A comparative study on fast convolution-based method for non-ordinary state-based peridynamics

Abstract

In this paper, a comprehensive comparison is conducted between the fast convolution-based and the traditional non-ordinary state-based peridynamics methods, in terms of computational accuracy, fracture paths, computational efficiency, volume correction, and surface effects. The numerical results indicate that fast convolution-based method for non-ordinary state-based peridynamics (FCBM-NOSBPD) exhibits good accuracy with better computational efficiency. A volume correction method has been proposed and firstly applied to the framework of FCBM-NOSBPD method with fast Fourier transform (FFT) algorithm to further enhance the accuracy. The surface effects near displacement boundaries observed with the FCBM-NOSBPD method are consistent with those observed with the NOSBPD method. However, near free surfaces with stress concentrations, the FCBM-NOSBPD method exhibits more pronounced surface effects. A spectral representation method with a finite deformation formulation is incorporated into the FCBM-NOSBPD framework for the first time. The feasibility of this approach is validated through comparisons with results obtained using small deformation formulations. The comparative study may provide insights into FCBM-NOSBPD method and enhance our understanding of efficiently solving finite deformation fracture problems using peridynamics (PD) methods.