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On morphoelastic rods. (English) Zbl 1379.74014
Summary: 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 proposed by A. DiCarlo and S. Quiligotti in the theory of three-dimensional bulk growth [Mech. Res. Commun. 29, No. 6, 449–456 (2002; Zbl 1056.74005)], it is possible to identify a universal coupling mechanism between stress and growth, conveyed by an Eshelbian driving force.

MSC:
74K10 Rods (beams, columns, shafts, arches, rings, etc.)
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