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An improved implicit numerical integration of a non-associated, three-invariant cap plasticity model with mixed isotropic-kinematic hardening for geomaterials

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INTERNATIONAL JOURNAL FOR numerical AND ANALYTICAL METHODS IN GEOMECHANICS 2015年第17期39卷 1853-1883页

作者： Motamedi, M. H. Foster, C. D. Univ Illinois Dept Civil & Mat Engn Chicago IL 60607 USA

The Sandia GeoModel is a continuum elastoplastic constitutive model that captures many features of the mechanical response for geological materials over a wide range of porosities and strain rates. Among the specific features incorporated into the formulation are a smooth compression cap, isotropic/kinematic hardening, nonlinear pressure dependence, strength differential effect, and rate sensitivity. This study attempts to provide enhancements regarding computational tractability, domain of applicability, and robustness of the model. A new functional form is presented for the yield and plastic potential functions. This reformulation renders a more accurate, robust, and efficient model as it eliminates spurious solutions attributed to the original form. In addition, we achieve a high-performance implementation, because the local iterative method is allowed to recast residual vectors with a uniform dimensionality. The model is also furnished with a smooth, elliptical tension cap to account for the tensile yielding. Moreover, an efficient algorithm is introduced, which decreases the computational cost by differentiating the updated shear yield surface from the cap surface based on the trial relative stress state. Finally, various numerical examples including a large-scale boundary value problem are presented to demonstrate the fidelity of the modified model and to analyze its numerical performance. Copyright (c) 2015 John Wiley & Sons, Ltd.

关键词： three-invariant plasticity geological material strengthening and mechanisms constitutive behavior finite elements numerical algorithms

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Thoughts on exascale numerical tank development for marine hydrodynamics

Thoughts on exascale numerical tank development for marine h...

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第二届全球华人水动学学术会议

作者： Jianming Yang Wenyang Duan Fidesi Solutions LLC College of Shipbuilding Engineering Harbin Engineering University

The rapid advancement of high-performance computers and computational fluid dynamics makes it possible to conduct high-fidelity simulations for marine hydrodynamics research and *** paper reviews various aspects,such as mathematical models,numerical algorithms,practical implementation considerations,etc.,that are crucial to the development of a cutting-edge numerical *** relative merits of different approaches are analyzed in terms of simplicity,accuracy,efficiency,and robustness from the perspectives of both users and developers.A numerical tank that is currently under active development embracing these findings is briefly discussed.

关键词： Marine hydrodynamics exascale numerical tank mathematical models numerical algorithms

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Novel approach to FE solution of crack problems in the Laplacian-based gradient elasticity

Novel approach to FE solution of crack problems in the Lapla...

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作者： Skalka, Petr Brno University of Technology

Stress/strain concentration around a crack tip in ceramic foam-like structures, where the characteristic size of the foam cell is comparable with a typical length over which field quantities change significantly, is analysed. It is convenient to replace the foam structure by an effective continuum which retains all necessary characteristic features of the foam. To this end a homogenized cracked open cell ceramic foam is analysed using the strain/stress model based upon an implicit dependence of the non-local stress and strain on the local stress and strain in the form of an inhomogeneous Helmholtz equation which is solved together with the equilibrium equations. To preserve the advantage of the uncoupled system of equations, which means that one set of equations is solved prior the other one and that two sets of shape functions can be chosen independently, are current sequence of well posed boundary value problems is constructed which can be solved using a classical 8-nodes isoparametric element for 2D problems. The key idea behind the suggested procedure consists in replacing the scale parameter l by a parameter increment dl chosen arbitrarily small. The given small disturbance causes are distribution of the local stress/displacement field. After the new local stress/displacement field is known, another disturbance is introduced and so on. The procedure is stopped when the solution, exhibiting boundary layer behaviour, leads to the cohesive-like zone with length reaching a value uniquely related to the scale parameter l.

关键词： Ceramic material Foam material Gradient elasticity Stress concentrations Finite elements numerical algorithms Keramické materiály Pěnové materiály Gradientní elasticita Koncentrace napětí Konečné prvky Numerické algoritmy

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numerical methods applied to option pricing models with transaction costs and stochastic volatility

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QUANTITATIVE FINANCE 2015年第8期15卷 1417-1424页

作者： Mariani, Maria C. Sengupta, Indranil Sewell, Granville Univ Texas El Paso Dept Math Sci El Paso TX 79968 USA N Dakota State Univ Dept Math Fargo ND 58105 USA

In this paper, we solve a complex partial differential equation motivated by applications in finance where the solution of the system gives the price of European options, including transaction costs and stochastic volatility. The model is based on theoretical analysis, and the resulting differential equation is solved using PDE2D software. The stability analysis agrees well with experimental results.

关键词： numerical algorithms Nonlinear partial differential equations Option pricing

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On advantages of the Kelvin mapping in finite element implementations of deformation processes

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ENVIRONMENTAL EARTH SCIENCES 2016年第11期75卷 937-937页

作者： Nagel, Thomas Goerke, Uwe-Jens Moerman, Kevin M. Kolditz, Olaf UFZ Helmholtz Ctr Environm Res Leipzig Germany Trinity Coll Dublin Dublin Ireland MIT Media Lab Cambridge MA 02139 USA Tech Univ Dresden Dresden Germany

Classical continuum mechanical theories operate on three-dimensional Euclidian space using scalar, vector, and tensor-valued quantities usually up to the order of four. For their numerical treatment, it is common practice to transform the relations into a matrix-vector format. This transformation is usually performed using the so-called Voigt mapping. This mapping does not preserve tensor character leaving significant room for error as stress and strain quantities follow from different mappings and thus have to be treated differently in certain mathematical operations. Despite its conceptual and notational difficulties having been pointed out, the Voigt mapping remains the foundation of most current finite element programmes. An alternative is the so-called Kelvin mapping which has recently gained recognition in studies of theoretical mechanics. This article is concerned with benefits of the Kelvin mapping in numerical modelling tools such as finite element software. The decisive difference to the Voigt mapping is that Kelvin's method preserves tensor character, and thus the numerical matrix notation directly corresponds to the original tensor notation. Further benefits in numerical implementations are that tensor norms are calculated identically without distinguishing stress-or strain-type quantities, and tensor equations can be directly transformed into matrix equations without additional considerations. The only implementational changes are related to a scalar factor in certain finite element matrices, and hence, harvesting the mentioned benefits comes at very little cost.

