Wrinkling as a mechanical instability in growing annular hyperelastic plates

Mehta, Sumit and Raju, Gangadharan and Saxena, Prashant (2022) Wrinkling as a mechanical instability in growing annular hyperelastic plates. International Journal of Mechanical Sciences, 229. pp. 1-14. ISSN 0020-7403

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Growth-induced instabilities are ubiquitous in biological systems and lead to diverse morphologies in the form of wrinkling, folding, and creasing. The current work focusses on the mechanics behind growth-induced wrinkling instabilities in an incompressible annular hyperelastic plate. The governing differential equations for a two-dimensional plate system are derived using a variational principle with no apriori kinematic assumptions in the thickness direction. A linear bifurcation analysis is performed to investigate the stability behaviour of the growing hyperelastic annular plate by considering both axisymmetric and asymmetric perturbations. The resulting differential equations are then solved numerically using the compound matrix method to evaluate the critical growth factor that leads to wrinkling. The effect of boundary constraints, thickness, and radius ratio of the annular plate on the critical growth factor is studied. For most of the considered cases, an asymmetric bifurcation is the preferred mode of instability for an annular plate. Our results are useful to model the physics of wrinkling phenomena in growing planar soft tissues, swelling hydrogels, and pattern transition in two-dimensional films growing on an elastic substrate. © 2022 The Author(s)

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IITH Creators:
IITH CreatorsORCiD
Raju, Gangadharanhttps://orcid.org/0000-0002-6612-8280
Item Type: Article
Additional Information: Prashant Saxena acknowledges the financial support of the EPSRC, UK grant no. EP/V030833/1 .
Uncontrolled Keywords: Bifurcation; Growth; Nonlinear elasticity; Plate theory
Subjects: Physics > Mechanical and aerospace
Divisions: Department of Mechanical & Aerospace Engineering
Depositing User: . LibTrainee 2021
Date Deposited: 21 Jul 2022 11:09
Last Modified: 21 Jul 2022 11:09
URI: http://raiith.iith.ac.in/id/eprint/9849
Publisher URL: http://doi.org/10.1016/j.ijmecsci.2022.107481
OA policy: https://v2.sherpa.ac.uk/id/publication/12584
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