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Implementation and application of a temperature-dependent Chaboche model

INTERNATIONAL JOURNAL OF PLASTICITY 2015年 75卷 121-140页

作者： Zhou, C. Chen, Z. Lee, J. W. Lee, M. G. Wagoner, R. H. S China Univ Technol Sch Mech & Automot Engn Guangzhou 510641 Guangdong Peoples R China Ohio State Univ Dept Mat Sci & Engn Columbus OH 43210 USA Pohang Univ Sci & Technol Grad Inst Ferrous Technol Pohang 790784 South Korea Korea Inst Mat Sci Mat Deformat Dept Chang Won 642831 South Korea Korea Univ Dept Mat Sci & Engn Seoul 136713 South Korea

The literature shows that shear fracture of advanced high strength steels (AHSS) is affected by strain hardening at large strain, as well as the temperature dependence of flow stress and strain hardening. The role of non-isotropic hardening, such as would be expected to be important in reverse strain paths as encountered during draw-bend testing or drawing sheet metal into forming dies, has been difficult to assess without a practical constitutive model combining temperature-dependence and non-isotropic hardening capabilities. Such a model has been developed and implemented in Abaqus Standard via the UMAT subroutine. In order to apply and test the constitutive implementation, the material model was fit using alternate parameter-identification procedures starting from compression-tension (CT) data: 1) fit directly from reverse-path, CT data, and 2) fit indirectly, by combining the direct CT data plus extrapolated data at larger strains where the extrapolation uses verified large-strain monotonic hardening character. The resulting material models were used to simulate draw-bend fracture (DBF) tests for six AHSS. The results show that the indirect method improves the predictions of shear fracture significantly, allowing accurate predictions. It was also shown that the influence of non-isotropic hardening aspects are not critical to accurate predictions as long as the high-strain strain hardening is reproduced accurately. These results suggest a practical and effective method for extending measured tensile hardening to otherwise unattainable strains based on the constant ratio (a in the H/V model) of power-law and saturation-stress strain hardening at a given temperature. The success of this approach suggests that a is a material constant (describing the fundamental strain-hardening character) that depends on temperature but is unaffected by the details of transient hardening following abrupt path changes. Furthermore, the essentially transient nature of hardening follo

关键词： Constitutive behaviour Fracture Thermomechanical processes numerical algorithms Advanced High Strength Steel (AHSS)

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Nonlinear Generalized Lifting-Line Coupling algorithms for Pre/Poststall Flows

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AIAA JOURNAL 2015年第7期53卷 1784-1792页

作者： Gallay, S. Laurendeau, E. Ecole Polytech Montreal PQ H3C 3A7 Canada

numerical algorithms and solutions of generalized nonlinear lifting-line theory over an elliptical wing are examined, with emphasis on near/poststall flows. First, a thorough analysis on the circulation-based and angle-of-attack-based correction methods ( and methods, respectively) highlights their respective numerical poststall characteristics. The stability of the method is demonstrated, producing single and multiple solutions in the pre- and poststall regions, respectively. Second, artificial dissipation added to the method is shown to be an effective means of controlling the poststall flow region. Finally, a strongly coupled algorithm is presented, allowing to bypass the interpolation phase via the use of Legendre polynomials. The model sheds light on poststall flow behavior, in agreement with several papers studying formation of stall cell patterns.

关键词： Lift Coefficient Kutta Joukowski Theorem numerical algorithms Viscosity Aspect Ratio Wing Root Vortex Lattice Method Vortices Nonlinear Systems Newton Raphson Method

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On the inverse problem of thermal conductivity determination in nonlinear heat and moisture transfer model within textiles

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APPLIED MATHEMATICS AND COMPUTATION 2015年 264卷 284-299页

作者： Yu, Yue Xu, Dinghua Zhejiang Sci Tech Univ Coll Sci Dept Math Hangzhou 310018 Zhejiang Peoples R China

This paper focuses on an inverse problem of textile thermal conductivity determination (IPTCD) based on the nonlinear heat and moisture transfer model under low temperature. The conditional well-posedness of the analytical solution and the stability for numerical solution to the inverse problem of determining the left boundary value (IPLB) are derived respectively. The mathematical formulation of IPTCD is presented and deduced to an optimization problem with least squares. By means of Parametrized Fibonacci (PF) search method and Genetic Algorithm (GA), the approximate solution to the IPTCD is numerically obtained. (C) 2015 Elsevier Inc. All rights reserved.

