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 drift away from the ship. The key characteristics of the icebreaking process can be obtained using the peridynamic model such as the dynamic generation of cracks in the ice sheet, propagation and accumulation of ice fragments, as well as collision, rotation, and sliding of the ice fragments along the ship hull. The simulation results obtained for the ice loads and icebreaking process were validated against those determined from the Lindqvist empirical formula and there is good agreement between the results.

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.…”

Investigating Load Calculation for Broken Ice and Cylindrical Structures Using the Discrete Element Method

“…Xue [15] provided a comprehensive summary of the latest experimental techniques in studying ice loads, particularly emphasizing their application to ships, and conducted extensive foundational studies in this area. Dynamic methods have been employed by researchers to examine the impact of factors, including ice thickness and navigation speed, on average ice loads [16,17]. Wang developed a timedomain numerical calculation method to assess the icebreaking capabilities of ships by studying continuous icebreaking loads and ship motions [18].…”

Investigation of the fracture mechanism of level ice with extended finite element method

“…Over the decades, the development of numerical methods has provided new ways for the calculation of ship-ice interaction. Common numerical methods for simulation of ice breaking include Finite Element Method (Gürtner, 2009;Liu et al, 2011;Xu et al, 2019), Discrete Element Method (Lilja et al, 2019;Liu and Ji, 2021;Ni et al, 2021), Peridynamics (Vazic et al, 2019;Xue et al, 2019), et al Finite element method has been widely used to simulate ice breaking by removing solid elements or by separating two adherent elements, the latter also known as cohesive element method. Ehlers and Kujala (2014) used a plastic material model and element removing method in LS-DYNA to simulate the bending failure of ice beams.…”