Kreisbeck, Carolin (2017) A NOTE ON 3D-1D DIMENSION REDUCTION WITH DIFFERENTIAL CONSTRAINTS. DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES S, 10 (1). pp. 55-73. ISSN 1937-1632, 1937-1179
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Starting from three-dimensional variational models with energies subject to a general type of PDE constraint, we use Gamma-convergence methods to derive reduced limit models for thin strings by letting the diameter of the cross section tend to zero. A combination of dimension reduction with homogenization techniques allows for addressing the case of thin strings with fine heterogeneities in the form of periodically oscillating structures. Finally, applications of the results in the classical gradient case, corresponding to nonlinear elasticity with Cosserat vectors, as well as in micromagnetics are discussed.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | FREE VECTOR-FIELDS; A-QUASICONVEXITY; NONLINEAR ELASTICITY; LOWER SEMICONTINUITY; 2-SCALE CONVERGENCE; MEMBRANE THEORY; GAMMA-LIMIT; HOMOGENIZATION; FUNCTIONALS; RELAXATION; Dimension reduction; Gamma-convergence; homogenization; multiscale problems; PDE constraints; A-quasiconvexity |
| Subjects: | 500 Science > 510 Mathematics |
| Divisions: | Mathematics |
| Depositing User: | Dr. Gernot Deinzer |
| Date Deposited: | 14 Dec 2018 13:01 |
| Last Modified: | 26 Feb 2019 12:55 |
| URI: | https://pred.uni-regensburg.de/id/eprint/518 |
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