Finite element modeling of micromorphic continua in the context of three-dimensional elasticity

Abstract

The micromorphic theory (MMT) is one of the most general higher-order continuum theories capable of describing the behavior of materials when the microstructure of body is important, in which the micro-deformation degrees of freedom (DOFs) of material particles are taken into account. In this article, a new size-dependent finite element approach is developed for the mechanical analysis of micromorphic continua based on the three-dimensional (3D) elasticity. To this end, the linear MMT is first formulated within the framework of 3D elasticity. Relations are matricized in order to use in the finite element method. Then, a 3D size-dependent element is developed with taking the effects of micro-deformation and micro-rotation DOFs of material particles into account. Micromorphic rectangular plates subject to different sets of boundary conditions are considered as the problem under study whose free vibration is investigated. The effects of thickness-to-length scale parameter and side length-to-thickness ratios on the resonant frequencies of plates are studied in the given results. Also, the results of MMT are compared to those of micropolar theory and classical elasticity. © 2019, Springer-Verlag GmbH Germany, part of Springer Nature.