Vol. 13, No. 4, 2018

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Growth-induced instabilities of an elastic film on a viscoelastic substrate: analytical solution and computational approach via eigenvalue analysis

Iman Valizadeh, Paul Steinmann and Ali Javili

Vol. 13 (2018), No. 4, 571–585
Abstract

The objective of this contribution is to study for the first time the growth-induced instabilities of an elastic film on a viscoelastic substrate using an analytical approach as well as computational simulations via eigenvalue analysis. The growth-induced instabilities of a thin film on a substrate is of particular interest in modeling living tissues such as skin, brain, and airways. The analytical solution is based on Airy’s stress function adopted to viscoelastic constitutive behavior. The computational simulations, on the other hand, are carried out using the finite deformation continuum theory accounting for growth via the multiplicative decomposition of the deformation gradient into elastic and growth parts. To capture the critical growth of elastic films and the associated folding pattern, eigenvalue analysis is utilized, in contrast to the commonly used perturbation strategy. The eigenvalue analysis provides accurate, reliable, and reproducible solutions as contrasted to the perturbation approach. The numerical results obtained from the finite element method show an excellent agreement between the computational simulations and the proposed analytical solution.

Keywords
growth-induced instabilities, viscoelasticity, wrinkling, finite element method
Milestones
Received: 3 August 2018
Revised: 2 September 2018
Accepted: 9 September 2018
Published: 13 December 2018
Authors
Iman Valizadeh
Department of Mechanical Engineering
TU-Dortmund
Dortmund
Germany
Paul Steinmann
Chair of Applied Mechanics
Universität Erlangen-Nürnberg
Erlangen
Germany
Glasgow Computational Engineering Centre, School of Engineering
University of Glasgow
Glasgow
UK
Ali Javili
Department of Mechanical Engineering
Bilkent University
Ankara
Turkey