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Representative volume element size for elastic composites: A numerical study

JOURNAL OF THE MECHANICS AND PHYSICS OF SOLIDS 1997年第9期45卷 1449-1459页

作者： Gusev, AA Departement Werkstoffe Institut für Polymere ETH Zentrum CH-8092 Zürich Switzerland

Monte Carlo (MC) runs are employed to generate statistically independent realizations of a periodic elastic composite with a disordered unit cell made up of 8, 27, and 64 nonoverlapping identical spheres. In the limit of an infinite number of spheres in the disordered unit cell, this periodic composite obeys the Percus-Yevick hard-sphere statistics. By construction, the MC realizations studied have the same inclusion fraction. A constant-strain-tetrahedra displacement-based finite element code with an iterative solver is used to calculate the overall elastic constants of these periodic MC realizations. It appears that the scatter in the individual elastic constants already obtained with a few dozen spheres in the disordered unit cell is remarkably small and the averages obtained with varying numbers of spheres are practically stationary. (C) 1997 Elsevier Science Ltd.

关键词： microstructures constitutive behavior elastic material inhomogeneous material numerical algorithms

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Unsteady Preconditioned Characteristic Boundary Conditions for Direct numerical Simulation of Incompressible Flows

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AIAA JOURNAL 2020年第4期58卷 1476-1489页

作者： Parseh, Kaveh Hejranfar, Kazem Sharif Univ Technol Dept Aerosp Engn Tehran 11365 Iran

The unsteady preconditioned characteristic boundary conditions (UPCBCs) based on the artificial compressibility (AC) method are formulated and applied at artificial boundaries for the direct numerical simulation (DNS) of incompressible flows. The compatibility equations including the unsteady terms are mathematically derived in the generalized curvilinear coordinates and then incorporated as boundary conditions (BCs) in a high-order accurate incompressible flow solver. The spatial derivative terms of the system of equations are discretized using the fourth-order compact finite difference (FD) scheme, consistent with the high-order accuracy required for the DNS. The time integration is carried out using an implicit dual time-stepping method, and the robustness and performance of the numerical algorithm are enhanced by applying the preconditioning technique and calculating the automated AC parameter based on the local flow conditions. At first, the steady viscous incompressible flow for a two-dimensional plane jet is computed to assess the accuracy and performance of the solution method by applying the UPCBCs in comparison with the simplified BCs. Then, the simulation of the unsteady incompressible viscous flow around a two-dimensional NACA0012 airfoil at the Reynolds number 800 and the angle of attack 20 degrees is performed, and it is indicated that the computational cost of the solution is considerably decreased by implementing the UPCBCs at the artificial far-field boundary compared with the simplified BCs, which is remarkably valuable for the DNSs. Finally, the computation of the transition to unsteady for the incompressible flow around a three-dimensional NACA0012 wing at the same conditions of the two-dimensional case is successfully performed, and the results obtained are compared with those of previous studies that exhibit good agreement. Indications are that the present solution method by applying the UPCBCs at the artificial far-field boundary can be effect

关键词： Incompressible Viscous Flow Direct numerical Simulation Lift Coefficient Airfoil Freestream Conditions Flow Characteristics numerical algorithms Curvilinear Coordinates Strouhal Number Solution Algorithm

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A modified Gurson-type plasticity model at finite strains: formulation, numerical analysis and phase-field coupling

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COMPUTATIONAL MECHANICS 2018年第4期62卷 815-833页

作者： Aldakheel, Fadi Wriggers, Peter Miehe, Christian Leibniz Univ Hannover Inst Continuum Mech Appelstr 11 D-30167 Hannover Germany Univ Stuttgart Inst Appl Mech CE Chair 1 D-70569 Stuttgart Germany

The modeling of failure in ductile materials must account for complex phenomena at the micro-scale, such as nucleation, growth and coalescence of micro-voids, as well as the final rupture at the macro-scale, as rooted in the work of Gurson (J Eng Mater Technol 99:2-15, 1977). Within a top-down viewpoint, this can be achieved by the combination of a micro-structure-informed elastic-plastic model for a porous medium with a concept for the modeling of macroscopic crack discontinuities. The modeling of macroscopic cracks can be achieved in a convenient way by recently developed continuum phase field approaches to fracture, which are based on the regularization of sharp crack discontinuities, see Miehe et al. (Comput Methods Appl Mech Eng 294:486-522, 2015). This avoids the use of complex discretization methods for crack discontinuities, and can account for complex crack patterns. In this work, we develop a new theoretical and computational framework for the phase field modeling of ductile fracture in conventional elastic-plastic solids under finite strain deformation. It combines modified structures of Gurson-Tvergaard-Needelman GTN-type plasticity model outlined in Tvergaard and Needleman (Acta Metall 32:157-169, 1984) and Nahshon and Hutchinson (Eur J Mech A Solids 27:1-17, 2008) with a new evolution equation for the crack phase field. An important aspect of this work is the development of a robust Explicit-Implicit numerical integration scheme for the highly nonlinear rate equations of the enhanced GTN model, resulting with a low computational cost strategy. The performance of the formulation is underlined by means of some representative examples, including the development of the experimentally observed cup-cone failure mechanism.

