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

Valizadeh I, Steinmann P, Javili A (2018)

Publication Type: Journal article

Publication year: 2018

Journal

Journal of Mechanics of Materials and Structures

Book Volume: 13

Pages Range: 571-585

Journal Issue: 4

DOI: 10.2140/jomms.2018.13.571

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.

Authors with CRIS profile

Paul Steinmann Lehrstuhl für Technische Mechanik

Involved external institutions

Technische Universität Dortmund DE Germany (DE) Bilkent University / Bilkent Üniversitesi TR Turkey (TR)

How to cite

APA:

Valizadeh, I., Steinmann, P., & Javili, A. (2018). Growth-induced instabilities of an elastic film on a viscoelastic substrate: Analytical solution and computational approach via eigenvalue analysis. Journal of Mechanics of Materials and Structures, 13(4), 571-585. https://dx.doi.org/10.2140/jomms.2018.13.571

MLA:

Valizadeh, Iman, Paul Steinmann, and Ali Javili. "Growth-induced instabilities of an elastic film on a viscoelastic substrate: Analytical solution and computational approach via eigenvalue analysis." Journal of Mechanics of Materials and Structures 13.4 (2018): 571-585.

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