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Modeling and algorithms for two-scale time homogenization of viscoelastic-viscoplastic solids under large numbers of cycles

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INTERNATIONAL JOURNAL OF PLASTICITY 2015年 70卷 98-125页

作者： Haouala, S. Doghri, I. Univ Catholique Louvain UCL Inst Mech Mat & Civil Engn IMMC B-1348 Louvain Belgium

A two-scale time homogenization formulation and the corresponding algorithms are proposed for coupled viscoelastic viscoplastic (VE-VP) homogeneous solids subjected to large numbers of cycles. The main aim is to predict the long time response while reducing the computational cost considerably. The method is based on the definition of macro and micro-chronological time scales, and on asymptotic expansions of the unknown variables. First, the VE-VP constitutive model is formulated based on a thermodynamical framework. Next, the original VE-VP initial-boundary value problem is decomposed into coupled micro-chronological (fast time scale) and macro-chronological (slow time-scale) problems. The former is purely VE, and solved once for each macro time step, whereas the latter problem is nonlinear and solved iteratively using fully implicit time integration. For micro-scale time averaging, one-point and multi-point integration algorithms are developed. Several numerical simulations on uniaxial and multiaxial cyclic loadings illustrate the computational efficiency and the accuracy of the proposed methods. (C) 2015 Elsevier Ltd. All rights reserved.

关键词： Time homogenization Cyclic loading Viscoelastic (VE) - viscoplastic (VP) material numerical algorithms Asymptotic analysis

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cusFFT: A High-Performance Sparse Fast Fourier Transform Algorithm on GPUs

cusFFT: A High-Performance Sparse Fast Fourier Transform Alg...

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IEEE International Parallel and Distributed Processing Symposium

作者： Cheng Wang Sunita Chandrasekaran Barbara Chapman Dept. of Comput. Sci. Univ. of Houston Houston TX USA Dept. of Comput. & Inf. Sci. Univ. of Delaware Newark DE USA

ISBN: (纸本)9781509021413

The Fast Fourier Transform (FFT) is one of the most important numerical tools widely used in many scientific and engineering applications. The algorithm performs O(nlogn) operations on n input data points in order to calculate only small number of k large coefficients, while the rest of n - k numbers are zero or negligibly small. The algorithm is clearly inefficient, when n points input data lead to only k << n non-zero coefficients in the transformed domain. MIT in 2012 developed a sparse FFT (sFFT) algorithm that provides a solution to this problem. In this paper, we explore the challenges and propose effective solutions to efficiently port sFFT to massively parallel processors, such as GPUs, using CUDA. GPGPUs are being increasingly adopted as popular HPC platforms because of their tremendous computing power and remarkable cost efficiency. However, sFFT algorithm is a complex and computationally challenging memory-bound algorithm that is not straightforward to be implemented on GPUs. In this paper, we present some of the optimization strategies such as index coalescing, loop splitting, asynchronous data layout transformation, linear time selection algorithm that are required to compute sFFT on such massively parallel architectures. Our CUDA-based sFFT, cusFFT, performs over 10x faster than the state-of-the-art cuFFT library on GPUs and over 28x faster than the parallel FFTW on multicore CPUs.

关键词： numerical algorithms Fourier Transforms CUDA GPGPU

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numerically robust spectral methods for crystal plasticity simulations of heterogeneous materials

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INTERNATIONAL JOURNAL OF PLASTICITY 2015年 66卷 31-45页

作者： Shanthraj, P. Eisenlohr, P. Diehl, M. Roters, F. Max Planck Inst Eisenforsch GmbH D-40237 Dusseldorf Germany Michigan State Univ E Lansing MI 48824 USA

Efficient spectral methods are developed to predict the micromechanical behaviour of plastically deforming heterogeneous materials. The direct and mixed variational conditions for mechanical equilibrium and strain compatibility are formulated in a framework that couples them to a general class of non-linear solution methods. Locally evolving micromechanical fields in a sheared polycrystalline material governed by a phenomenological crystal plasticity constitutive law are used to validate the methods, and their performance at varying material heterogeneities is benchmarked. The results indicate that the solution method has a dominant influence on performance and stability at large material heterogeneities, and significant improvements over the conventional fixed-point approach are obtained when higher-order solution methods are employed. Optimal solution strategies are devised based on this and applied to an idealised dual-phase polycrystalline aggregate. (C) 2014 Elsevier Ltd. All rights reserved.

关键词： Spectral method numerical algorithms Crystal plasticity High-resolution periodic volume element Voids and inclusions

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Quality-by-design by skewed spherical structured singular value

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IET CONTROL THEORY AND APPLICATIONS 2015年第15期9卷 2202-2210页

作者： Kishida, Masako Braatz, Richard D. Univ Canterbury Elect & Comp Engn Christchurch 8140 New Zealand MIT Dept Chem Engn Cambridge MA 02139 USA

This study develops numerical algorithms to compute an ellipsoidal set of input parameters, called a design space, that ensures that the system outputs lie within a set of design specifications in quality-by-design. The algorithm is based on a proposed skewed spherical structured singular value (s), for which this study derives upper bounds and proves the (scaled) main loop theorems and small-gain theorem for the Frobenius norm. Three examples are included to illustrate applications of the numerical algorithms.