关键词： Ductile fracture Porous plasticity GTN model numerical algorithms Phase-field modeling

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Field Dislocation Mechanics for heterogeneous elastic materials: A numerical spectral approach

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COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING 2017年 315卷 921-942页

作者： Djaka, Komlan Senam Villani, Aurelien Toupin, Vincent Capolungo, Laurent Berbenni, Stephan Univ Lorraine CNRS UMR 7239 Lab Etud Microstruct & Mecan Mat F-57045 Metz 1 France Ecole Mines St Etienne CNRS UMR 5307 158 Cours Fauriel F-42023 St Etienne France Los Alamos Natl Lab Div Mat Sci & Technol Los Alamos NM 87544 USA

Spectral methods using Fast Fourier Transform (FFT) algorithms have recently seen a surge in interest in the mechanics of materials community. The present contribution addresses the critical question of determining accurate local mechanical fields using FFT methods without artificial fluctuations arising from materials and defects induced discontinuities. Precisely, the present work introduces a numerical approach based on intrinsic discrete Fourier transforms for the simultaneous treatment of material discontinuities arising from the presence of dislocations and from elastic stiffness heterogeneities. To this end, the elasto-static equations of the field dislocation mechanics theory for periodic heterogeneous materials are numerically solved with FFT in the case of dislocations in proximity of inclusions of varying stiffness. An optimal intrinsic discrete Fourier transform method is sought based on two distinct schemes. A centered finite difference scheme for differential rules are used for numerically solving the Poisson-type equation in the Fourier space, while centered finite differences on a rotated grid is chosen for the computation of the modified Fourier Green's operator associated with the Lippmann Schwinger-type equation. By comparing different methods with analytical solutions for an edge dislocation in a composite material, it is found that the present spectral method is accurate, devoid of any numerical oscillation, and efficient even for an infinite phase elastic contrast like a hole embedded in a matrix containing a dislocation. The present FFT method is then used to simulate physical cases such as the elastic fields of dislocation dipoles located near the matrix/inclusion interface in a 2D composite material and the ones due to dislocation loop distributions surrounding cubic inclusions in 3D composite material. In these configurations, the spectral method allows investigating accurately the elastic interactions and image stresses due to dislocation

关键词： Dislocation mechanics Heterogeneous media Elastic fields Spectral method FFT numerical algorithms

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An orthogonal genetic algorithm with quantization for global numerical optimization

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IEEE TRANSACTIONS ON EVOLUTIONARY COMPUTATION 2001年第1期5卷 41-53页

作者： Leung, YW Wang, YP Hong Kong Baptist Univ Dept Comp Sci Kowloon Tong Hong Kong Peoples R China Xidian Univ Dept Appl Math Xian 710071 Peoples R China

We design a genetic algorithm called the orthogonal genetic algorithm with quantization for global numerical optimization with continuous variables. Our objective is to apply methods of experimental design to enhance the genetic algorithm, so that the resulting algorithm can be more robust and statistically sound. A quantization technique is proposed to complement an experimental design method called orthogonal design. We apply the resulting methodology to generate an initial population of points that are scattered uniformly over the feasible solution space, so that the algorithm can evenly scan the feasible solution space once to locate good points for further exploration in subsequent iterations. In addition, we apply the quantization technique and orthogonal design to tailor a new crossover operator, such that this crossover operator can generate a small, but representative sample of points as the potential offspring. We execute the proposed algorithm to solve 15 benchmark problems with 30 or 100 dimensions and very large numbers of local minima. The results show that the proposed algorithm can find optimal or close-to-optimal solutions.

关键词： evolutionary computation experimental design methods genetic algorithms numerical algorithms numerical optimization orthogonal array orthogonal design

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numerical COMPUTATION OF WAVE LOCALIZATION IN LARGE DISORDERED BEAM-LIKE LATTICE TRUSSES

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AIAA JOURNAL 1994年第8期32卷 1724-1732页

作者： XIE, WC ARIARATNAM, ST University of Waterloo Waterloo Ontario N2L 3G1 Canada

Wave localization in randomly disordered multiwave structures is investigated. The smallest localization factor is of particular interest and is related to the smallest positive Lyapunov exponent. The numerical algorithm by Wolf et al. is modified to determine all of the Lyapunov exponents. The wave localization in a large beamlike lattice truss modeled as an equivalent continuous Timoshenko beam is studied.

