Asymptotic analysis of thin structures with point-dependent energy growth

Abstract

In this paper, 3D–2D-dimensional reduction for hyperelastic thin films modeled through energies with point-dependent growth, assuming that the sample is clamped on the lateral boundary, is performed in the framework of $\mathrm{\Gamma }$-convergence. Integral representation results, with a more regular Lagrangian related to the original energy density, are provided for the lower dimensional limiting energy, in different contexts.