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Dynamics of inelastic deformation of porous rocks and formation of localized compaction zones studied by numerical modeling

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JOURNAL OF THE MECHANICS AND PHYSICS OF SOLIDS 2011年第11期59卷 2323-2340页

作者： Stefanov, Yu P. Chertov, M. A. Aidagulov, G. R. Myasnikov, A. V. Schlumberger Moscow Res Moscow 119285 Russia

The paper presents a numerical analysis of the inelastic deformation process in porous rocks during different stages of its development and under non-equiaxial loading. Although numerous experimental studies have already investigated many aspects of plasticity in porous rocks, numerical modeling gives valuable insight into the dynamics of the process, since experimental methods cannot extract detailed information about the specimen structure during the test and have strong limitations on the number of tests. The numerical simulations have reproduced all different modes of deformation observed in experimental studies: dilatant and compactive shear, compaction without shear, uniform deformation, and deformation with localization. However, the main emphasis is on analysis of the compaction mode of plastic deformation and compaction localization, which is characteristic for many porous rocks and can be observed in other porous materials as well. The study is largely inspired by applications in petroleum industry, i.e. surface subsidence and reservoir compaction caused by extraction of hydrocarbons and decrease of reservoir pressure. Special attention is given to the conditions, evolution, and characteristic patterns of compaction localization, which is often manifested in the form of compaction bands. Results of the study include stress-strain curves, spatial configurations and characteristics of localized zones, analysis of bifurcation of stress paths inside and outside localized zones and analysis of the influence of porous rocks properties on compaction behavior. Among other results are examples of the interplay between compaction and shear modes of deformation. To model the evolution of plastic deformation in porous rocks, a new constitutive model is formulated and implemented, with the emphasis on selection of adequate functions defining evolution of yield surface with deformation. The set of control parameters of the model is kept as short as possible;the paramete

关键词： Compaction localization Constitutive behavior Rock Dynamics numerical algorithms

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numerical algorithms for polynomial plus/minus factorization

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INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL 2007年第8期17卷 786-802页

作者： Hromcik, M. Sebek, M. Czech Tech Univ Fac Elect Engn Ctr Appl Cybernet CR-16635 Prague Czech Republic Czech Tech Univ Fac Elect Engn Dept Control Engn CR-16635 Prague Czech Republic

Two new algorithms are presented in the paper for the plus/minus factorization of a scalar discrete-time polynomial. The first method is based on the discrete Fourier transform theory (DFT) and its relationship to the Z-transform. Involving DFT computational techniques and the famous fast Fourier transform routine brings high computational efficiency and reliability. The method is applied in the case study of H-2-optimal inverse dynamic filter to an audio equipment. The second numerical procedure originates in a symmetric spectral factorization routine, namely the Bauer's method of the 1950s. As a by-product, a recursive LU factorization procedure for Toeplitz matrices is devised that is of more general impact and can be of use in other areas of applied mathematics as well. Performance of the method is demonstrated by an l(1) optimal controller design example. Copyright (c) 2006 John Wiley & Sons, Ltd.

关键词： polynomial design methods numerical algorithms polynomial factorizations

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High order numerical differentiation and approximation of Laplace fields using regular grid data

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NUCLEAR INSTRUMENTS & METHODS IN PHYSICS RESEARCH SECTION A-ACCELERATORS SPECTROMETERS DETECTORS AND ASSOCIATED EQUIPMENT 2011年第1期645卷 292-299页

作者： Berdnikov, A. S. Inst Analyt Instrumentat St Petersburg 190103 Russia

Specialized numerical schemes for calculation of high order field derivatives are considered. The input data are a regular rectangular mesh with potential values at its nodes, the output data are high order derivative values at grid nodes and associated expressions which enable the calculation of potentials, field values or high order derivatives inside a grid cell with high accuracy. An important feature is that differentiation and approximation techniques are based on a priori knowledge about the Laplace equation which allow the production of numerical schemes with higher order properties. (C) 2011 Elsevier B.V. All rights reserved.

关键词： Field calculation Finite difference methods FDM algorithms Harmonic functions CPO simulations numerical algorithms

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High order numerical differentiation and approximation of Laplace fields using regular grid data

High order numerical differentiation and approximation of La...

