A new quadrature algorithm consisting of volume and integral domain corrections for two-dimensional peridynamic models

Peridynamic (PD) models using the equation of motion in the integral form are applied to describe the failure and damage of materials. At present, the most commonly used volume correction algorithms (VCAs) cannot accurately calculate the volume of the intersecting region between a PD point and its neighbouring cells, particularly for the non-uniform discrete regions, which decreases the accuracy of the PD models. In this study, a new precise VCA is proposed to accurately calculate the volumes of intersecting regions for two-dimensional PD models. The integral domain is also corrected to eliminate the error in numerical integration implementation. The calculation accuracy of the proposed integral algorithm is verified by comparing the corrected volume and strain energy density with those computed by other correction algorithms and the theoretical values. The effects of different integration methods on the simulation results are also investigated in this study. The uniaxial tensile loading and transverse shear loading of the prefabricated central plate and the crack propagation simulation of the pre-notched plate proved the effectiveness of the proposed algorithm.