Post-buckling behaviour of a growing elastic rod.

Author: 

Almet, A
Byrne, H
Maini, P
Moulton, D

Publication Date: 

February 2019

Journal: 

Journal of mathematical biology

Last Updated: 

2019-08-11T10:21:00.8+01:00

Issue: 

3

Volume: 

78

DOI: 

10.1007/s00285-018-1292-0

page: 

777-814

abstract: 

We consider mechanically-induced pattern formation within the framework of a growing, planar, elastic rod attached to an elastic foundation. Through a combination of weakly nonlinear analysis and numerical methods, we identify how the shape and type of buckling (super- or subcritical) depend on material parameters, and a complex phase-space of transition from super- to subcritical is uncovered. We then examine the effect of heterogeneity on buckling and post-buckling behaviour, in the context of a heterogeneous substrate adhesion, elastic stiffness, or growth. We show how the same functional form of heterogeneity in different properties is manifest in a vastly differing post-buckled shape. Finally, a fourth form of heterogeneity, an imperfect foundation, is incorporated and shown to have a more dramatic impact on the buckling instability, a difference that can be qualitatively understood via the weakly nonlinear analysis.

Symplectic id: 

904969

Submitted to ORA: 

Submitted

Publication Type: 

Journal Article