No abstract

We seek for a solution of Saint-Venant's problem for inhomogeneous and anisotropic materials under the assumptions, introduced by Voigt, that the stress is either constant along the axis of the cylinder or depends linearly on the axial coordinate. We first prove the uniqueness of the solution in terms of resultants, then we exhibit an explicit formula for such a solution; we show finally how Clebsch's hypothesis, that the stress vector on axial planes is parallel to the axis, is compatible with Voigt's hypotheses provided that the symmetry group of the material comprising the cylinder contains the reflections on the cross-section.

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

The equivalence between the inequalities of Korn, Friedrichs, Magenes-Stampacchia-Nečas and Babuška-Aziz is derived using some elementary properties of the gradient, divergence and curl operators implied by these inequalities.