Table of Content

Peridynamics and its Current Progress

Submission Deadline: 31 May 2023 Submit to Special Issue

Guest Editors

Prof. Fei Han, Dalian University of Technology, China
Prof. Erkan Oterkus, University of Strathclyde, UK
Dr. Patrick Diehl, Louisiana State University, USA


The peridynamics proposed by Silling [1] is a non-local theory of solid mechanics. It redefines the problems by using integral equations rather than partial differential equations. It is assumed that the equilibrium of a material point is attained by an integral of internal forces exerted by non-adjacent points across a finite distance. This non-local model allows crack initiation and evolution simultaneously at multiple sites, with spontaneous paths inside the material and without formulating a complex crack growth criterion. These advantages have attached considerable attention to peridynamics in the past ten years. The research areas related to peridynamics have also been extended to the fields of thermal, electricity, fluids, soft matter, etc. However, there are still many research areas to explore in the peridynamic framework. These research directions include constitutive modeling, parameter calibration, surface effect correction, application of boundary conditions, multiphysics and multiscale modeling, coupling of peridyanmics and classical theories, high-performance computation, machine learning strategy, software development, etc. Advances in these researches will further promote peridynamics to serve engineering applications better. Therefore, this special issue invites contributions to recent developments on the peridynamic theory and its current progress.


Topics of interest (Including but not limited to the following):

•      Peridynamic modeling for advanced materials

•      Fracture modelling by using peridynamics

•      Multiphysics analysis by using peridynamics

•      Multiscale modeling by using peridynamics

•      Peridynamic parameter calibration

•      Surface effect correction

•      Application of boundary conditions

•      Coupling of peridynamic and classical theories

•      Data-driven and machine learning strategies

•      High performance computing to run large scale peridynamic simulations


[1] S.A. Silling(2000), Reformulation of elasticity theory for discontinuities and long-range forces, Journal of the Mechanics and Physics of Solids, 48(1), 175-209.


Peridynamics; Damage and Fracture; Non-local; Multiphysics; Multiscale Methods

Published Papers

  • Open Access


    ABAQUS and ANSYS Implementations of the Peridynamics-Based Finite Element Method (PeriFEM) for Brittle Fractures

    Fei Han, Zhibin Li, Jianyu Zhang, Zhiying Liu, Chen Yao, Wenping Han
    CMES-Computer Modeling in Engineering & Sciences, Vol.136, No.3, pp. 2715-2740, 2023, DOI:10.32604/cmes.2023.026922
    (This article belongs to this Special Issue: Peridynamics and its Current Progress)
    Abstract In this study, we propose the first unified implementation strategy for peridynamics in commercial finite element method (FEM) software packages based on their application programming interface using the peridynamics-based finite element method (PeriFEM). Using ANSYS and ABAQUS as examples, we present the numerical results and implementation details of PeriFEM in commercial FEM software. PeriFEM is a reformulation of the traditional FEM for solving peridynamic equations numerically. It is considered that the non-local features of peridynamics yet possesses the same computational framework as the traditional FEM. Therefore, this implementation benefits from the consistent computational frameworks of both PeriFEM and the traditional… More >

  • Open Access


    Study on Crack Propagation Parameters of Tunnel Lining Structure Based on Peridynamics

    Zhihui Xiong, Xiaohui Zhou, Jinjie Zhao, Hao Cui, Bo Wang
    CMES-Computer Modeling in Engineering & Sciences, Vol.135, No.3, pp. 2449-2478, 2023, DOI:10.32604/cmes.2023.023353
    (This article belongs to this Special Issue: Peridynamics and its Current Progress)
    Abstract The numerical simulation results utilizing the Peridynamics (PD) method reveal that the initial crack and crack propagation of the tunnel concrete lining structure agree with the experimental data compared to the Japanese prototype lining test. The load structure model takes into account the cracking process and distribution of the lining segment under the influence of local bias pressure and lining thickness. In addition, the influence of preset cracks and lining section form on the crack propagation of the concrete lining model is studied. This study evaluates the stability and sustainability of tunnel structure by the Peridynamics method, which provides a… More >

  • Open Access


    The Coupled Thermo-Chemo-Mechanical Peridynamics for ZrB2 Ceramics Ablation Behavior

    Yuanzhe Li, Qiwen Liu, Lisheng Liu, Hai Mei
    CMES-Computer Modeling in Engineering & Sciences, Vol.135, No.1, pp. 417-439, 2023, DOI:10.32604/cmes.2022.021258
    (This article belongs to this Special Issue: Peridynamics and its Current Progress)
    Abstract The ablation of ultra-high-temperature ceramics (UTHCs) is a complex physicochemical process including mechanical behavior, temperature effect, and chemical reactions. In order to realize the structural optimization and functional design of ultra-high temperature ceramics, a coupled thermo-chemo-mechanical bond-based peridynamics (PD) model is proposed based on the ZrB2 ceramics oxidation kinetics model and coupled thermo-mechanical bond-based peridynamics. Compared with the traditional coupled thermo-mechanical model, the proposed model considers the influence of chemical reaction process on the ablation resistance of ceramic materials. In order to verify the reliability of the proposed model, the thermo-mechanical coupling model, damage model and oxidation kinetic model are… More >

