A one-dimensional model for elastic ribbons: A little stretching makes a big difference

Starting from the theory of elastic plates, we derive a non-linear one-dimensional model for ribbons with thickness t, width and length ℓ, assuming t≪a≪ℓ. It takes form rod specific constitutive law accounting both stretching bending ribbon mid-surface. The is asymptotically correct can handle finite rotations. Two popular theories be recovered as limiting cases, namely Kirchhoff’s small twisting strains, |κi|≪t∕a2, Sadowsky’s inextensible |κi|≫t∕a2; point out that may poor approximation even having very thin cross-section (say, t∕a 0.02). By way illustration, applied (i) to lateral-torsional instability ribbon, showing good agreement experiments finite-element shell simulations, (ii) stability twisted subjected tensile force. non-convexity discussed; it addressed by convexification argument.