Quantitative aspects of the rigidity of branching microstructures in shape memory alloys via H-measures
Simon, T.M.
Research article (journal) | Peer reviewedAbstract
Based on a geometrically linearized theory, we describe the partition into twins observed in microstructures of shape memory alloys undergoing cubic-to-tetragonal transformations in an ansatz-free way using H-measures, a tool of microlocal analysis to describe the direction of oscillations and concentration effects of weakly convergent sequences. As an application, we give a 𝐵1,∞2/3-estimate for the characteristic functions of twins generated by finite energy sequences in the spirit of compactness for Γ-convergence. Heuristically, this suggests that the larger-scale interfaces, such as habit planes, can cluster on a set of Hausdorff-dimension 3−23. We provide evidence indicating that this fractional dimension is optimal. Furthermore, we get an essentially local lower bound for the blow-up behavior of the limiting energy density close to a habit plane.
Details about the publication
Authors from the University of Münster
| Simon, Theresa | Juniorprofessorship of Applied Mathematics (Prof. Simon) |
Vorträge zur Publikation
| Rigidity of branching microstructures in shape memory alloys Simon, Theresa (19/05/2021) SIAM Conference on Mathematical Aspects of Materials Science, Basque Center for Applied Mathematics, Bilbao, Spain Type of talk: scientific talk | |
| Rigidity of branching microstructures in shape memory alloys Simon, Theresa (06/10/2017) Materials Working Group Seminar, New York University, New York, USA Type of talk: scientific talk | |
| Rigidity of branching microstructures in shape memory alloys Simon, Theresa (21/07/2017) Graduate Seminar PDE in the Sciences, Rheinische Friedrich-Wilhelms-Universtität Bonn, Bonn, Deutschland Type of talk: scientific talk | |
| Rigidity of branching microstructures in shape memory alloys Simon, Theresa (14/07/2017) Oberseminar Mathematik in den Naturwissenschaften, Julius-Maximilians-Universität Würzburg, Würzburg, Deutschland Type of talk: scientific talk | |
| Rigidity of shape memory alloys Simon, Theresa (17/03/2017) Arbeitsgemeinschaft Angewandte Analysis, Max-Planck-Institut für Mathematik in den Naturwissenschaften, Leipzig, Deutschland Type of talk: scientific talk |