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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 |
Issue 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. |
URI: | http://bura.brunel.ac.uk/handle/2438/512 |
Appears in Collections: | Dept of Mathematics Research Papers Mathematical Sciences |
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