Rigidity and Flexibility in the Modelling of Shape-Memory Alloys

Abstract: In the modelling of shape-memory alloys, a striking dichotomy between rigid and flexible behaviour emerges: On the one hand, in many physically relevant settings, exactly stress-free structures of sufficiently high regularity can be shown to satisfy the kinematic compatibility conditions given by the characteristics of the compatibility equations. The solutions are rigid. On the other hand, when dropping these regularity conditions, the method of convex integration shows that a plethora of wild, irregular solutions exist which do not satisfy the kinematic conditions in general. These solutions can approximate a large class of boundary data and are thus flexible. In this talk, I discuss an approach towards investigating this dichotomy in more detail based on scaling laws. For a class of simplified models, we show that the complexity of the microstructure is captured by these scaling laws both in settings with displacement and with nucleation boundary conditions.

The talk is based on joint work with P. Cesana, F. Della Porta, J. M. Taylor, A. Tribuzio, Ch. Zillinger, B. Zwicknagl.

MathematicsPhysics

Audience: researchers in the topic

Nečas Seminar on Continuum Mechanics

Series comments: This seminar was founded on December 14, 1966.

Faculty of Mathematics and Physics, Charles University, Sokolovská 83, Prague 8. If not written otherwise, we will meet on Mondays at 15:40 in lecture hall K3 (2nd floor)