Cosserat continuum or micropolar mechanics theory is an alternative methodology for size-dependent problems which cannot be explained by classical theory. While its applicable fields are diverse, there are few developments or improvements of finite element method but just modifications of conventional ones only to solve particular size-dependent problems such as prediction of shear band, crack analysis. Hence, development of new elements using base elements including triangular, quadrilateral is considered for general micropolar plane problems.
In this study, two types of Cosserat plane quadrilateral finite elements with additional degrees of freedom are developed to minimize total degrees of freedom and obtain calculation performance not inferior to established quadratic elements. In the finite element approximation of translational displacements, one uses generalized node method fully and the other reduced form of it with assumed stress field. Microrotations which are independent variable to translational displacements in Cosserat theory are approximated linearly at element vertices. So all nodal variables are defined only at element vertices in both cases. The elements pass modified patch test proposed by Macneal and Harder and show better or quasi equivalent performances compared with existing Cosserat quadrilateral elements in pure bending tests. In the stress concentration problem, the element with assumed stress field doesn’t have superiority to simple four -node element.