A Finite Element Formulation for Crack Problem in Couple-Stress Elasticity

Abstract

In this research, we investigated the crack behavior in the Mode I fracture in a plane strain state, considering the size effects and under the couple-stress theory using finite element method (FEM). First, using the eigenfunction expansion technique, we provided the stress, couple-stress, displacement, strain, and curvature fields at the crack-tip. Then, using the FEM, fundamental parameters that determine the stress and couple-stress fields at the crack-tip (i.e., stress intensity factor and couple-stress intensity factor) were obtained. In the formulation of FEM, we used a mixed variational method, in which displacement and rotation are considered as independent variables, and their kinematic constraints are applied using Lagrange multipliers. Based on this formulation, it was possible to implement the classical quarter-point elements for the crack-tip. The results show that under the framework of the couple-stress theory, energy release rate can still be considered as the fundamental measure and determinant parameter for the crack behavior, but the stress intensity factor alone cannot appropriately describe the crack behavior.