3D-2D asymptotic analysis for inhomogeneous thin films (Q2733848)

The authors present in the context of fully nonlinear elasticity, a general approach that allows for material heterogeneity as well as rapidly varying profiles. A dimension reduction analysis is undertaken using \(\Gamma\)-convergence techniques within a relaxation theory for 3D nonlinear elastic thin domains of the form NEWLINE\[NEWLINE\Omega_\varepsilon =\bigl\{ (x_1, x_2, x_3)\mid (x_1,x_2) \in\omega,\;|x_3|<\varepsilon f_\varepsilon (x_1,x_2) \bigr\},NEWLINE\]NEWLINE where \(\omega\) is a bounded domain of \(\mathbb{R}^2\) and \(f_\varepsilon\) is an \(\varepsilon\)-dependent profile. Moreover an abstract representation of the effective 2D energy is obtained, and specific characterizations are found for nonhomogeneous plate models, periodic profiles, and within the context of optimal design for thin films.