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The Boundary Element Method for ordinary state-based peridynamics

Computer Modeling in Engineering & Sciences 2024年第6期139卷 2807-2834页

作者： Xue Liang Linjuan Wang State Key Laboratory for Turbulence and Complex Systems Department of Mechanics and Engineering ScienceCollege of EngineeringPeking UniversityBeijing100871China CAPT-HEDPS and IFSA Collaborative Innovation Center of MoECollege of EngineeringPeking UniversityBeijing100871China School of Astronautics Beihang UniversityBeijing100191China

The peridynamics(PD),as a promising nonlocal continuum mechanics theory,shines in solving discontinuous *** to now,various numerical methods,such as the peridynamic mesh-free particlemethod(PD-MPM),peridynamic finite element method(PD-FEM),and peridynamic boundary element method(PD-BEM),have been ***-BEM,in particular,outperforms other methods by eliminating spurious boundary softening,efficiently handling infinite problems,and ensuring high computational ***,the existing PD-BEM is constructed exclusively for bond-based peridynamics(BBPD)with fixed Poisson’s ratio,limiting its applicability to crack propagation problems and scenarios involving infinite or semi-infinite *** this paper,we address these limitations by introducing the boundary element method(BEM)for ordinary state-based peridynamics(OSPD-BEM).Additionally,we present a crack propagationmodel embeddedwithin the framework ofOSPD-BEM to simulate crack *** validate the effectiveness of OSPD-BEM,we conduct four numerical examples:deformation under uniaxial loading,crack initiation in a double-notched specimen,wedge-splitting test,and threepoint bending *** results demonstrate the accuracy and efficiency of OSPD-BEM,highlighting its capability to successfully eliminate spurious boundary softening phenomena under varying Poisson’s ***,OSPDBEMsignificantly reduces computational time and exhibits greater consistencywith experimental results compared to PD-MPM.

关键词： ordinary state-based peridynamics boundary element method crack propagation fracture toughness

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Simulating earth deformation evolution caused by groundwater pumping through ordinary state-based peridynamics method

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JOURNAL OF HYDROLOGY 2024年 634卷

作者： Zhu, Lin Li, Jiangtao Gong, Huili Ye, Miao Dai, Zhenxue Li, Xiaojuan Teatini, Pietro Capital Normal Univ Coll Resource Environm & Tourism Beijing Lab Water Resources Secur Lab Cultivat Base Environm Proc & Digital Simulat Beijing Peoples R China MOE Key Lab Mech Prevent & Mitigat Land Subsidence Beijing Peoples R China Jilin Univ Coll Construct Engn Changchun Peoples R China Univ Padua Dept Civil Environm & Architectural Engn Padua Italy

Earth deformation including land subsidence and the related earth fissures caused by the over-exploitation of groundwater resources is threatening countries all over the World. At present, the simulation of earth deformation of aquifer system is mainly based on continuum and contact mechanics. These approaches lead to two main challenges, i.e. the need of knowing the location of possible earth fissures in advance and using meshes that must be adjusted during the rupture propagation. Here, ordinary state-based peridynamics method is firstly introduced to simulate the evolution of continuous and discontinuous earth deformation due to groundwater withdrawal. A failure criteria accounting for shear and tensile strain simultaneously is proposed. The approach is used to simulate the evolution of land subsidence and earth fissures in compressible sedimentary soils with buried rigid ridges. Two case studies are reproduced: one is a test carried out in laboratory and the other one concerns Guangming village, Yangtze River delta. In both cases, the presence of a shallow buried bedrock crossing the alluvial deposits is responsible for the initiation and growth of earth fissure that a satisfactory captured by the model. For the lab experiment, a 0.1 m deep fissure appearing above the rocky tip is computed. In Guangming village area, results show that some small fissure groups were initiated. Then, three main earth fissures developed rapidly with the maximum depth of 32.5 m. This study proposes a consistency modelling framework to simulate continuum earth deformation and discontinuous fissures due to groundwater withdrawal in specific geological settings, and supply a reliable scientific tool for early warning of this geo-hazard.

