Journal title
Journal of Mathematical Biology
DOI
10.1007/s00285-018-1292-0
Issue
3
Volume
78
Last updated
2024-09-23T13:24:57.267+01:00
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
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Publication type
Journal Article
Publication date
11 Sep 2018