Mathematical analysis of microstructures and low hysteresis shape memory alloys

Friday, May 20, 2011 - 9:00am - 9:30am
Lind 305
Barbara Zwicknagl (Carnegie-Mellon University)
For certain martensitic phase transformations, one observes a close
relation between the width of the thermal hysteresis and the
compatibility of two phases. The latter is in the context of geometrically
non-linear elasticity measured by the deviation of the middle eigenvalue
of the transformation stretch matrix from one. This observation forms the
basis of a theory of hysteresis that assigns an important role to the
energy of the transition layer (Zhang, James, Müller, Acta mat.
57(15):4332–4352, 2009). Following this ansatz, we study the energy
barriers leading to hysteresis, and analyze the shapes of
energetically optimal transition layers for low hysteresis alloys.