Stress-driven two-phase integral elasticity for torsion of nano-beams

• Published in: Composites. Part B, Engineering Engineering, 2018-07, Vol.145, p.62-69
• Main Authors: Barretta, R., Ali Faghidian, S., Luciano, R., Medaglia, C.M., Penna, R.
• Format: Article
• Language: English
• Subjects: Analytical modeling; Hellinger-Reissner variational principle; Mixtures; Nano-beams; Nonlocal integral elasticity; Size effects; Torsion
• ISSN: 1359-8368; 1879-1069
• DOI: 10.1016/j.compositesb.2018.02.020

Size-dependent structural behavior of nano-beams under torsion is investigated by two-phase integral elasticity. An effective torsional model is proposed by convexly combining the purely nonlocal integral stress-driven relation with a local phase. Unlike Eringen's strain-driven mixture, the projected model does not exhibit singular behaviors and leads to well-posed elastostatic problems in all cases of technical interest. The new theory is illustrated by studying torsional responses of cantilever and doubly-clamped nano-beams under simple loading conditions. Specifically, the integral convolution of the two-phase mixture is done by considering the special bi-exponential kernel. With this choice, the stress-driven two-phase model is shown to be equivalent to a differential problem equipped with higher-order constitutive boundary conditions. Exact solutions are established and comparisons with pertinent results obtained by the Eringen strain-driven two-phase mixture and by the strain gradient theory of elasticity are carried out. The outcomes could be useful for the design and optimization of nano-devices and provide new benchmarks for numerical analyses.