Special Issue "Recent Developments on Peridynamics"

Submission Deadline: 15 April 2019 (closed)
Guest Editors
Prof. Jianxiang Wang, Peking University, Beijing, China;
Prof. Qing Zhang, Hohai University, Nanjing, China;
Prof. Xiaoying Zhuang, Leibniz University Hanover, Germany;


Peridynamics is a nonlocal continuum mechanics theory. Because of its mathematical formulation, it removes the computational challenges inherent in the classical continuum mechanics, and enables the solution of complex governing field equations in the presence of jump discontinuities or singularities while providing a length scale to capture physical phenomena showing nonlocal behavior. Moreover, original peridynamic formulation has been extended to model mass and heat diffusions and fluid dynamics. Therefore, peridynamics can now be used as a multiphysics and multiscale framework with damage predicting capability. This special issue focuses on the recent developments of peridynamics mechanical and mathematical models, multiscale and multiphysics models, numerical solution methods, and practical engineering application of peridynamics across different disciplines such as computational material design, failure of materials and structures, rock mechanics, composites, optimization, etc., by using high performance computing.

Peridynamics, mechanical and mathematical models, numerical solution methods, practical engineering application

Published Papers

  • A Dual-Support Smoothed Particle Hydrodynamics for Weakly Compressible Fluid Inspired By the Dual-Horizon Peridynamics
  • Abstract A dual-support smoothed particle hydrodynamics (DS-SPH) that allows variable smoothing lengths while satisfying the conservations of linear momentum, angular momentum and energy is developed. The present DS-SPH is inspired by the dual-support, a concept introduced from dual-horizon peridynamics from the authors and applied here to SPH so that the unbalanced interactions between the particles with different smoothing lengths can be correctly considered and computed. Conventionally, the SPH formulation employs either the influence domain or the support domain. The concept of dual-support identifies that the influence domain and the support domain involves the duality and should be simultaneously in the SPH… More
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  • A Possible Reason About Origin of Singularity and Anomalous Dispersion in Peridynamics
  • Abstract In the benchmark problems of peridynamics, there are some eccentric results, for example, singularity of uniaxial tension and anomalous dispersion of wave. The reasons to give rise to these results are investigated. We calculated local tension and wave of an infinite rod after adding a divergence of local stress in the peridynamic motion equation. The acquired results verify that the singularity in the peridynamic solution of local tension problem and anomalous dispersion of peridynamic wave are all eliminated. Therefore, the anomalous features of some peridynamic solutions likely stem from the lack of local stress characterizing contact interactions. More
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  • A Hybrid Local/Nonlocal Continuum Mechanics Modeling and Simulation of Fracture in Brittle Materials
  • Abstract Classical continuum mechanics which leads to a local continuum model, encounters challenges when the discontinuity appears, while peridynamics that falls into the category of nonlocal continuum mechanics suffers from a high computational cost. A hybrid model coupling classical continuum mechanics with peridynamics can avoid both disadvantages. This paper describes the hybrid model and its adaptive coupling approach which dynamically updates the coupling domains according to crack propagations for brittle materials. Then this hybrid local/nonlocal continuum model is applied to fracture simulation. Some numerical examples like a plate with a hole, Brazilian disk, notched plate and beam, are performed for verification… More
  •   Views:1826       Downloads:480        Download PDF

  • Coupled Digital Image Correlation and Peridynamics for Full-Field Deformation Measurement and Local Damage Prediction
  • Abstract Digital image correlation (DIC) measurement technique and peridynamics (PD) method have been applied in specific fields extensively owing to their respective advantages in obtaining full-field deformation and local failure of loaded materials and structures. This study provides a simple way to couple DIC measurements with PD simulations, which can circumvent the difficulties of DIC in dealing with discontinuous deformations. Taking the failure analysis of a compact tension specimen of aluminum alloy and a static three-point bending concrete beam as examples, the DIC experimental system firstly measures the full-field displacements, and then the PD simulation is applied on potential damage regions… More
  •   Views:1428       Downloads:423        Download PDF

  • 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… More
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  • Peridynamic Modeling and Simulation of Ice Craters By Impact
  • Abstract In the present work, a state-based peridynamics with adaptive particle refinement is proposed to simulate water ice crater formation due to impact loads. A modified Drucker-Prager constitutive model was adopted to model ice and was implemented in the state-based peridynamic equations to analyze the elastic-plastic deformation of ice. In simulations, we use the fracture toughness failure criterion in peridynamics to simulate the quasi-brittle failure of ice. An adaptive particle refinement method in peridynamics was proposed to improve computational efficiency. The results obtained using the peridynamic model were compared with the experiments in previous literatures. It was found that the peridynamic… More
  •   Views:2604       Downloads:369        Download PDF

  • The Multi-Horizon Peridynamics
  • Abstract We present a novel refinement approach in peridynamics (PD). The proposed approach takes advantage of the PD flexibility in choosing the shape of the horizon by introducing multiple domains (with no intersections) to the nodes of the refinement zone. We will show that no ghost forces are needed when changing the horizon sizes in both subdomains. The approach is applied to both bond-based and state-based peridynamics and verified for a simple wave propagation refinement problem illustrating the efficiency of the method. More
  •   Views:1715       Downloads:301        Download PDF

  • Numerical Simulation of Dynamic Interaction Between Ice and Wide Vertical Structure Based on Peridynamics
  • Abstract In the ice-covered oceanic region, the collision between sea ice and offshore structures will occur, causing the crushing failure of ice and the vibration of structures. The vibration can result in fatigue damage of structure and even endanger the crews’ health. It is no doubt that this ice-structure interaction has been noted with great interest by the academic community for a long time and numerous studies have been done through theoretical analysis, experimental statistics and numerical simulation. In this paper, the bond-based Peridynamics method is applied to simulate the interaction between sea ice and wide vertical structures, where sea ice… More
  •   Views:1295       Downloads:313        Download PDF

  • Numerical Simulations of the Ice Load of a Ship Navigating in Level Ice Using Peridynamics
  • Abstract In this study, a numerical method was developed based on peridynamics to determine the ice loads for a ship navigating in level ice. Convergence analysis of threedimensional ice specimen with tensile and compression loading are carried out first. The effects of ice thickness, sailing speed, and ice properties on the mean ice loads were also investigated. It is observed that the ice fragments resulting from the icebreaking process will interact with one another as well as with the water and ship hull. The ice fragments may rotate, collide, or slide along the ship hull, and these ice fragments will eventually… More
  •   Views:3047       Downloads:328        Download PDF