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An efficient explicit-implicit adaptive method for peridynamic modeling of quasi-static fracture formation and evolution

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ENGINEERING FRACTURE MECHANICS 2025年 320卷

作者： Hu, Shiwei Xiao, Tianbai Han, Mingshuo Li, Zuoxu Oterkus, Erkan Oterkus, Selda Zhang, Yonghao Chinese Acad Sci Inst Mech Ctr Interdisciplinary Res Fluids Beijing 100190 Peoples R China Univ Chinese Acad Sci Sch Engn Sci Beijing 100049 Peoples R China Univ Strathclyde Dept Naval Architecture Ocean & Marine Engn Glasgow G1 1QN Scotland

Understanding the quasi-static fracture formation and evolution is essential for assessing the mechanical properties and structural load-bearing capacity of materials. Peridynamics (PD) provides an effective computational method to depict fracture mechanics. The explicit adaptive dynamic relaxation (ADR) method and the implicit methods are two mainstream PD approaches to simulate evolution of quasi-static fractures. However, no comprehensive and quantitative studies have been reported to compare their accuracy and efficiency. In this work, we first develop an implicit method for bond-based peridynamics (BBPD) based on the full nonlinear equilibrium equation and the degenerate form of the bond failure function, where the Jacobian matrices are derived using the Newton-Raphson (NR) scheme. Subsequently, we analyze the solvability of the implicit BBPD scheme. Second, a consistent and comprehensive comparison of accuracy and efficiency of the explicit ADR and implicit methods is conducted, which reveals computational efficiency of the implicit methods and their limitations in accurately describing crack formation. Finally, by utilizing the unique advantage of both methods, we develop an adaptive explicit-implicit method and propose a switching criterion to deploy appropriate scheme accordingly. Four typical quasi-static problems are employed as the numerical experiments, which show the acceleration ratios of the current method range from 6.4 to 141.7 when compared to the explicit ADR. Therefore, the explicit-implicit adaptive method provides a powerful method to simulate quasi-static fracture formation and evolution.

关键词： Peridynamics Quasi-static fracture mechanics Computational mechanics implicit method Explicit ADR

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An implicit method for incorporating common-cause failures in system analysis

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IEEE TRANSACTIONS ON RELIABILITY 1998年第2期47卷 173-180页

作者： Vaurio, JK Lappeenranta Univ Technol Lappeenranta Finland

A general procedure incorporates common-cause (CC) failures into system analysis by an implicit method;ie, after first solving the system probability equation without CC failures. Components of subsets are assumed to be equally vulnerable to CC of any particular multiplicity The method allows for age-dependent hazard rates, repairable & non-repairable components, systems with multiple CC groups, and systems where not all components are statistically-identical or subject to CC failures. Key equations are given both for reliability block-diagrams and fault-trees (success and failure models), considering the system reliability, availability and failure intensity functions. Initial failures and certain human errors are included, mainly for standby-system applications. The implicit method can dramatically simplify the Boolean manipulation and quantification of fault trees. Possible limitations & extensions are discussed.

关键词： common-cause failure implicit method system reliability availability failure intensity

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AN implicit method FOR TRANSIENT GAS-FLOWS IN PIPE NETWORKS

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INTERNATIONAL JOURNAL OF HEAT AND FLUID FLOW 1994年第5期15卷 378-383页

作者： KIUCHI, T [a]Toyo Engineering Corporation Chiba Japan

This paper describes a fully implicit finite-difference method for calculating the unsteady gas flow in pipeline networks. The algorithm for solving the finite-difference equations of a pipe is based on the Newton-Raphson method. The Von Neumann stability analysis on the finite-difference equations of a pipe shows that the equations are unconditionally stable. An iterative convergence method is applied to the calculation of node pressure at junctions in networks. The parameter study on the convergence shows that the stability depends on the convergence tolerance. Calculation results of a few sample cases are compared with those of the method of characteristics and the two-step Lax-Wendroff method. An excellent agreement between the methods is obtained when a small time step is used. Computation time can be greatly reduced by using the implicit method.

关键词： PIPELINE FLUID TRANSIENTS implicit method COMPRESSIBLE FLOW

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An implicit method for finding common solutions of variational inequalities and systems of equilibrium problems and fixed points of infinite family of nonexpansive mappings

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NONLINEAR ANALYSIS-THEORY methodS & APPLICATIONS 2009年第7-8期71卷 2708-2715页

作者： Colao, Vittorio Lopez-Acedo, Genaro Marino, Giuseppe Univ Calabria Dept Math Arcavacata Di Rende Italy Univ Seville Dept Math Anal Seville Spain

Let H be a Hilbert space. Consider on H a sequence of nonexpansive mappings {T-n} with common fixed points, a finite family of equilibrium functions {G(i)}(i=1,...,K), a contraction f with coefficient 0 < alpha < 1 and a strongly positive linear bounded operator A with coefficient (gamma) over bar > 0. Let 0 < gamma < (gamma) over bar/alpha. Assuming there are common equilibrium points of the family {G(i)}i=(1,...,K) which are also fixed points for {T-n}, we define a suitable sequence which strongly converges to the unique such point which also satisfies the variational inequality <(A - gamma f)x*, x - x*> >= 0 for all the x in the intersection of the equilibrium points and the common fixed points of the sequence {T-n}. (C) 2009 Elsevier Ltd. All rights reserved.

