Assumed strain finite element method based on the theory of strain gradient

An assumed strain finite element method based on the theory of strain gradient was proposed to explore the size effect that frequently exhibited in micro-beam bending. In element design, strain gradient terms were obtained by using numerical integration of a cell constructing around a Gaussian point. An equivalent strain gradient term was incorporated into the constitutive model to reflect the effect of highly localized inhomogeneous deformation. In this way, an assumed strain finite element method program was developed. To validate the performance of the proposed method, a numerical simulation of micro-beam bending was carried out. Numerical resuits show a good agreement with the reported experimental data. It is concluded that the proposed approach is of good capability to reflect the response of microstructure.