关键词： Kelvin mapping Voigt mapping Finite elements numerical algorithms OpenGeoSys

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Leading-order cross term correction of three-dimensional parabolic equation models

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JOURNAL OF THE ACOUSTICAL SOCIETY OF AMERICA 2016年第1期139卷 263-270页

作者： Sturm, Frederic Univ Lyon Ecole Cent Lyon CNRS 5509 Lab Mecan Fluides & AcoustUnite Mixte Rech 36 Ave Guy Collongue F-69134 Ecully France

The issue of handling a leading-order cross-multiplied term in three-dimensional (3D) parabolic equation (PE) based models is addressed. In particular, numerical results obtained incorporating a leading-order cross-term correction in an existing 3D PE model, written in cylindrical coordinates, based on higher-order Pade approximations in both depth and azimuth, and a splitting operator technique are reported. Note that the numerical algorithm proposed in this paper could be used in the future to update any 3D PE codes that neglect cross terms and use a splitting numerical technique. The 3D penetrable wedge benchmark problem is chosen to illustrate the accuracy of the now-fully wide-angle enhanced 3D PE model. The comparisons with a 3D reference solution based on the image source clearly show that handling the leading-order cross term in the 3D PE computation is sufficient to remove the phase errors inherent to any 3D PE models that neglect cross terms in their formulations. (C) 2016 Acoustical Society of America.

关键词： Three dimensional image processing Acoustic modeling Speed of sound numerical modeling numerical algorithms

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Optimal distributions for multiplex logistic networks

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CHAOS 2016年第6期26卷 065312-065312页

作者： Conde, Luis E. Sola Used, Javier Romance, Miguel Univ Trent Dipartimento Matemat Trento Italy Univ Rey Juan Carlos ESCET Dept Biol & Geol Fis & Quim Inorgan Mostoles Spain Univ Rey Juan Carlos ESCET Dept Matemat Aplicada Ciencia & Ingn Mat & Tecnol Mostoles Spain Tech Univ Madrid CTB Madrid Spain

This paper presents some mathematical models for distribution of goods in logistic networks based on spectral analysis of complex networks. Given a steady distribution of a finished product, some numerical algorithms are presented for computing the weights in a multiplex logistic network that reach the equilibrium dynamics with high convergence rate. As an application, the logistic networks of Germany and Spain are analyzed in terms of their convergence rates. Published by AIP Publishing.

关键词： Polytopes Networks Eigenvalues Tensor methods numerical algorithms

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Efficient algorithms for general periodic Lorentz gases in two and three dimensions

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JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL 2016年第2期49卷 025001-025001页

作者： Kraemer, Atahualpa S. Kryukov, Nikolay Sanders, David P. Univ Dusseldorf Inst Theoret Phys Soft Matter 2 D-40225 Dusseldorf Germany Univ Nacl Autonoma Mexico Fac Ciencias Dept Fis Mexico City 04510 DF Mexico

We present efficient algorithms to calculate trajectories for periodic Lorentz gases consisting of square lattices of circular obstacles in two dimensions, and simple cubic lattices of spheres in three dimensions;these become increasingly efficient as the radius of the obstacles tends to 0, the so-called Boltzmann-Grad limit. The 2D algorithm applies continued fractions to obtain the exact disc with which a particle will collide at each step, instead of using periodic boundary conditions as in the classical algorithm. The 3D version incorporates the 2D algorithm by projecting to the three coordinate planes. As an application, we calculate distributions of free path lengths close to the Boltzmann-Grad limit for certain Lorentz gases. We also show how the algorithms may be applied to deal with general crystal lattices.

关键词： Lorentz gas numerical algorithms billard models free paths

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An iterative predictor-corrector approach for modeling static and kinetic friction in interactive simulations

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GRAPHICAL MODELS 2015年 82卷 29-42页

作者： Arikatla, Venkata S. De, Suvranu Rensselaer Polytech Inst Dept Mech Aerosp & Nucl Engn Ctr Modeling Simulat & Imaging Med 1108th St Troy NY 12180 USA

In this paper we propose a novel iterative predictor-corrector (IPC) approach to model static and kinetic friction during interactions with deformable objects. The proposed IPC method works within the purview of the implicit mixed linear complementarity problem (MLCP) formulation of collision response. In IPC, first the potential directions of frictional force are determined at each contact point by leveraging the monotonic convergence of an iterative MLCP solver. All the contacts are then categorized into either static or kinetic frictional states. Linear projection constraints (LPCs) are used to enforce 'stiction' for contacts in static friction. We propose a modified iterative constraint anticipation (MICA) approach that can resolve the LKs while simultaneously solving the MLCP. Our method can handle arbitrary models including asymmetric and anisotropic friction models. IPC requires low memory and is highly tunable. Multiple example problems are solved to demonstrate the method. (C) 2015 Elsevier Inc. All rights reserved.

关键词： Finite element Simulation numerical algorithms

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Implementation and application of a temperature-dependent Chaboche model

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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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