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Title: An Example of Microstructure with Multiple Scales
Authors: Winter, M
Keywords: Calculus of variations, Singular perturbation
Young measure, martensitic phase transformation
Publication Date: 1997
Publisher: Cambridge University Press
Citation: European J Appl Math 8 (1997), 185-207
Abstract: 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 nonconvex function of the gradient with exactly four minima. We prove that the Young measure corresponding to a minimising 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.
Appears in Collections:Mathematical Science
Dept of Mathematics Research Papers

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