关键词： Inverse problems Thermal conductivity Heat and moisture transfer Well-posedness Conditional stability numerical algorithms

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Forerunning mode transition in a continuous waveguide

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JOURNAL OF THE MECHANICS AND PHYSICS OF SOLIDS 2015年 78卷 32-45页

作者： Slepyan, Leonid Ayzenberg-Stepanenko, Mark Mishuris, Gennady Tel Aviv Univ Sch Mech Engn IL-69978 Tel Aviv Israel Shamoon Coll Engn IL-84105 Beer Sheva Israel Aberystwyth Univ Inst Math & Phys Ceredigion SY23 3BZ Wales

We have discovered a forerunning mode transition as the periodic wave changing the state of a uniform continuous waveguide. The latter is represented by an elastic beam initially rested on an elastic foundation. Under the action of an incident sinusoidal wave, the separation from the foundation occurs propagating in the form of a transition wave. The critical displacement is the separation criterion. Under these conditions, the steady-state mode exists with the transition wave speed independent of the incident wave amplitude. We show that such a regime exists only in a bounded domain of the incident wave parameters. Outside this domain, for higher amplitudes, the steady-state mode, is replaced by a set of local separation segments periodically emerging at a distance ahead of the main transition point. The crucial feature of this waveguide is that the incident wave group speed is greater than the phase speed. This allows the incident wave to deliver the energy required for the separation. The analytical solution allows us to show in detail how the steady-state mode transforms into the forerunning one. The latter studied numerically turns out to be periodic. As the incident wave amplitude grows the period decreases, while the transition wave speed averaged over the period increases to the group velocity of the wave. As an important part of the analysis, the complete set of solutions is presented for the waves excited by the oscillating or/and moving force acting on the free beam. In particular, an asymptotic solution is evaluated for the resonant wave corresponding to a certain relation between the load's speed and frequency. (C) 2015 Elsevier Ltd. All rights reserved.

关键词： Delamination Dynamics Beams and columns Transition waves numerical algorithms

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Concurrent atomistic-continuum simulations of dislocation-void interactions in fcc crystals

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INTERNATIONAL JOURNAL OF PLASTICITY 2015年 65卷 33-42页

作者： Xiong, Liming Xu, Shuozhi McDowell, David L. Chen, Youping Iowa State Univ Dept Aerosp Engn Ames IA 50011 USA Georgia Inst Technol Sch Mat Sci & Engn Atlanta GA 30332 USA Georgia Inst Technol Woodruff Sch Mech Engn Atlanta GA 30332 USA Univ Florida Dept Mech & Aerosp Engn Gainesville FL 32611 USA

Dislocation interactions with distributed condensed vacancy clusters in fcc metals were simulated via a concurrent atomistic-continuum method. Due to void strengthening, the dislocation lines are found to bow as a result of pinning on the original glide plane and undergo depinning through drawing out screw dipoles and forming prismatic loops on the secondary slip plane. We discovered an inertia-induced transition between Hirsch looping and void shearing mechanisms as the void spacing ranges from the scale of nm to hundreds of nm. Contrary to prior understanding, simulations suggest that large voids nm in diameter) can behave as weak barriers to dislocation motions under high strain-rate dynamic conditions. (C) 2014 Elsevier Ltd. All rights reserved.

关键词： Dislocations Strengthening mechanisms Metallic material Finite elements numerical algorithms

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Refinement of a Newton Reciprocal Algorithm for Arbitrary Precision Numbers

Refinement of a Newton Reciprocal Algorithm for Arbitrary Pr...

