Two-well rigidity and multidimensional sharp-interface limits for solid–solid phase transitions

Davoli E, Friedrich M (2020)

Publication Type: Journal article

Publication year: 2020

Journal

Calculus of Variations and Partial Differential Equations Springer Verlag (Germany)

Book Volume: 59

Article Number: 44

Journal Issue: 2

DOI: 10.1007/s00526-020-1699-5

Abstract

We establish a quantitative rigidity estimate for two-well frame-indifferent nonlinear energies, in the case in which the two wells have exactly one rank-one connection. Building upon this novel rigidity result, we then analyze solid–solid phase transitions in arbitrary space dimensions, under a suitable anisotropic penalization of second variations. By means of Γ -convergence, we show that, as the size of transition layers tends to zero, singularly perturbed two-well problems approach an effective sharp-interface model. The limiting energy is finite only for deformations which have the structure of a laminate. In this case, it is proportional to the total length of the interfaces between the two phases.

Authors with CRIS profile

Manuel Friedrich

Involved external institutions

Technische Universität Wien / Vienna University of Technology AT Austria (AT) Westfälische Wilhelms-Universität (WWU) Münster DE Germany (DE)

How to cite

APA:

Davoli, E., & Friedrich, M. (2020). Two-well rigidity and multidimensional sharp-interface limits for solid–solid phase transitions. Calculus of Variations and Partial Differential Equations, 59(2). https://doi.org/10.1007/s00526-020-1699-5

MLA:

Davoli, Elisa, and Manuel Friedrich. "Two-well rigidity and multidimensional sharp-interface limits for solid–solid phase transitions." Calculus of Variations and Partial Differential Equations 59.2 (2020).

BibTeX: Download