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Peridynamic Theory and Multi-physical/Multiscale Methods for Complex Material Behavior

Submission Deadline: 30 November 2025 (closed) View: 1191 Submit to Special Issue

Guest Editors

Prof. Lisheng Liu, Wuhan University of Technology, China
Prof. Dan Huang, Hohai University, China
A.Prof. Hailong Chen, University of Kentucky, USA
A.Prof. Yile Hu, Shanghai Jiao Tong University, China
A.Prof. Xin Lai, Wuhan University of Technology, China


Summary

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 decade. 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, multi-physics and multiscale modeling, coupling of Peridynamics and classical theories, high-performance computation, machine learning strategy, software development, etc. Advances in these directions will further promote Peridynamics to serve engineering applications better. Therefore, this special issue invites contributions to recent developments on the Peridynamic theory and the multi-physical/multiscale modeling method for complex material behavior.

 

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

•      Peridynamic theory and models for material failure in extreme condition

•      Peridynamic theory and algorithm for complex fracture

•      Multiphysics analysis by using Peridynamics

•      Multiscale modeling by using Peridynamics

•      Peridynamic theory and its numerical implementation and commercialization

•      Peridynamic parameter calibration

•      Surface effect correction

•      Application of boundary conditions

•      Coupling of Peridynamic and classical theories

•      Coupling Peridynamics with Phase Field

•      Mathematical analysis

•      Data-driven and machine learning strategies

•      High performance computing and large-scale algorithm development


[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.


Keywords

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

Published Papers


  • Open Access

    ARTICLE

    Dynamic Compressive Behavior and Stress Wave Attenuation Characteristics of Ti-6Al-4V Lattice Structure

    Shuai Zhang, Xin Lai, Haiyan Niu, Lisheng Liu, Shifu Wang, Jinyong Zhang
    CMES-Computer Modeling in Engineering & Sciences, Vol.144, No.1, pp. 739-762, 2025, DOI:10.32604/cmes.2025.067442
    (This article belongs to the Special Issue: Peridynamic Theory and Multi-physical/Multiscale Methods for Complex Material Behavior)
    Abstract This study investigates the dynamic compressive behavior of three periodic lattice structures fabricated from Ti-6Al-4V titanium alloy, each with distinct topologies: simple cubic (SC), body-centered cubic (BCC), and face-centered cubic (FCC). Dynamic compression experiments were conducted using a Split Hopkinson Pressure Bar (SHPB) system, complemented by high-speed imaging to capture real-time deformation and failure mechanisms under impact loading. The influence of cell topology, relative density, and strain rate on dynamic mechanical properties, failure behavior, and stress wave propagation was systematically examined. Finite element modeling was performed, and the simulated results showed good agreement with experimental… More >

  • Open Access

    ARTICLE

    Analytical Solutions for 1-Dimensional Peridynamic Systems by Considering the Effect of Damping

    Zhenghao Yang, Erkan Oterkus, Selda Oterkus, Konstantin Naumenko
    CMES-Computer Modeling in Engineering & Sciences, Vol.143, No.2, pp. 2491-2508, 2025, DOI:10.32604/cmes.2025.062998
    (This article belongs to the Special Issue: Peridynamic Theory and Multi-physical/Multiscale Methods for Complex Material Behavior)
    Abstract For the solution of peridynamic equations of motion, a meshless approach is typically used instead of utilizing semi-analytical or mesh-based approaches. In contrast, the literature has limited analytical solutions. This study develops a novel analytical solution for one-dimensional peridynamic models, considering the effect of damping. After demonstrating the details of the analytical solution, various demonstration problems are presented. First, the free vibration of a damped system is considered for under-damped and critically damped conditions. Peridynamic solutions and results from the classical theory are compared against each other, and excellent agreement is observed between the two More >

  • Open Access

    ARTICLE

    An Updated Lagrangian Particle Hydrodynamics (ULPH)-NOSBPD Coupling Approach for Modeling Fluid-Structure Interaction Problem

    Zhen Wang, Junsong Xiong, Shaofan Li, Xin Lai, Xiang Liu, Lisheng Liu
    CMES-Computer Modeling in Engineering & Sciences, Vol.141, No.1, pp. 491-523, 2024, DOI:10.32604/cmes.2024.052923
    (This article belongs to the Special Issue: Peridynamic Theory and Multi-physical/Multiscale Methods for Complex Material Behavior)
    Abstract A fluid-structure interaction approach is proposed in this paper based on Non-Ordinary State-Based Peridynamics (NOSB-PD) and Updated Lagrangian Particle Hydrodynamics (ULPH) to simulate the fluid-structure interaction problem with large geometric deformation and material failure and solve the fluid-structure interaction problem of Newtonian fluid. In the coupled framework, the NOSB-PD theory describes the deformation and fracture of the solid material structure. ULPH is applied to describe the flow of Newtonian fluids due to its advantages in computational accuracy. The framework utilizes the advantages of NOSB-PD theory for solving discontinuous problems and ULPH theory for solving fluid… More >

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