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8th International Conference on Charged Particle Optics

作者： Berdnikov, A. S. Inst Analyt Instrumentat St Petersburg 190103 Russia

关键词： Field calculation Finite difference methods FDM algorithms Harmonic functions CPO simulations numerical algorithms

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A multiscale method for dislocation nucleation and seamlessly passing scale boundaries

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INTERNATIONAL JOURNAL OF PLASTICITY 2011年第12期27卷 2103-2124页

作者： Fan, Jinghong Stewart, Ross J. Zeng, Xiangguo Alfred Univ Kazuo Inamori Sch Engn Alfred NY 14802 USA Shichuan Univ Dept Engn Mech Chengdu 610065 Peoples R China

In the concurrent multiscale analysis, it is difficult to have truly seamless transition between the atomistic and continuum scale. This situation is even worse when defects pass through the boundary between different scales. For example, there is a lack of effective methods to handle the dislocation passing through scale boundaries which is important to investigate plasticity at the nanoscale. In this paper, the generalized particle (GP) method proposed by the first author is further developed so that a seamless transition and dislocation passing between different scales can be realized. Specifically, the linkage between different scales is through material neighbor-link cells (NLC) with scale duality. This indicates that material elements can be high-scale particles through a lumping process and can also be atoms via decomposition depending on the needs of the simulation. At the interface, the information transfer from bottom scale-up or from top scale-down is through the particles or atoms in the NLC. They are with the same material structure, all possess nonlocal constitutive behavior;thus, the smooth transition at the interface between different scales can be attained and validated to avoid non-physical responses. To save degrees of freedom, atoms are lumped together into a generalized particle in the domain in which the deformation gradient is near homogeneous. On the other hand, when defects such as dislocations in the atomistic domain are near the particle domain, the particles along dislocation propagation path and its surrounding region will be decomposed into atoms so dislocations can freely pass through the scale boundary and propagate inside the model just as it propagates in the deformed atomistic crystal structure. The method is verified first for seamless transition of variables at the scale boundary by a one-dimensional model and then verified for dislocation nucleation and propagation passing through scale boundaries in two cases, one is near the f

关键词： Dislocations Constitutive behavior numerical algorithms Metallic material

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Soft-Core Potentials in Thermodynamic Integration: Comparing One- and Two-Step Transformations

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JOURNAL OF COMPUTATIONAL CHEMISTRY 2011年第15期32卷 3253-3263页

作者： Steinbrecher, Thomas Joung, InSuk Case, David A. Univ Karlsruhe Inst Phys Chem D-76131 Karlsruhe Germany Rutgers State Univ BioMaps Inst Piscataway NJ 08854 USA

Molecular dynamics-based free energy calculations allow the determination of a variety of thermodynamic quantities from computer simulations of small molecules. Thermodynamic integration (TI) calculations can suffer from instabilities during the creation or annihilation of particles. This "singularity" problem can be addressed with "soft-core" potential functions which keep pair-wise interaction energies finite for all configurations and provide smooth free energy curves. "One-step" transformations, in which electrostatic and van derWaals forces are simultaneously modified, can be simpler and less expensive than "two-step" transformations in which these properties are changed in separate calculations. Here, we study solvation free energies for molecules of different hydrophobicity using both models. We provide recommended values for the two parameters alpha(LJ) and beta(C) controlling the behavior of the soft-core Lennard-Jones and Coulomb potentials and compare one-and two-step transformations with regard to their suitability for numerical integration. For many types of transformations, the one-step procedure offers a convenient and accurate approach to free energy estimates. (C) 2011 Wiley Periodicals, Inc. J Comput Chem 32: 3253-3263, 2011

关键词： free energy calculation molecular dynamics thermodynamic integration free energy of solvation numerical algorithms separation shifted scaling soft-core potentials

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Sequential evaluation of continuous deformation field of semi-crystalline polymers during tensile deformation accompanied by neck propagation

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INTERNATIONAL JOURNAL OF PLASTICITY 2011年第12期27卷 2085-2102页

作者： Uchida, Makoto Tada, Naoya Okayama Univ Grad Sch Nat Sci & Technol Kita Ku Okayama 7008530 Japan

The localized deformation field of high density polyethylene and polypropylene during a tensile test accompanied by neck propagation was quantitatively evaluated based on the network digital image correlation method. In the proposed method, the continuity of the deformation field around a point of interest was introduced for accurate evaluation of the displacement. The accuracy of the proposed method was verified through test images. Using the proposed method, the development of a non-uniform displacement field during tensile tests was evaluated from sequential digital images. The local strain rate was almost uniform until the nominal stress reached its maximum value. After the maximum stress was reached, non-uniform deformation developed at a part of the gauge region of the specimen. A decrease in nominal stress induced a reduction of the local strain rate at regions other than the necked zone. In this study, the cross section average local true stress, strain, and strain rate can be evaluated from the local displacement field. Thus, the relationship between these quantities was evaluated during the tensile tests. Using the proposed method, the local response under wide ranges of strain and strain rate can be evaluated from a few test conditions of tensile strain rate and a small range of tensile strain. Finally, the relationships between gradients of stress, strain, and strain rate under uniaxial tension are discussed. These non-local quantities deviated from those predicted by constitutive equations when the domain size used to evaluate the local quantities was large. (C) 2011 Elsevier Ltd. All rights reserved.

