An example of microstructure with multiple scales

Matthias Winter

Research output: Contribution to journalArticlepeer-review

5 Citations (Scopus)


This paper studies a vectorial problem in the calculus of variations arising in the theory of martensitic microstructure. The functional has an integral representation where the integrand is a non-convex function of the gradient with exactly four minima. We prove that the Young measure corresponding to a minimizing sequence is homogeneous and unique for certain linear boundary conditions. We also consider the singular perturbation of the problem by higher-order gradients. We study an example of microstructure involving infinite sequential lamination and calculate its energy and length scales in the zero limit of the perturbation.

Original languageEnglish
Pages (from-to)185-207
Number of pages23
JournalEuropean Journal of Applied Mathematics
Issue number2
Publication statusPublished - Apr 1997


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