Improved Timoshenko beam-based micropolar peridynamic method incorporating particle geometry

Abstract

Shear effect is a crucial factor in determining crack propagation of mode II and mixed-mode fractures for brittle and quasi-brittle materials. Based on Timoshenko beam theory, shear effect is introduced into micropolar peridynamic model. The peridynamic parameters for two-dimensional and three-dimensional cases are derived with energy equivalence principle. Particle geometry is originally considered in the derived formulations to obtain independent rotational stiffness. An implicit algorithm in finite element framework is adopted to calculate elastic deformation and to simulate quasi-static crack propagation. Several numerical examples are conducted to verify the accuracy and efficiency of the developed model. The results show that the proposed model possesses high accuracy and numerical stability in simulating crack propagation of mode I, mode II and mixed-mode fractures.