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The objective of these lecture notes is to provide an introduction to, review of and examples on the interplay between scaling laws and a striking dichotomy between rigidity and flexibility which arises in the modelling of shape-memory alloys. This has been the content of various recent results of the author and her coworkers. The lecture notes are based on these results (in particular, on the articles Rüland et al., J Nonlinear Sci, 1–48 (2018); Rüland and Tribuzio, Arch Rational Mech Anal 243(1):401–431, 2022) and on lectures given by the author at two summer schools, in Münster in September 2022, and in Cetraro, in July 2023.

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Microstructures in the Modelling of Shape-Memory Alloys: Rigidity, Flexibility and Scaling

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  • 发表日期：

    2025年

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  • Angkana Rüland

摘要

The objective of these lecture notes is to provide an introduction to, review of and examples on the interplay between scaling laws and a striking dichotomy between rigidity and flexibility which arises in the modelling of shape-memory alloys. This has been the content of various recent results of the author and her coworkers. The lecture notes are based on these results (in particular, on the articles Rüland et al., J Nonlinear Sci, 1–48 (2018); Rüland and Tribuzio, Arch Rational Mech Anal 243(1):401–431, 2022) and on lectures given by the author at two summer schools, in Münster in September 2022, and in Cetraro, in July 2023.