In this paper we derive, by means of $\Gamma $-convergence, the periodically wrinkled plate model starting from three dimensional nonlinear elasticity. We assume that the thickness of the plate is ${h}^{2}$ and that the mid-surface of the plate is given by $({x}_{1},{x}_{2})\to ({x}_{1},{x}_{2},{h}^{2}\theta (\frac{{x}_{1}}{h},\frac{{x}_{2}}{h}))$, where $\theta $ is ${[0,1]}^{2}$ periodic function. We also assume that the strain energy of the plate has the order ${h}^{8}={\left({h}^{2}\right)}^{4}$, which corresponds to the Föppl-von Kármán model in the case of the ordinary plate. The obtained model mixes the bending part of the energy with the stretching part.
@article{ASNSP_2013_5_12_2_275_0, author = {Vel\v ci\'c, Igor}, title = {Periodically wrinkled plate model of the F\"oppl-von K\'arm\'an type}, journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze}, publisher = {Scuola Normale Superiore, Pisa}, volume = {Ser. 5, 12}, number = {2}, year = {2013}, pages = {275-307}, zbl = {1271.74290}, mrnumber = {3114006}, language = {en}, url = {http://www.numdam.org/item/ASNSP_2013_5_12_2_275_0} }
Velčić, Igor. Periodically wrinkled plate model of the Föppl-von Kármán type. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Serie 5, Volume 12 (2013) no. 2, pp. 275-307. http://www.numdam.org/item/ASNSP_2013_5_12_2_275_0/
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