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2016 IEEE International Conference on Progress in Informatics and Computing

作者： Yiping Cheng Ze Liu School of Electronic and Information Engineering Beijing Jiaotong University

For arbitrary precision numbers, reciprocal computing algorithms based on Newton iteration is asymptotically the fastest. In this work we provide a refined a lgorithm based on the Newton reciprocal algorithm by Brent and Zimmermann in their MCA book. The key techniques used in the refinement are D1 balancing, clear specification, r emainder o peration, and economical multiplication. The refined algorithm is more general,and gives exact and unique result. numerical results show that these improvements are made without the cost of time *** is still the potential to further improve the efficiency by utilizing a short multiplication algorithm.

关键词： Newton iteration numerical algorithms computer algebra multi-precision computing

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A unified approach for the convergence of certain numerical algorithms, using recurrent functions

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COMPUTING 2010年第3-4期90卷 131-164页

作者： Argyros, Ioannis K. Hilout, Said Cameron Univ Dept Math Sci Lawton OK 73505 USA Univ Poitiers Lab Math & Applicat F-86962 Futuroscope France

The Kantorovich analysis (Argyros in Convergence and applications of Newton-type iterations, Springer, New York, 2008;Argyros and Hi lout in Efficient methods for solving equations and variational inequalities, Polimetrica Publisher, Milano, 2009;Kantorovich and Akilov in Functional analysis, Pergamon Press, Oxford, 1982), and recurrent relation's approach (Gutierrez et al. in J Comput Appl Math 115:181-192,2000) are the most popular ways for generating sufficient conditions for the convergence of numerical algorithms to a solution of a nonlinear equations as well as providing the corresponding error estimates on the distances involved. We introduce the new approach of recurrent functions to show that a finer convergence analysis can be provided under the same hypotheses, and computational cost. numerical examples are provided where our results apply, hut not earlier ones.

关键词： numerical algorithms Banach space Majorizing sequence Newton-Kantorovich hypothesis Semilocal convergence Recurrent functions Boundary value problem with a Green's kernel

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Modeling of forming limit for multilayer sheets based on strain-rate potentials

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INTERNATIONAL JOURNAL OF PLASTICITY 2015年 75卷 63-99页

作者： Kim, Daeyong Kim, Hyunki Kim, Ji Hoon Lee, Myoung-Gyu Kim, Kee Joo Barlat, Frederic Lee, Youngseon Chung, Kwansoo Korea Inst Mat Sci Mat Deformat Dept Chang Won 642831 Gyeongnam South Korea Korea Univ Sci & Technol Daejeon 305350 South Korea Seoul Natl Univ Res Inst Adv Mat Engn Res Inst Dept Mat Sci & Engn Seoul 151744 South Korea Pusan Natl Univ Sch Mech Engn Busan 609736 South Korea Korea Univ Dept Mat Sci & Engn Seoul 151744 South Korea Seojeong Coll Dept Automobile Engn Eunhyun Myun 482777 Gyeonggi Do South Korea POSTECII Grad Inst Ferrous Technol Pohang 790784 Gyeongbuk South Korea

