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|Title:||An Example of Microstructure with Multiple Scales|
|Keywords:||Calculus of variations, Singular perturbation;Young measure, martensitic phase transformation|
|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:||Dept of Mathematics Research Papers|
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