Analysis on the influence of Poisson’s ratio on brittle fracture by applying uni-bond dual-parameter peridynamic model

Abstract

Poisson’s ratio is a crucial mechanical parameter of materials, but its significance is normally underrated in practical application. Aiming at investigating how Poisson’s ratio influences the fracture of brittle materials by using peridynamic (PD) method, a uni-bond dual-parameter peridynamic (UDPD) model is proposed. The expressions of normal stiffness and tangential stiffness by elastic modulus and Poisson’s ratio are derived. The two-parameter characteristic makes UDPD break the limitation of the specific Poisson's ratio of bond-based peridynamics, thus the modeling of the mechanical behavior of materials with various Poisson's ratio can be achieved. With single-bond property, UDPD inherits the simplicity and stability of the traditional bond-based peridynamics. In addition, the critical value of micro strain energy density for UDPD model is given to judge the damage. The validity and accuracy of UDPD model are illustrated by three numerical examples: the plate deformation subject to static load, the Kalthoff-Winkler experiment and the brittle plate fracture subject to biaxial loads. Ultimately, by simulating and comparing the damage of brittle plates under tension of different Poisson’s ratio, it is concluded that Poisson’s ratio has substantial effect on fracture initiation time and crack propagation path. The larger Poisson’s ratio has the plate, the earlier the fracture initiates. The cut-through locations and crack propagation paths in plates of different Poisson’s ratio are significantly different.