Tuesday Apr 30, 2013, 03.30 pm
Rigidity, non-rigidity and scaling of the cubic-to-orthorhombic phase transition in the linear theory of elasticity
Angkana Rüland (Universität Bonn)
In this talk I present recent results on rigidity properties of the cubic-to-orthorhombic phase transition in the linear theory of elasticity. Using the framework of convex integration, it is proved that this model provides an example of a martensitic phase transition in which already in the linear theory of elasticity no rigidity properties can be expected without requiring additional regularity conditions on the phase interfaces.
As a complementary result, it is demonstrated that in the generic piecewise po- lygonal situation, i.e. if the phases are separated by a finite number of piecewise polygonal interfaces, the material is rigid. Hence, in this situation locally the only possible configurations are laminates and crossing twins. Finally, in a redu- ced model for the cubic-to-orthorhombic transition involving interfacial energy, a scaling result for crossing twin structures is derived. This reflects the stability of crossing twin structures under small perturbations. These results are part of the author's diploma and PhD theses and are in collaboration with Prof. Dr. Felix Otto.
Time: 03:30 pm
Location: Seminargebäude, Room SG 11, Wüllnerstraße 5 b, 52062 Aachen