关键词： Polymeric material Mechanical testing Nondestructive evaluation numerical algorithms

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Low order-value approach for solving VaR-constrained optimization problems

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JOURNAL OF GLOBAL OPTIMIZATION 2011年第4期51卷 715-742页

作者： Birgin, E. G. Bueno, L. F. Krejic, N. Martinez, J. M. Univ Sao Paulo Dept Comp Sci IME USP BR-05508090 Sao Paulo Brazil Univ Estadual Campinas Inst Math Stat & Sci Comp IMECC Dept Appl Math BR-13083859 Campinas SP Brazil Univ Novi Sad Dept Math & Informat Novi Sad 21000 Serbia

In Low Order-Value Optimization (LOVO) problems the sum of the r smallest values of a finite sequence of q functions is involved as the objective to be minimized or as a constraint. The latter case is considered in the present paper. Portfolio optimization problems with a constraint on the admissible Value at Risk (VaR) can be modeled in terms of a LOVO problem with constraints given by Low order-value functions. Different algorithms for practical solution of this problem will be presented. Using these techniques, portfolio optimization problems with transaction costs will be solved.

关键词： Optimization Augmented Lagrangian Order-value optimization Low order-value optimization Value at risk numerical algorithms

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An efficient algorithm for the solution of a coupled Sylvester equation appearing in descriptor systems

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AUTOMATICA 2011年第1期47卷 244-248页

作者： Shahzad, Amir Jones, Bryn Ll Kerrigan, Eric C. Constantinides, George A. Univ London Imperial Coll Sci Technol & Med Dept Elect & Elect Engn London SW7 2AZ England Scottish Marine Inst Scottish Assoc Marine Sci Oban PA37 1QA Argyll Scotland Univ London Imperial Coll Sci Technol & Med Dept Aeronaut London SW7 2AZ England

Descriptor systems consisting of a large number of differential-algebraic equations (DAEs) usually arise from the discretization of partial differential-algebraic equations. This paper presents an efficient algorithm for solving the coupled Sylvester equation that arises in converting a system of linear DAEs to ordinary differential equations. A significant computational advantage is obtained by exploiting the structure of the involved matrices. The proposed algorithm removes the need to solve a standard Sylvester equation or to invert a matrix. The improved performance of this new method over existing techniques is demonstrated by comparing the number of Floating-point operations and via numerical examples. (C) 2010 Elsevier Ltd. All rights reserved.

关键词： Descriptor systems Matrix equations numerical algorithms Coupled Sylvester equation Efficient algorithms

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A constitutive model for rate dependent and rate independent inelasticity. Application to IN718

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INTERNATIONAL JOURNAL OF PLASTICITY 2011年第4期27卷 596-619页

作者： Becker, Martin Hackenberg, Hans-Peter MTU Aero Engines GmbH D-80995 Munich Germany

In this paper, a constitutive model for the unified description of rate dependent and rate independent material behavior is proposed. It is applicable to isotropic metals subjected to arbitrary thermomechanical loading conditions at small strains. The focus of the model formulation is its validity for the full range of thermal and mechanical loading conditions to be covered in an industrial context by e.g. modern aero-engine designs. Consequently, the proposed model describes the material behavior on a macroscopic level covering the full temperature range from room temperature to the upper application limit under monotonic as well as cyclic loading. Special emphasis is also put on the correct representation of the observed ratcheting behavior. The most prominent features of the model are the combined treatment of both, rate dependent, as well as rate independent inelasticity through a limit surface concept, the description of primary, secondary and tertiary creep behavior and the application of an appropriate backstress evolution equation. A fully implicit integration algorithm for the proposed model is developed and implemented in connection with uniaxial integration point drivers as well as three alternative Finite Element packages. The parameters of the proposed model can be identified based on a limited number of complex cyclic tests and monotonic creep tests. After reporting on the fitting results for such tests for the Nickel-base superalloy IN718 the predictive capabilities of the proposed model are assessed for a number of isothermal and nonisothermal tests. Finally, the performance of the algorithmic implementation into the Finite Element packages is briefly addressed. (C) 2010 Elsevier Ltd. All rights reserved.

关键词： Constitutive behavior Cyclic loading Elastic-viscoplastic material Finite elements numerical algorithms

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