关键词： Aquifer over-exploitation Earth deformation ordinary state-based peridynamics Discontinuous deformation

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A new method based on Taylor expansion and nearest-node strategy to impose Dirichlet and Neumann boundary conditions in ordinary state-based peridynamics

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COMPUTATIONAL MECHANICS 2022年第1期70卷 1-27页

作者： Scabbia, Francesco Zaccariotto, Mirco Galvanetto, Ugo Univ Padua Ctr Studies & Act Space CISAS G Colombo Dept Ind Engn Via Venezia 15 I-35131 Padua Italy Univ Padua Dept Ind Engn Via Venezia 1 I-35131 Padua Italy

peridynamics is a non-local continuum theory which is able to model discontinuities in the displacement field, such as crack initiation and propagation in solid bodies. However, the non-local nature of the theory generates an undesired stiffness fluctuation near the boundary of the bodies, phenomenon known as "surface effect". Moreover, a standard method to impose the boundary conditions in a non-local model is not currently available. We analyze the entity of the surface effect in ordinary state-based peridynamics by employing an innovative numerical algorithm to compute the peridynamic stress tensor. In order to mitigate the surface effect and impose Dirichlet and Neumann boundary conditions in a peridynamic way, we introduce a layer of fictitious nodes around the body, the displacements of which are determined by multiple Taylor series expansions based on the nearest-node strategy. Several numerical examples are presented to demonstrate the effectiveness and accuracy of the proposed method.

关键词： ordinary state-based peridynamics Surface effect Peridynamic boundary conditions Peridynamic stress tensor Extrapolation over fictitious nodes

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Coupling of FEM and ordinary state-based peridynamics for brittle failure analysis in 3D

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MECHANICS OF ADVANCED MATERIALS AND STRUCTURES 2021年第9期28卷 875-890页

作者： Ni, Tao Zaccariotto, Mirco Zhu, Qi-Zhi Galvanetto, Ugo Hohai Univ Coll Civil & Transportat Engn Nanjing 210098 Jiangsu Peoples R China Hohai Univ Key Lab Minist Educ Geomech & Embankment Engn Nanjing Jiangsu Peoples R China Univ Padua Ind Engn Dept Padua Italy Univ Padua Ctr Studies & Act Space CISAS G Colombo Padua Italy

This paper presents a method to couple FEM meshes with ordinary state-based peridynamic grids. It generates a computational tool that is as efficient as computer methods based on classical continuum mechanics and as flexible as peridynamics in dealing with crack propagation. Moreover, it removes most of the problems due to the surface effects typical of nonlocal methods such as OSB-PD. The adaptive dynamic relaxation approach is used to solve linear elastic and crack propagation problems. The method is successfully applied to a complex crack propagation case in 3 D and is able to accurately reproduce the shape of the experimentally observed crack.

关键词： Adaptive coupling ordinary state-based peridynamics FEM Crack propagation Three-dimensional model

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Fluid-elastic structure interaction simulation by using ordinary state-based peridynamics and peridynamic differential operator

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ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS 2020年 121卷 126-142页

作者： Gao, Yan Oterkus, Selda Univ Strathclyde Dept Naval Architecture Ocean & Marine Engn 100 Montrose St Glasgow G4 0LZ Lanark Scotland

The fluid-structure interaction phenomenon is often encountered in the ocean engineering field. In the present work, a non-local numerical model is developed for the simulations of weakly compressible viscous fluid and elastic structure interactions. The peridynamic theory is adopted for both the structure and fluid modelling. The elastic structure is described by using the ordinary state-based peridynamics, while the fluid is modelled by utilizing the peridynamic differential operator. Furthermore, the updated Lagrangian description is adopted for the fluid including the relative deformation gradient expressed by the peridynamic differential operator. The fluid-structure interface and its normal direction are calculated via the gradient of a colour function, which varies with the fluid motion and structure deformation. Besides, the interaction force exerted from fluid to structure is constrained to be always perpendicular to the moving interface. Hence the fluid motion and structural deformation are predicted simultaneously. The validation of the developed model is conducted through the simulation of a water dam break with a rubber gate. The good agreement between the peridynamic and the experiment results demonstrates the capability of the current model for solving fluid-elastic structure interaction problems.