关键词： Equilibrium problem Fixed point Nonexpansive mapping Variational inequality implicit method Minimization problem

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Efficient analysis of welding thermal conduction using the Newton-Raphson method, implicit method, and their combination

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INTERNATIONAL JOURNAL OF ADVANCED MANUFACTURING TECHNOLOGY 2020年第7-8期111卷 1929-1940页

作者： Feng, Zhongyuan Ma, Ninshu Li, Wangnan Narasaki, Kunio Lu, Fenggui Osaka Univ Joining & Welding Res Inst 11-1 Mihogaoka Osaka Ibaraki 5670047 Japan Osaka Univ Grad Sch Engn Osaka 5650871 Japan Hubei Univ Arts & Sci Sch Phys & Elect Engn Xiangyang 441053 Peoples R China Shanghai Jiao Tong Univ Sch Mat Sci & Engn Shanghai 200240 Peoples R China

Finite element analysis is commonly used to investigate the thermal-mechanical phenomena during welding. To improve the computing efficiency of finite element analysis for welding thermal conduction, a novel Newton-Raphson method (NRM) without the computation of inverse matrix and a hybrid method combing the NRM and conventional implicit method (IMP) were developed. Comparison of computing time between the hybrid method implemented in an in-house software JWRIAN and the IMP used in a commercial software ABAQUS indicated that the computing speed of the former was about 4.5 times faster than that of the latter. Additionally, compared to the conventional IMP, the NRM exhibited higher computing efficiency in the analysis of transient thermal conduction during the welding heating process. Meanwhile, a combined hybrid method of the NRM and IMP was verified to be more efficient in analyzing the welding thermal conduction throughout the heating and cooling processes. Moreover, the thermal cycles computed by the hybrid method were consistent with those from experimental measurement, indicating the high accuracy of the hybrid method. Furthermore, the hybrid method was used to predict the temperature field of the corner boxing fillet joint welded by a low transformation temperature weld metal for generation of compressive residual stress.

关键词： Newton-Raphson method implicit method Hybrid method Welding thermal conduction Efficient computation

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RESERVOIR SIMULATION USING AN ADAPTIVE implicit method

SOCIETY OF PETROLEUM ENGINEERS JOURNAL

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SOCIETY OF PETROLEUM ENGINEERS JOURNAL 1983年第5期23卷 759-768页

作者： THOMAS, GW THURNAU, DH Scientific Software Intercomp

Abstract. This paper deals with a new implicit method for reservoir simulation. Rather than provide a fixed degree of implicitness in every gridblock at every time step or iteration, the adaptive implicit method operates with different levels of implicitness in adjacent gridblocks. These levels shift in space and time as needed to maintain stability. Shifting is accomplished automatically without user intervention. The technique can be applied to any simulation problem involving N unknowns. The advantage is substantial reduction in computing time and storage requirements compared to fully implicit formulations, while still yielding unconditionally stable *** mathematical procedure involves labeling the implicit/explicit mix of unknowns and then composing the matrix problem. The latter is reducible as long as there is one or more unknowns to be computed explicitly; consequently, appropriate operations are performed to put it in reduced form. This leads to matrix equations of lower order than the original problem that are solved at less cost. We demonstrate each step of the mathematical procedure with an ***, applications to a three-phase coning problem and a three-dimensional (3D) Cartesian problem are presented. By using special displays we demonstrate the degrees of implicitness in each cell and how they shift in space and time during simulation. We also present information regarding the savings in computer time and storage compared with a fixed, fully implicit procedure.

关键词： upstream oil & gas timestep gridblock stability simulator iteration modeling & simulation reservoir simulation total number implicit method Reservoir Simulation

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Explicit concomitance of implicit method to solve vibration equation

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Earthquake Engineering and Engineering Vibration 2012年第2期11卷 269-272页

作者： Li, Changqing Jiang, Lizhong School of civil engineering Central South University Changsha 410075 China

It has been proven that the implicit method used to solve the vibration equation can be transformed into an explicit method,which is called the concomitant explicit *** constant acceleration method's concomitant explicit method was used as an example and is described in detail in this *** relationship between the implicit method and explicit method is defined,which provides some guidance about how to create a new explicit method that has high precision and computational efficiency.

