An optimized unibond dual-parameter peridynamic model for deformation and fracture simulation of quasi-brittle materials

Peridynamic is a nonlocal theory, which is an effective tool for predicting fracture in solids. The unibond dual-parameter peridynamic (UDPD) model can break through the Poisson's ratio limitation compared with the bond-based peridynamic model. However, the traditional algorithm for the integrated volume is designed according to the analytical value of partial length in the one-dimensional model, which will produce non-negligible errors for the two- and three-dimensional models. Besides, the classical UDPD model is restricted to ideal brittle materials rather than quasi-brittles, and the long-range force effect is generally omitted for simplified analysis. In this work, an optimized UDPD model is developed to overcome the above drawbacks in simulating the deformation and fracture of quasi-brittle materials. First, the novel algorithm to obtain a more accurate integrated volume is introduced into the UDPD model. Second, considering the long-range force effect and the deformation characteristics, the nonlinear constitutive force function coupled with the cosine type influence function is developed for the UDPD model. Then, the corresponding bond stiffnesses are derived. The proposed model is verified through several representative numerical applications, which suggests that the predicted results match well with the experimental observations and former simulations. It is indicated that the proposed model reveals a significant improvement in the convergence and precision of results, which can not only retain the stability of the classical UDPD model, but also precisely analyze the deformation behavior and damage evolution process of quasi-brittle materials.