Morphoelastic rods III: Differential growth and curvature generation in elastic filaments

In many growing filamentary structures such as neurons, roots, and stems, the intrinsic shapes and material response is produced by differential growth of the tissue. Therefore, a key problem is to link the growth field at the microscopic level to the macroscopic shape and properties of the filaments. Here, starting with a morphoelastic tubular structure and assuming a form of the growth tensor, we use dimensional reduction to obtain the overall curvature, torsion, and material parameters of a growing filament. Various examples of curvature and torsion generation are given and the impact of residual stress on the generation of curvature is demonstrated.