The review of the bond-based peridynamics modeling

Abstract

Peridynamics theory is a nonlocal meshless method that replaces differential equations with spatial integral equations, and has shown good applicability and reliability in the analysis of discontinuities. Further, with characteristics of clear physical meaning and simple and reliable numerical calculation, the bond-based peridynamics method has been widely applied in the field. However, this method describes the interaction between material points simply using a single elastic “spring”, and thus leads to a fixed Poisson’s ratio, relatively low computational efficiency and other inherent problems. As such, the goal of this review paper is to provide a summary of the various methods of bond-based peridynamics modeling, particularly those that have overcome the limitations of the Poisson’s ratio, considered the shear deformation and modeling of two-dimensional thin plates for bending and three-dimensional anisotropic composites, as well as explored coupling with finite element methods. This review will determine the advantages and disadvantages of such methods and serve as a starting point for researchers in the development of peridynamics theory.

Morphological aspects of crack growth in rock materials with various flaws

“…Crack growth process of rock specimens with various flaws under compression: (A) to (D) are fracturing patterns observed in physical test results . (E) to (H) are fracturing behaviors captured in numerical results [Colour figure can be viewed at wileyonlinelibrary.com]…”

“…The bond‐based peridynamics has been widely used for predicting fracturing patterns in materials without further assumptions for crack initiation, propagation, and coalescence. The theory, however, presents some limitations regarding the material properties, which thereby leads itself to be restricted to the elastic brittle materials with a fixed Poisson's ratio (1/4 in 3D, 1/3 in 2D), as the interaction between particles is subject mainly to a central force potential . To overcome this Poisson's ratio restriction, the state‐based peridynamics, in which an effective strain tensor derives from dyadic products of all the pairwise force vectors interacting with a node, are proposed.…”

“…The theory, however, presents some limitations regarding the material properties, which thereby leads itself to be restricted to the elastic brittle materials with a fixed Poisson's ratio (1/4 in 3D, 1/3 in 2D), as the interaction between particles is subject mainly to a central force potential. 20,21,26 To overcome this Poisson's ratio restriction, the state-based peridynamics, 27 in which an effective strain tensor derives from dyadic products of all the pairwise force vectors interacting with a node, 28 are proposed. Indeed, the theory utilizes stress-strain relations and material constitutive matrix rather than using equivalent properties for the stiffness in the interactions between two points.…”

A stable non‐ordinary state‐based peridynamic model for laminated composite materials

“…Based on these characteristics, PD has been widely used in damage and failure analysis of materials 6‐9 . Generally, PD formulations have three types: bond‐based peridynamics (BBPD), 10‐13 ordinary state‐based peridynamics (OSBPD), 14‐16 and non‐ordinary state‐based peridynamics (NOSBPD) 17,18 . BBPD has the restriction on the Poisson's ratio, and cannot distinguish the distortional and volumetric deformations 4,19 .…”

Numerical Simulations of the Ice Load of a Ship Navigating in Level Ice Using Peridynamics

“…Even though still model tests in ice tanks are typically used to investigate the ice loads of ships navigating in Arctic areas, these tests are time-consuming and costly, especially in the design and optimization of hull forms [Kim, Lee, Lee et al (2013)]. Meshfree methods are certainly advantageous to model the fracturing process and crack growth of ice sheets because these methods are independent of the element grids during the computational process [Han, Zhang, Wang et al (2018); Li and Liu (2002); Wang, Wang, Zan et al (2017)]. Libersky et al [Libersky and Petschek (1991)] first applied the Smoothed Particle Hydrodynamics (SPH) approach to solid mechanics.…”