Commutativity and non-commutativity of limits in the nonlinear bending theory for prestrained microheterogeneous plates

2024/10/21 by Boehnlein, Klaus, Bouck, Lucas, Neukamm, Stefan +2
#49S05 74K20 74Q05 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2410.15679

Abstract

In this paper we study the derivation of nonlinear bending models for prestrained elastic plates from three-dimensional non-linear elasticity via homogenization and dimension reduction. We compare effective models obtained by either simultaneously or consecutively passing to the Γ-limits as the thickness h≪1 and the size of the material microstructure \e≪1 vanish. In the regime \e≪ h we show that the consecutive and simultaneous limit are equivalent, and also analyze the rate of convergence. In contrast, we observe that there are several different limit models in the case h≪ \e.

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