On morphoelastic rods

Morphoelastic rods are thin bodies which can grow and can change their intrinsic curvature and torsion. We deduce a system of equations ruling accretion and remodeling in a morphoelastic rod by combining balance laws involving non-standard forces with constitutive prescriptions filtered by a dissipation principle that takes into account both standard and non-standard working. We find that, as in the theory of three-dimentional bulk growth proposed in [A. DiCarlo and S. Quiligotti, Mech. Res. Commun. 29 (2002) 449-456], it is possible to identify a universal coupling mechanism between stress and growth, conveyed by an Eshelbian driving force.