Saint-Venant torsion based on strain gradient theory

In this study, the Saint-Venant torsion problem based on strain gradient theory is developed. A total form of Mindlin's strain gradient theory is used to acquire a general Saint-Venant torsion problem of micro-bars formulation. A new Finite Element formulation based on strain gradient elasticity theory is presented to solve the Saint-Venant torsion problem of micro-bars. Moreover, the problem is solved for both micro and macro scale. In addition, six different cross sections in solid and hollow condition are considered, which the Saint-Venant torsion problem is solved on them. Torsional response of micro-bars is predicted by using the modified couple stress theory and the strain gradient theory of Aifantis which both of them employ only one length scale parameter. Some micro-bars with different cross-sectional area are investigated to show the performance of current study and conclusions are drawn from the micron-scale torsional feedback for micro-bars.