Kreisbeck, Carolin and Kromer, Stefan (2016) HETEROGENEOUS THIN FILMS: COMBINING HOMOGENIZATION AND DIMENSION REDUCTION WITH DIRECTORS. SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 48 (2). pp. 785-820. ISSN 0036-1410, 1095-7154
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We analyze the asymptotic behavior of a multiscale problem given by a sequence of integral functionals subject to differential constraints conveyed by a constant-rank operator with two characteristic length scales, namely, the film thickness and the period of oscillating microstructures, by means of Gamma-convergence. On a technical level, this requires a subtle merging of homogenization tools, such as multiscale convergence methods, with dimension reduction techniques for functionals subject to differential constraints. One observes that the results depend critically on the relative magnitude between the two scales. Interestingly, this even regards the fundamental question of locality of the limit model and, in particular, leads to new findings also in the gradient case.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | HIGHER-ORDER PERTURBATIONS; 2-SCALE CONVERGENCE; EQUI-INTEGRABILITY; A-QUASICONVEXITY; RELAXATION; FUNCTIONALS; SEMICONTINUITY; VECTOR; dimension reduction; homogenization; Gamma-convergence; multiscale problems; PDE constraints; A-quasiconvexity; nonlocality |
| Subjects: | 500 Science > 510 Mathematics |
| Divisions: | Mathematics |
| Depositing User: | Dr. Gernot Deinzer |
| Date Deposited: | 15 Mar 2019 09:06 |
| Last Modified: | 15 Mar 2019 09:06 |
| URI: | https://pred.uni-regensburg.de/id/eprint/2712 |
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