关键词： dynamic analysis explicit method implicit method structural dynamics

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An arbitrary Lagrangian-Eulerian method for analyzing finite-amplitude viscous acoustic waves radiated from vibrational solid boundaries: An implicit method

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WAVE MOTION 2023年第1期121卷

作者： Li, Yapeng Qu, Yegao Xie, Fangtao Meng, Guang Shanghai Jiao Tong Univ Sch Mech Engn Shanghai 200240 Peoples R China Shanghai Jiao Tong Univ Sch Mech Engn 800 Dongchuan Rd Shanghai Peoples R China

This paper is concerned with the development of an arbitrary Lagrangian-Eulerian (ALE) method for predicting nonlinear acoustic waves radiated from large-amplitude vibrational solid boundaries immersed in viscous fluids of infinite extent. The method is formulated based on a nonlinear acoustic model characterized by velocity potential and acoustic pressure. Unsplit implementations of three perfectly matched layer (PML) techniques are presented, namely conventional PML, convolution PML, and complex frequency-shifted PML (CFS-PML), to enable bounded-domain modeling of nonlinear acoustic waves propagating in an unbounded fluid medium. The long-time stability characteristics of the three distinct PML techniques are examined through theoretical analysis and numerical verification of their ability to absorb evanescent waves. Our results reveal that the CFS-PML technique exhibits superior long-time stability per-formance compared to the other two techniques. The CFS-PML is also compared to two different absorbing layer techniques: the Kosloff Absorbing Layer (KAL) technique and the Acoustic Black Hole (ABH) technique. The finite element method is adopted for spatial discretization of the finite-amplitude acoustic wave model, and an implicit predictor-corrector algorithm is proposed for time advancement. Several benchmark problems, including acoustic waves produced by a vibrational piston, and transversely oscillating and pulsating cylinders, are analyzed by the proposed method. It is found that the proposed method attains a second-order rate of convergence for spatial discretiza-tion, and the convergence rate in terms of the time step size is about first-order. The application of the method to acoustic levitation problems is also demonstrated, and the nonlinear phenomenon of acoustic waves in a single-axis acoustic levitator is discussed. & COPY;2023 Elsevier B.V. All rights reserved.

关键词： Nonlinear acoustic waves Absorbing layer Finite element method implicit method Long-time stability

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A parallel domain decomposition-based implicit method for the Cahn-Hilliard-Cook phase-field equation in 3D

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JOURNAL OF COMPUTATIONAL PHYSICS 2015年 285卷 55-70页

作者： Zheng, Xiang Yang, Chao Cai, Xiao-Chuan Keyes, David Columbia Univ Dept Appl Phys & Appl Math New York NY 10027 USA Chinese Acad Sci Inst Software Beijing 100190 Peoples R China Univ Colorado Dept Comp Sci Boulder CO 80309 USA King Abdullah Univ Sci & Technol Thuwal 23955 Saudi Arabia Chinese Acad Sci State Key Lab Comp Sci Beijing 100190 Peoples R China

We present a numerical algorithm for simulating the spinodal decomposition described by the three dimensional Cahn-Hilliard-Cook (CHC) equation, which is a fourth-order stochastic partial differential equation with a noise term. The equation is discretized in space and time based on a fully implicit, cell-centered finite difference scheme, with an adaptive time-stepping strategy designed to accelerate the progress to equilibrium. At each time step, a parallel Newton-Krylov-Schwarz algorithm is used to solve the nonlinear system. We discuss various numerical and computational challenges associated with the method. The numerical scheme is validated by a comparison with an explicit scheme of high accuracy (and unreasonably high cost). We present steady state solutions of the CHC equation in two and three dimensions. The effect of the thermal fluctuation on the spinodal decomposition process is studied. We show that the existence of the thermal fluctuation accelerates the spinodal decomposition process and that the final steady morphology is sensitive to the stochastic noise. We also show the evolution of the energies and statistical moments. In terms of the parallel performance, it is found that the implicit domain decomposition approach scales well on supercomputers with a large number of processors. (C) 2015 Elsevier Inc. All rights reserved.

关键词： Cahn-Hilliard-Cook Thermal fluctuation implicit method Newton-Krylov-Schwarz Parallel scalability Steady state solutions

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Water hammer simulation by implicit method of characteristic

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INTERNATIONAL JOURNAL OF PRESSURE VESSELS AND PIPING 2008年第12期85卷 851-859页

作者： Afshar, M. H. Rohani, M. Iran Univ Sci & Technol Dept Civil Engn Tehran Iran

An implicit method of Characteristics is proposed in this paper to alleviate the shortcomings and limitations of the mostly used conventional method of Characteristics (MOC). An element-wise definition is used for all the devices that may be used in a pipeline system and the corresponding equations are derived in an element-wise manner. The proper equations defining the behavior of each device including pipes are derived and assembled to form the final system of equations to be solved for the unknown nodal heads and flows. Proposed method allows for any arbitrary combination of devices in the pipeline system. The method is used to solve two example problems of transient flow caused by closure of a valve and failure of a pump system and the results are presented and compared with those of the explicit MOC. The results show the ability of the proposed method to accurately predict the variations of head and flow in all cases considered. (C) 2008 Elsevier Ltd. All rights reserved.

关键词： Water hammer method of characteristics Pipeline system implicit method Explicit method Boundary conditions

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