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Based on the micropolar elasticity theory, a size-dependent rectangular element is proposed in this article to investigate the nonlinear mechanical behavior of plates. To this end, a novel three-dimensional formulation for the micropolar theory with the capability of being used easily in the finite element approach is developed first. Afterward, in order to study the micropolar plates, the obtained general formulation is reduced to that based on the Mindlin plate theory. Accordingly, a rectangular plate element is developed in which the displacements and microrotations are estimated by quadratic shape functions. To show the efficiency of the developed element, it is utilized to address the nonlinear bending problem of micropolar plates with different types of boundary conditions. It is revealed that the present finite element formulation can be efficiently employed for the nonlinear modeling of small-scale plates by considering the micropolar effects.

Within the framework of micromorphic elasticity theory, a finite element approach capable of capturing the microstructure effect is developed to describe the bending behavior of microplates. To this end, the micromorphic theory is generally formulated first. The matrix representation of this formulation is then given from which a prism micromorphic element, including the effects of micro-deformation degrees of freedom of material particles, is proposed. The element is applied to the bending problem of micromorphic rectangular and circular plates subject to different boundary conditions. Selected numerical results are presented to show the microstructure influence on the bending of plates with various geometrical parameters. It is revealed that the element is capable of predicting the mechanical behavior of micromorphic continua in an efficient way.