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.

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► 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.