Mathematics - Colloquium
Thursday, February 21, 2013
11:00 AM-12:00 PM
ABSTRACT: We study the zero-energy states of monoclinic-I martensite, which is the most-common shape memory alloy. We have two surprising results:
First, there is an open set in which the energy minimising microstructures are infinite-rank laminates (commonly known as T3s). This is, to our knowledge, the first "real-world" occurrence of these non-(finite)-laminate microstructures. (We suspect that, as a consequence, the symmetrized rank-one convex hull/envelope of monoclinic-I martensite is strictly larger/lower than the lamination convex hull/envelope. If so, this would be the first material for which this is known to be true.)
Second, there are in fact two types of monoclinic-I martensite, indistinguishable in their symmetry but differing as to their convex-polytope structure. Curiously all known materials belong to one of these types. Since these differ in their zero-energy states, it is possible that the other type would have superior mechanical properties.
Our analysis is in the context of geometrically-linear elasticity and ignores interfacial energy. A novel feature is the use of algebraic methods, primarily the theory of convex polytopes. This is joint work with Anja Schloemerkemper, University of Wuerzburg.
Suggested Audiences: Adult, College
Last Modified: February 15, 2013 at 9:45 AM