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

2024/11/05 by Hui Li, Li, Hui
Computer Science · Engineering · Medicine · #74K20 #74K25 #Advanced Mathematical Modeling in Engineering #Advanced Numerical Methods in Computational Mathematics #Analysis of PDEs (math.AP) #Cardiology #Elasticity and Material Modeling #FOS: Mathematics #FOS: Physical sciences #Materials science #Mathematical Physics (math-ph) #Medicine

paper · pdf · doi:10.48550/arxiv.2411.02777

published in arXiv (Cornell University) (Cornell University)

openalex publication_date 2024/11/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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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