On the Föppl-von Kármán theory for elastic prestrained films with varying thickness

2024/11/05 by Li, Hui
#74K20 #74K25 #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph)

paper · doi:10.48550/arxiv.2411.02777

Abstract

We derive the variational limiting theory of thin films, parallel to the Föppl-von Kármán theory in the nonlinear elasticity, for films that have been prestrained and whose thickness is a general non-constant function. Using Γ-convergence, we extend the existing results to the variable thickness setting, calculate the associated Euler-Lagrange equations of the limiting energy, and analyze the convergence of equilibria. The resulting formulas display the interrelation between deformations of the geometric mid-surface and components of the growth tensor.

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