  • Open Access


    Peridynamic Shell Model Based on Micro-Beam Bond

    Guojun Zheng, Zhaomin Yan, Yang Xia, Ping Hu, Guozhe Shen
    CMES-Computer Modeling in Engineering & Sciences, Vol.134, No.3, pp. 1975-1995, 2023, DOI:10.32604/cmes.2022.021415
    (This article belongs to this Special Issue: Peridynamics and its Current Progress)
    Abstract Peridynamics (PD) is a non-local mechanics theory that overcomes the limitations of classical continuum mechanics (CCM) in predicting the initiation and propagation of cracks. However, the calculation efficiency of PD models is generally lower than that of the traditional finite element method (FEM). Structural idealization can greatly improve the calculation efficiency of PD models for complex structures. This study presents a PD shell model based on the micro-beam bond via the homogenization assumption. First, the deformations of each endpoint of the micro-beam bond are calculated through the interpolation method. Second, the micro-potential energy of the axial, torsional, and bending deformations… More >

  • Open Access


    A Peridynamic Approach for the Evaluation of Metal Ablation under High Temperature

    Hui Li, Liping Zhang, Yixiong Zhang, Xiaolong Fu, Xuejiao Shao, Juan Du
    CMES-Computer Modeling in Engineering & Sciences, Vol.134, No.3, pp. 1997-2019, 2023, DOI:10.32604/cmes.2022.020792
    (This article belongs to this Special Issue: Peridynamics and its Current Progress)
    Abstract In this paper, the evaluations of metal ablation processes under high temperature, i.e., the Al plate ablated by a laser and a heat carrier and the reactor pressure vessel ablated by a core melt, are studied by a novel peridynamic method. Above all, the peridynamic formulation for the heat conduction problem is obtained by Taylor’s expansion technique. Then, a simple and efficient moving boundary model in the peridynamic framework is proposed to handle the variable geometries, in which the ablated states of material points are described by an additional scalar field. Next, due to the automatic non-interpenetration properties of peridynamic… More >

    Graphic Abstract

    A Peridynamic Approach for the Evaluation of Metal Ablation under High Temperature

  • Open Access


    A Hybrid Local/Nonlocal Continuum Mechanics Modeling of Damage and Fracture in Concrete Structure at High Temperatures

    Runze Song, Fei Han, Yong Mei, Yunhou Sun, Ao Zhang
    CMES-Computer Modeling in Engineering & Sciences, Vol.133, No.2, pp. 389-412, 2022, DOI:10.32604/cmes.2022.021127
    (This article belongs to this Special Issue: Peridynamics and its Current Progress)
    Abstract This paper proposes a hybrid peridynamic and classical continuum mechanical model for the high-temperature damage and fracture analysis of concrete structures. In this model, we introduce the thermal expansion into peridynamics and then couple it with the thermoelasticity based on the Morphing method. In addition, a thermomechanical constitutive model of peridynamic bond is presented inspired by the classic Mazars model for the quasi-brittle damage evolution of concrete structures under high-temperature conditions. The validity and effectiveness of the proposed model are verified through two-dimensional numerical examples, in which the influence of temperature on the damage behavior of concrete structures is investigated.… More >

  • Open Access


    Implementation of OpenMP Parallelization of Rate-Dependent Ceramic Peridynamic Model

    Haoran Zhang, Yaxun Liu, Lisheng Liu, Xin Lai, Qiwen Liu, Hai Mei
    CMES-Computer Modeling in Engineering & Sciences, Vol.133, No.1, pp. 195-217, 2022, DOI:10.32604/cmes.2022.020495
    (This article belongs to this Special Issue: Peridynamics and its Current Progress)
    Abstract A rate-dependent peridynamic ceramic model, considering the brittle tensile response, compressive plastic softening and strain-rate dependence, can accurately represent the dynamic response and crack propagation of ceramic materials. However, it also considers the strain-rate dependence and damage accumulation caused by compressive plastic softening during the compression stage, requiring more computational resources for the bond force evaluation and damage evolution. Herein, the OpenMP parallel optimization of the rate-dependent peridynamic ceramic model is investigated. Also, the modules that compute the interactions between material points and update damage index are vectorized and parallelized. Moreover, the numerical examples are carried out to simulate the… More >

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