In order to evaluate the forming limits of planar anisotropic multilayer sheet materials, the Marciniak-Kuczynski (M-K) model was formulated based on the strain-rate potential. A common practice to predict the forming limits of sheet materials has been based on yield stress potentials defined in the stress field. As an alternative, a method based on plastic stain-rate potentials, which are especially convenient to apply for rigid-viscoplasticity, was considered in this work. The formulation based on the strain-rate potential facilitates the modeling of forming limits for multilayer sheet materials because the number of unknown variables is significantly reduced by assuming the iso-strain condition for each layer without delamination. As for the strain-rate potential, Srp2003-2d, which is the pseudo-conjugate of the yield stress potential Yld2000-2d, was applied along with Hill's 1948 strain-rate potential for comparison. In the approach proposed, rigid-viscoplasticity was formulated according to the incremental deformation theory based on the minimum plastic work path. The rotation of anisotropic symmetry axes in the groove region was also properly accounted for in the formulation. For verification purposes, the predicted forming limit criteria such as the strain-based forming limit diagram (FLD), the stress-based forming limit diagram (FLSD) and the effective strain-based forming limit diagram (x-EPS) were experimentally validated for a monolithic aluminum alloy (AA5182-O) sheet and a three-layer AA5182-O/polypropylene/AA5182-O (AA/PP/AA) sandwich sheet, which confirmed good agreement. In addition, the path-sensitivity of the strain-based FLD and the path-insensitivity of the FLSD and x-EPS were numerically proven based on the M-K model for the three-layer sandwich sheet. Finally, the M K model was compared with a maximum force model most recently developed. (C) 2015 Elsevier Ltd. All rights reserved.

关键词： Anisotropic material Ideally plastic material Layered material numerical algorithms Anisotropic plastic strain-rate potential

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A dislocation-based model for deformation and size effect in multi-phase steels

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INTERNATIONAL JOURNAL OF PLASTICITY 2015年 72卷 44-59页

作者： Lyu, Hao Ruimi, Annie Zbib, Hussein M. Washington State Univ Sch Mech & Mat Engn Pullman WA 99164 USA Texas A&M Univ Dept Mech Engn Doha Qatar

In this work, we investigate the mechanical behavior of multi-phase steels using a continuum dislocation dynamic model (CDD) coupled with a viscoplastic self-consistent (VPSC) model that accounts for both the effect of dislocations evolution inside the grain as well as grain grain interactions. Because the conventional viscoplasticity theory does not capture the grain size effect, we introduce an intrinsic length scale within the concepts of geometrically necessary dislocations (GND) by means of the Nye's dislocation tensor. The effect of the GND density is implemented into the model for the mean free path of dislocations and is shown to contribute to strain hardening. As a validation of this multiscale model, we investigate the mechanical behavior of various dual phase steels. The stress-strain response obtained from this approach is compared to experimental data found in the literature and reveal good agreement between experimental results and predictions. The model also predicts the evolution of dislocation densities in each phase and suggests the connection between underlying deformation mechanisms and macroscopic material hardening. The relation between flow stress and grain size is also investigated. The model predictions follow the Hall Fetch relation of strength versus grain size for grains larger than one micron meter but deviates from this relation for grains in the order of tens of nanometers. (C) 2015 Elsevier Ltd. All rights reserved.

关键词： Multiscale modeling Dislocations viscoplastic material Crystal plasticity numerical algorithms

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A generic anisotropic continuum damage model integration scheme adaptable to both ductile damage and biological damage-like situations

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INTERNATIONAL JOURNAL OF PLASTICITY 2015年 66卷 46-70页

作者： Mengoni, M. Ponthot, J. P. Univ Liege ULg Dept Aerosp & Mech Engn Nonlinear Computat Mech MN2L Liege Belgium

This paper aims at presenting a general versatile time integration scheme applicable to anisotropic damage coupled to elastoplasticity, considering any damage rate and isotropic hardening formulations. For this purpose a staggered time integration scheme in a finite strain framework is presented, together with an analytical consistent tangent operator. The only restrictive hypothesis is to work with an undamaged isotropic material, assumed here to follow a J(2) plasticity model. The only anisotropy considered is thus a damage-induced anisotropy. The possibility to couple any damage rate law with the present algorithm is illustrated with a classical ductile damage model for aluminium, and a biological damage-like application. The later proposes an original bone remodelling law coupled to trabecular bone plasticity for the simulation of orthodontic tooth movements. All the developments have been considered in the framework of the implicit non-linear finite element code Metafor (developed at the LTAS/(MNL)-L-2, University of Liege, Belgium - ***). (C) 2014 Elsevier Ltd. All rights reserved.

关键词： Continuum damage mechanics Anisotropic material Elastic-plastic material Constitutive behaviour numerical algorithms

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