach for predicting the properties of the MM structure that will be observed for a particular material has been lacking.

In this work, we develop a framework for the interpretation of MMs as natural features of the material’s energy landscape (expressed as a function of the lattice parameters and individual atomic positions within a perfect infinite crystal). From this energy-based framework, a new understanding of MMs as a mixture of two short-period Base Martensite phases is developed. Using only a small set of input data associated with the two Base Martensites, this MM Mixture Model (M^4) is capable of accurately predicting the energy, lattice constants, and structural details of an arbitrary Modulated Martensite phase. This is demonstrated by comparing the M^4 predictions to computational results from a particular empirical atomistic model.

Bio:
Ryan S. Elliott received his B.S. in engineering mechanics from Michigan State University. He received a M.S.E. in aerospace engineering, an M.S. in mathematics, and a Ph.D. in aerospace engineering and scientific computing, all from The University of Michigan. In 2004 he was a Research Fellow at The University of Michigan. Elliott was appointed, as an assistant professor, in January 2005 to the faculty of the Aerospace Engineering and Mechanics (AEM) Department at The University of Minnesota, Minneapolis. In 2011 he was promoted to associate professor with tenure and to professor in 2018. In 2010 he held the position of visiting researcher at the Laboratoire de Mecanique des Solides (LMS) of The Ecole Polytechnique, Palaiseau, France. Elliott served as the first KIM Editor for the Knowledgebase of Interatomic Models (KIM) (https://openkim.org) from 2012–2018. Elliott was appointed to the Journal of Elasticity Board of Editors in 2015, and to the International Journal of Solids and Structures Board of Editors in 2017. In 2017, Elliott was elected Fellow of the American Society of Mechanical Engineers (ASME). In 2020 he became Director of Graduate Studies for the AEM Department.

Dr. Elliot’s research deals with stability and instability problems related to structures, materials, and microstructured materials. This broad area of engineering science encompasses phenomena such as the crumpling of a car body and frame when involved in a crash, the buckling of railroad tracks on extremely hot and sunny days, the flutter of aircraft wings (where flapping-like vibrations can be amplified and ultimately rip the wings or tail fins off the craft), and the instabilities that can lead to collapse of space truss and frame structures commonly used in satellites and space station construction. Professor Elliott’s research program has three major themes: (I) development of nonlinear modeling of discrete and continuum solid-state materials and structures, capable of accurately predicting instability behavior and the associated multiple stable states of real systems; (II) development of analytical and computational methodologies (based on theories of symmetry, bifurcation, and pattern formation) that combine applied mathematics and scientific computing to systematically discover the multiple stable states predicted by a given nonlinear model; and (III) development of open source scientific software, and the creation and support of user communities who benefit from these software packages. The specific research projects pursued by Professor Elliott and his research group each involve one or more of these major themes which serve as common threads connecting them all. Elliott is co-author (with E.B. Tadmor and R.E. Miller) of the book “Continuum Mechanics and Thermodynamics: From Fundamental Concepts to Governing Equations”, Cambridge University Press, 2011. He has received numerous awards, including: the Tau Beta Pi Matthews Fellowship (1998), the U.S. D.O.E. Computational Science Graduate Fellowship (2000), the Ivor K. McIvor Award in Applied Mechanics, the Frederick A. Howes Scholar in Computational Science award (2005), a National Science Foundation CAREER grant (2007), a University of Minnesota McKnight Land-Grant Professorship (2009), the Russell J. Penrose Faculty Fellowship (2012), and the Thomas J.R. Hughes Young Investigator award (2014). Elliott’s research has been presented at numerous national and international conferences.