An improved bond-associated peridynamic model and its adaptive coupling with CCM for fracture analysis

Abstract

This paper reformulates the correction factor in the force-state of the bond-associated peridynamic (BAPD) model. The reformulation is established from the strain energy density equivalence between the BAPD model and the classical continuum mechanics (CCM) model at a material point. With the FEM solution taken as the reference, the proposed correction factor improves the accuracy of the BAPD solution in this study. Furthermore, a BAPD-CCM coupled model is developed based on the above energy density equivalence, and a ``Morphing" function is introduced to achieve a smooth transition between the two models. For time integration, explicit schemes are adopted for both quasi-static and dynamic problems. In the spatial discretization, the CCM model is discretized by elements, whereas the BAPD model is discretized by particles. The solution accuracy of the coupled model is validated by comparison with the FEM solution and by evaluating the $L^{2}$ norm, the $H^{1}_{\mathrm{semi}}$, and the energy norm of the displacement error. Two- and three-dimensional numerical examples show that the proposed model has higher computational efficiency. For example, in the Mode I crack propagation problem, its computational cost is reduced by more than 72\% compared with that of the pure BAPD model, and the predicted crack patterns agree with experimental results.