Morphoelastic rods. Part I: A single growing elastic rod

A theory for the dynamics and statics of growing elastic rods is presented. First, a single growing rod is considered and the formalism of three-dimensional multiplicative decomposition of morphoelasticity is used to describe the bulk growth of Kirchhoff elastic rods. Possible constitutive laws for growth are discussed and analysed. Second, a rod constrained or glued to a rigid substrate is considered, with the mismatch between the attachment site and the growing rod inducing stress. This stress can eventually lead to instability, bifurcation, and buckling.

Graphical abstractFigure optionsDownload full-size imageDownload as PowerPoint slideHighlights► A theory for growing elastic rods is developed based on the Kirchhoff equations. ► The generic formulation is based on the decomposition of deformation gradient in three-dimensional elasticity. ► A constitutive framework is built to model a growing rod on a rigid foundation. ► Buckling instabilities due to growth and external interactions are demonstrated.