Morphoelastic rods are thin bodies which can grow and can change their intrinsic curvature and torsion. We deduce a system of equations that rule 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-dimensional bulk growth proposed [DiCarlo, A and Quiligotti, S. Mech Res Commun 2002; 29: 449-456], it is possible to identify a universal coupling mechanism between stress and growth, conveyed by an Eshelbian driving force.
Tiero, A., & Tomassetti, G. (2016). On morphoelastic rods. MATHEMATICS AND MECHANICS OF SOLIDS, 21(8), 941-965 [10.1177/1081286514546178].