Finite element analysis of micromorphic and micropolar continua based on two-dimensional elasticity

Abstract

In this paper, within the framework of two-dimensional (2D) elasticity, a novel finite element formulation is proposed based on the micropolar theory (MPT) and the micromorphic theory (MMT). First, general formulations are developed for the micromorphic and micropolar continua in the context of 2D elasticity. Then, they are presented in a matrix form which is useful from the computational viewpoint. In the next step, using the matricized MPT and MMT formulations, a linear finite element approach including the effects of micro-deformation and micro-rotation degrees of freedom (DOFs) of material particles is developed, and a quadratic size-dependent element is proposed accordingly. Two test problems are solved to reveal the efficiency of the developed formulation. The influence of the length scale parameter on the bending of micromorphic and micropolar plates is illustrated in the given examples. Furthermore, comparisons are made between the results obtained from classical elasticity theory and those calculated based upon MPT and MMT.