关键词： ordinary state-based peridynamics Peridynamic differential operator Non-local Fluid-structure interaction Dam break

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Elastoplastic Constitutive Modeling for Reinforced Concrete in ordinary state-based peridynamics

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JOURNAL OF MECHANICS 2020年第6期36卷 799-811页

作者： Li, Tianyi Gu, Xin Zhang, Qing Xia, Xiaozhou Hohai Univ Coll Mech & Mat Dept Engn Mech Nanjing 211100 Peoples R China

A non-local, ordinary state-based, peridynamic elastoplastic model is formulated to numerically simulate the fracture of reinforced concrete materials. Several basic definitions are first discussed to avoid confusion;and then, a detailed derivation of the force vector state is presented, leading to a unified expression of force state for one-, two- and three-dimensional elasticity problems. Furthermore, an ordinary state-based peridynamic (OSB PD) elastoplastic analysis approach is developed for both plastic compressible and incompressible materials, including the constitutive relationship, the yield function, the consistency condition and the plasticity flow rule. The peridynamic predictions of a quasi-static deformation of the steel rods are in good agreement with the analytical solution. Moreover, the OSB PD plasticity is verified by analyzing a square plate with or without a central hole suffering different loading-unloading paths. Finally, a two dimensional reinforced concrete clamped beam subjected to impact loading is simulated with the proposed OSB PD elastoplasticity, demonstrating its capability in capturing the damage characteristics and structural failure behavior. Simulation results show good accuracy of the peridynamics in simulating elastoplastic problems.

关键词： ordinary state-based peridynamics elastoplasticity reinforced concrete impact

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An improved mesoscale damage model for quasi-brittle fracture analysis of concrete with ordinary state-based peridynamics

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THEORETICAL AND APPLIED FRACTURE MECHANICS 2021年 112卷 102829-102829页

作者： Dong, Yijia Su, Chao Qiao, Pizhong Shanghai Jiao Tong Univ State Key Lab Ocean Engn Sch Naval Architecture Ocean & Civil Engn Shanghai 200240 Peoples R China Hohai Univ Coll Water Conservancy & Hydropower Engn Nanjing 210098 Peoples R China Washington State Univ Dept Civil & Environm Engn Pullman WA 99164 USA

ordinary state-based peridynamics (OSPD) is a promising computational method to analyze damage and fracture process because its equation of motion is still satisfied at the presence of discontinuities. Though OSPD has been introduced to evaluate mesoscopic behavior of concrete, there are many unsolved issues to tackle quasi-brittle behavior of mesoscopic constituents. In this paper, an improved mesoscale damage model for two-dimensional fracture analysis of concrete is proposed. Instead of modeling the interfacial transition zone (ITZ) with material points, the mechanical behavior of ITZ is embedded in the corresponding bonds of mortar and aggregates to improve modeling and computational efficiency. During the failure process, the damage initiation criterion is established based on the stress computed from the scalar force density;while the softening is characterized by the fracture energy and an exponential softening law. The proposed model is verified by simulating cracking of ITZ in uniaxial tension as well as crack propagation of concrete in three-point bending test. The prediction results show good agreements with either analytical or experimental results. Then, the model is employed to study mesoscale crack initiation and propagation of concrete under uniaxial tension, considering the distributions of mortar, aggregates, ITZ, and voids. Influences of the mesoscopic fracture properties on the macro constitutive relationship are also investigated through parametric studies. The improved mesoscale damage model presented is a simple yet effective tool for fracture analysis of concrete.

