Active filaments I: Curvature and torsion generation

In many filamentary structures, such as hydrostatic arms, roots, and stems, the active or growing part of material depends on contractile elongating fibers. Through their activation by muscular contraction growth, these fibers will generate internal stresses that are partially relieved filament acquiring intrinsic torsion curvature. This process is fundamental in morphogenesis but also plant tropism, nematic solid activation, motion organs elephant trunks octopus arms. Here, we provide a general theory links arbitrary at microscale to generation curvature macroscale. obtained dimensional reduction from full anelastic description three-dimensional bodies morphoelastic Kirchhoff rods. Hence, it geometry properties embedded shape stiffness rod. The applied wound helically around central core tapered untapered filaments.