Dynamic Fracture Analysis of Functionally Gradient Materials with Two Cracks By Peridynamic Modeling

Abstract

In the research, the dynamic fracture failure problem of functionally graded materials (FGMs) containing two pre-cracks was analyzed using a bond-based Peridynamic (PD) method numerical model. The two convergence of decreasing the area of PD horizon (δ-convergence) and uniform mesh refinement (m-convergence) were studied. The effects of both crack position and distance between two cracks on crack propagation pattern in FGMs plate under tensile loads are studied. Furthermore, the effects of different gradient patterns on the dynamic propagation of cracks in FGMs are also investigated. The simulate results suggest that the cracks positions and the distance between them can significantly influence the dynamic propagation of crack in FGMs. Gradient mode also has a certain effect on crack propagation, but the effect of specific gradient variation patterns on dynamic propagation of crack is finite.

Introduction for the Special Issue on Recent Developments of Peridynamics

“…Specifically, topics across dual-support smoothed particle hydrodynamics, multi-horizon peridynamics, theoretical analysis of singularity and anomalous dispersion, hybrid local/nonlocal continuum mechanics modeling, coupled digital image correlation (DIC) and peridynamics, fracture of functionally gradient materials, interaction between ice and structure and dynamic fracture of ice are included. Specifically, "A Dual-Support Smoothed Particle Hydrodynamics for Weakly Compressible Fluid Inspired by the Dual-Horizon Peridynamics" by Zhuang et al [Zhuang, Rabczuk and Ren (2019)], extends the dual-horizon peridynamics with variable horizon sizes to the fluid flow application of SPH, e.g., dam break; "A Possible Reason about Origin Of Singularity and Anomalous Dispersion in Peridynamics" by Huang [Huang (2019)] regards the singularity of uniaxial tension and anomalous dispersion of wave in peridynamics stemming from the lack of local stress characterizing contact interactions; "A Hybrid Local/Nonlocal Continuum Mechanics Modeling and Simulation of Fractures in Brittle Materials" by Han et al [Han, Wang and Lubineau (2019)] further develops a hybrid model of classical continuum mechanics and peridynamics and introduces their software for crack propagation of quasi-brittle materials; "Coupled Digital Image Correlation and Peridynamics for Full-Field Deformation Measurement and Local Damage Prediction" by Li et al [Li, Zhang, Gu et al (2019)], attempts to compensate the damage evolution and crack propagation with peridynamic simulation considering the DIC cannot capture the crack evolution continuously; "Dynamic Fracture Analysis of Functionally Gradient Materials with Two Cracks by Peridynamic Modeling" by Cheng et al [Cheng, Jin, Yuan et al (2019)], investigates the influences of cracks positions and distance, and FGMs gradient pattern on the crack propagation pattern with bond-based peridynamics; "Peridynamics Modeling and Simulation of Ice Craters by Impacts" by Song et al [Song, Yan, Li et al (2019)] develops a particle refinement technique in the non-ordinary state-based peridynamic simulation corresponding to a modified Drucker-Prager constitutive model for ice crater; "The Multi-horizon Peridynamics" by Jenabidehkordi et al [Jenabidehkordi and Rabczuk (2019)] proposes a refinement approach by introducing multiple domains to the nodes in the refinement zone; "Numerical Simulation of Dynamic Interaction between Ice and Wide Vertical Structure Based on Peridynamics" by Jia et al [Jia, Ju and Wang (2019)] tries to calculate ice damage, ice forces and vibration responses of structures in the duration through bondbased peridynamic simulation; "Numerical Simulations of the Ice Load of a Ship Navigating in Level Ice Using Peridynamics" by Xue et al [Xue, Liu, Liu et al (2019)] adopts the bond-based peridynamics to predict the ice loads for a ship navigating in level ice and dynamic fracture of ice. As a final remark, it is hoped that the presented topics will give this special issue a much more lasting value and make it appealing to a broad audience of researchers, practitioners, and students who are interested in peridynamics, and each reader can find in this special issue something useful or inspiring.…”

Peridynamics Model with Surface Correction Near Insulated Cracks for Transient Heat Conduction in Functionally Graded Materials

“…Based on the level of interaction between the two points, damage is incorporated into the theory, so localization and fracture occur naturally [16]. After nearly 20 years of development, the peridynamic theory has been widely accepted to simulate and predict the damage and fracture of materials and structures [18][19][20][21][22].…”

Peridynamic Simulation of Dynamic Fracture Process of Engineered Cementitious Composites (ECC) with Different Curing Ages

“…Liu et al [ 23 ] simulated the interaction of horizontal ice with a vertical cylindrical rigid structure at different velocities. Cheng et al [ 24 ] simulated the dynamic brittle fracture of functional gradient materials (FGM) using bond-based peridynamics and investigated the effects of loading conditions and gradient modes on the properties of FGM. Chen et al [ 25 ] proposed a peridynamic model based on the intermediate medium homogenization method to simulate the brittle damage of porous materials.…”