关键词： Concrete Mesoscale ordinary state-based peridynamics Fracture Quasi-brittle behavior

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Seismic Response Analysis for ordinary state-based peridynamics in a Linear Isotropic Elastic Material

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Journal of peridynamics and Nonlocal Modeling 2020年第2期2卷 185-204页

作者： Shimbo, Taiki Itto, Ryota Inaba, Koutaro Araki, Kouichi Watanabe, Naoto National institute of technology Ishikawa College Kitacyujo Ishikawa Tsubata 929-0392 Japan GODAI KAIHATSU Corporation 1-35 Kuroda Ishikawa Kanazawa City 921-8051 Japan KFC LTD 11-5 Yadaminami Higashi-ku Aichi Nagoya City 461-0048 Japan

Earthquakes may induce the failure of soil-structures built with a geo-material. It is therefore a crucially important aspect to study how a crack initiates and propagates in these soil-structures to analyze and improve their earthquake resistance. peridynamics, although a powerful method for such an analysis, has not been applied to seismic response analysis of soil-structures on a viscous boundary surface that can consider an input seismic wave. To apply seismic response analysis to ordinary state-based peridynamics (OSB-PD), this paper proposed a fictitious viscous boundary layer and Rayleigh damping components constructed with time derivative of force density vectors. OSB-PD was semi-verified through the comparison of calculated response acceleration via the proposed method and via the dynamic finite element method (FEM). The discussions were stressed on the effect of Poisson’s ratio, the frequency, and the Rayleigh damping components relative to the calculated response acceleration in both methods. Moreover, the seismic response acceleration at the top of the analysis model was calculated through the proposed method using an actual seismic acceleration time history, and then the result was compared with that calculated by the dynamic FEM. The results of both methods in the seismic response analysis agreed well with each other. From these results, we verified that the fictitious viscous layer can represent incoming/outgoing acceleration wave from the bottom of the analysis domain, and that Rayleigh damping can be expressed using the time derivative of force density vectors. © 2020, The Author(s).

关键词： Fictitious viscous layer ordinary state-based peridynamics Rayleigh damping components Seismic response analysis

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Analysis of the plastic zone near the crack tips under the uniaxial tension using ordinary state-based peridynamics

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FATIGUE & FRACTURE OF ENGINEERING MATERIALS & STRUCTURES 2018年第5期41卷 1159-1170页

作者： Zhou, X. P. Shou, Y. D. Berto, F. Chongqing Univ Sch Civil Engn Chongqing 400045 Peoples R China Norwegian Univ Sci & Technol Dept Mech Engn N-7491 Trondheim Norway

In this paper, the plastic model of ordinary state-based peridynamics is established. The size and shape of plastic zone around crack tips with the different inclination angles are simulated using ordinary state-based peridynamics. Comparison of the size and shape of plastic zone around the crack tips obtained from peridynamic solution and analytic solution is made. It is found that the relative errors between the analytical and peridynamic solution are very little. Therefore, it is feasible to predict the plastic zone around crack tips using ordinary state-based peridynamics.

关键词： crack tips ordinary state-based peridynamics the plastic zone the uniaxial tension

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Modelling of Granular Fracture in Polycrystalline Materials Using ordinary state-based peridynamics

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MATERIALS 2016年第12期9卷 977-977页

作者： Zhu, Ning De Meo, Dennj Oterkus, Erkan Univ Strathclyde Dept Naval Architecture Ocean & Marine Engn Glasgow G4 0LZ Lanark Scotland

An ordinary state-based peridynamic formulation is developed to analyse cubic polycrystalline materials for the first time in the literature. This new approach has the advantage that no constraint condition is imposed onmaterial constants as opposed to bond-based peridynamic theory. The formulation is validated by first considering static analyses and comparing the displacement fields obtained from the finite element method and ordinary state-based peridynamics. Then, dynamic analysis is performed to investigate the effect of grain boundary strength, crystal size, and discretization size on fracture behaviour and fracture morphology.

关键词： polycrystalline materials ordinary state-based peridynamics transgranular fracture intergranular fracture

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