A micropolar peridynamic differential operator and simulation of crack propagation

Abstract

The micropolar continuum explains the size effects in the materials with microstructures by attaching micro-rotations to the material points, but it still encounters difficulties when describing discontinuities. The peridynamic theory takes its advantage in dealing with discontinuous problems. This work formulates the micropolar continuum under the peridynamic differential operator framework. The micropolar elasticity field equations with spatial derivatives are rewritten in the spatial integral form such that the discontinuities can be naturally embedded in the micropolar continuum body. To check the accuracy and effectiveness of such micropolar peridynamic differential operator formulation, the stress concentration factor of a two-dimensional square plate with a central circular hole subjected to unidirectional constant stress was simulated and compared with the results of finite element analysis. The stationary crack propagation phenomena of three modes were reproduced respectively by considering a critical stretch with rotational degrees of freedom. The impact of characteristic length on the crack propagation was investigated. It is found that characteristic length has an insignificant effect on the mode I crack while significantly affects the mode II crack. The work provides some essential references for the fracture behavior modeling of materials with microstructures.