TL;DR
This paper introduces a Lagrangian-based method for tracking the evolving shape of surfaces in nonlinear elasticity problems, simplifying computations by fixing the initial geometry and applying it to various physical phenomena.
Contribution
It presents a concise Lagrangian crumpling equations approach that enables efficient analysis of evolving surfaces in nonlinear elasticity.
Findings
Effective in modeling bulging of thin plates under pressure
Accurately predicts buckling of spherical shells
Improves experimental agreement in capillary wrinkle simulations
Abstract
A concise method for following the evolving geometry of a moving surface using Lagrangian coordinates is described. All computations can be done in the fixed geometry of the initial surface despite the evolving complexity of the moving surface. The method is applied to three problems in nonlinear elasticity: the bulging of a thin plate under pressure (the original motivation for Foeppl-von Karman theory), the buckling of a spherical shell under pressure, and the phenomenon of capillary wrinkles induced by surface tension in a thin film. In this last problem the inclusion of a gravitational potential energy term in the total energy improves the agreement with experiment.
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