关键词： Trusses numerical algorithms Element Numbering Solar Power Stations Material Properties Space Structures Bending Stiffness numerical Simulation Vibrational Energy Structural System

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numerical investigation of instability and transition in an obstructed channel flow

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AIAA JOURNAL 2000年第7期38卷 1173-1178页

作者： Yang, KS Inha Univ Dept Engn Mech Nam Ku Inchon 402751 South Korea

Instability and transition in an obstructed channel how are investigated using direct numerical simulation. The flow geometry under consideration is a plane channel with two-dimensional thin obstacles (baffles) mounted symmetrically in the vertical direction and periodically in the streamwise direction. The flow is steady and symmetric at low Reynolds numbers. Above a certain Reynolds number, the flow undergoes a Hopf bifurcation, leading to a solution periodic in time. At high Reynolds numbers the unsteady flow exhibits a space-time symmetry-breaking bifurcation. A secondary instability is also observed at high Reynolds numbers, which is believed to be responsible for a subsequent chaotic breakdown of the flow. To study the secondary instability, we take the periodic solution, which results from the Hopf bifurcation, as the basic flow to be disturbed with small-amplitude random noise. Depending on the Reynolds number the basic Row becomes unstable to three-dimensional disturbances, which results in a chaotic how The numerical results obtained are consistent with experimental findings currently available.

关键词： Reynolds Numbers Direct numerical Simulation Channel Flow Laminar Turbulent Transition Navier Stokes Solver Bifurcation Theory Tollmien Schlichting waves Hydrodynamic Instability Navier Stokes Equations numerical algorithms

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A unified framework for the numerical solution of general quadratic matrix equations

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IMA JOURNAL OF MATHEMATICAL CONTROL AND INFORMATION 2007年第2期24卷 259-287页

作者： Tsachouridis, Vassilios A. Karcanias, Nicos Postlethwaite, Ian City Univ London Sch Engn & Math Sci London EC1V 0HB England Univ Leicester Dept Engn Leicester LE1 7RH Leics England

Algebraic quadratic equations are special cases of a single generalized algebraic quadratic matrix equation (GQME). This paper focuses on the numerical solution of the GQME using probability-1 homotopy methods. A synoptic review of these methods and their application to algebraic matrix equations is provided as background. A large variety of analysis and design problems in systems and control are reported as special cases of the presented framework and some of them are illustrated via numerical examples from the literature.

关键词： numerical algorithms homotopy methods matrix equations Riccati equations control systems

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numerical treatment of complete load-deflection curves

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INTERNATIONAL JOURNAL FOR numerical METHODS IN ENGINEERING 1998年第5期41卷 955-971页

作者： Magnusson, A Svensson, I Univ Lund Dept Solid Mech S-22100 Lund Sweden

A method for direct computation of complete load-deflection curves, including both primary and secondary branches, as well as exact calculation of singular points is presented. The method used for path following is the cylindrical arc-length method in accordance with Crisfield.(1) To calculate singular points, an extended system, as proposed by Keener and Keller,(2) has been adopted. The numerical problems arising from ill-conditioned stiffness matrices near the singular points, are circumvented using a deflation technique. By a modification of the constraint equation used in the arc-length method, a reliable method for branch switching has been obtained. This leads to a unified approach to complete path following of structures with limit and bifurcation points. The use of this approach is demonstrated both on a simple two-bar truss as well as on a star-shaped shallow truss dome which exhibits complex stability characteristics. Comparisons are made with calculations found in the literature. (C) 1998 John Wiley & Sons, Ltd.

关键词： numerical algorithms path following technique singular points deflation technique branch switching

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Analysis of ill-posedness and numerical methods of solving a nonlinear inverse problem in pharmacokinetics for the two-compartmental model with extravascular drug administration

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JOURNAL OF INVERSE AND ILL-POSED PROBLEMS 2012年第1期20卷 39-64页

作者： Ilyin, A. Kabanikhin, S. I. Nurseitov, D. B. Nurseitova, A. T. Asmanova, N. A. Voronov, D. A. Bakytov, D. Sci Ctr Antiinfect Drugs Alma Ata Kazakhstan ICM Novosibirsk Russia MG SB RAS Novosibirsk Russia NNLKP ICT KazNTU KI Satpayev Alma Ata Kazakhstan KazNPU Abay AT Nurseitova Alma Ata Kazakhstan

A nonlinear inverse problem of pharmacokinetics for the dual-compartment model with extravascular route of the drug administration is considered. The problem is significantly ill-posed: its solution is not unique and is unstable. We discuss nonuniqueness of the inverse problem and the degree of ill-posedness. The initial problem is reduced to a linear operator equation by linearization. It is demonstrated that the resolving ability of the inverse problem can be improved by varying of the location of measurement data points. Results of numerical experiments are presented. The question of choosing the initial approximations is considered.

关键词： Inverse pharmacokinetic problem nonuniqueness ill-posedness numerical algorithms

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