Micromorphic prism element

Abstract

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.