关键词： singular value decomposition set theory product design product quality quality-by-design skewed spherical structured singular value numerical algorithms design space main loop theorems small-gain theorem Frobenius norm

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Gradient crystal plasticity including dislocation-based work hardening and dislocation transport

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INTERNATIONAL JOURNAL OF PLASTICITY 2015年 69卷 152-169页

作者： Wulfinghoff, Stephan Boehlke, Thomas KIT Inst Engn Mech Continuum Mech D-76131 Karlsruhe Germany

This work aims at the formulation of a gradient crystal plasticity model which incorporates some of the latest developments in continuum dislocation theory and is, at the same time, well-suited for a three-dimensional numerical implementation. Specifically, a classical continuum crystal plasticity framework is extended by taking into account continuous dislocation density and curvature field variables which evolve according to partial differential equations (Hochrainer et al., 2014;Ebrahimi et al., 2014). These account, for dislocation transport and curvature-induced line-length production and have been derived from a higher-dimensional continuum dislocation theory. The dislocation density information is used to model work hardening as a consequence of dislocation entanglement. A composite microstructure is simulated consisting of a soft elasto-plastic matrix and hard elastic inclusions. The particles are assumed to act as obstacles to dislocation motion, leading to pile-ups forming at the matrix inclusion interface. This effect is modeled using gradient plasticity with a simplified equivalent plastic strain gradient approach (Wulfinghoff et al., 2013) which is used here in order to allow for an efficient numerical treatment of the three-dimensional numerical model. A regularized logarithmic energy is applied which is intended to approximate the higher order gradient stress of the statistical theory of Groma et al. (2003). (C) 2015 Elsevier Ltd. All rights reserved.

关键词： Crystal plasticity Dislocations Particulate reinforced material numerical algorithms Gradient plasticity

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A new viscoelastic model based on generalized method of cells for fiber-reinforced composites

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INTERNATIONAL JOURNAL OF PLASTICITY 2015年 65卷 22-32页

作者： Li, Huimin Zhang, Boming Beihang Univ Mat Sci & Engn Sch Beijing 100191 Peoples R China

A semi-analytical model is constructed to investigate the relaxation properties of polymer composites consisting of linearly viscoelastic matrices and transversely isotropic elastic fibers. A representative unit cell is subjected to some prescribed loadings to value the time-dependent properties of composite materials. The model is derived to describe the anisotropic viscoelastic properties of composite materials as functions of matrix and fiber properties. The present numerical algorithm is used to predict the viscoelastic properties of a graphite/epoxy composite and the results are compared with the finite element analysis of the micromechanical model. Very good agreement between numerical algorithm and finite element analysis results is illustrated for the viscoelastic properties of anisotropic composite materials. (C) 2014 Elsevier Ltd. All rights reserved.

关键词： Stress relaxation Fiber-reinforced composite material Viscoelastic material Characteristics numerical algorithms

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Thermally-activated non-Schmid glide of screw dislocations in W using atomistically-informed kinetic Monte Carlo simulations

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INTERNATIONAL JOURNAL OF PLASTICITY 2015年 65卷 108-130页

作者： Stukowski, Alexander Cereceda, David Swinburne, Thomas D. Marian, Jaime Tech Univ Darmstadt Inst Mat Sci D-64287 Darmstadt Germany Lawrence Livermore Natl Lab Phys & Life Sci Directorate Livermore CA USA Univ Politecn Madrid Inst Fus Nucl E-28006 Madrid Spain Univ London Imperial Coll Sci Technol & Med Dept Phys London SW7 2AZ England Culham Sci Ctr CCFE Abingdon OX14 3DB Oxon England

Thermally-activated 1/2 screw dislocation motion is the controlling plastic mechanism at low temperatures in body-centered cubic (bcc) crystals. Dislocation motion proceeds by nucleation and propagation of atomic-siz... 详细信息

Thermally-activated 1/2 < 111 > screw dislocation motion is the controlling plastic mechanism at low temperatures in body-centered cubic (bcc) crystals. Dislocation motion proceeds by nucleation and propagation of atomic-sized kink pairs in close-packed planes. The atomistic character of kink pairs can be studied using techniques such as molecular dynamics (MD). However, MD's natural inability to properly sample thermally-activated processes as well as to capture {110} screw dislocation glide calls for the development of other methods capable of overcoming these limitations. Here we develop a kinetic Monte Carlo (kMC) approach to study single screw dislocation dynamics from room temperature to 0.5T(m), and at stresses 0 < sigma < 0.9 sigma(P), where T-m and sigma(P) are the melting point and the Peierls stress. The method is entirely parameterized with atomistic simulations using an embedded atom potential for tungsten. To increase the physical fidelity of our simulations, we calculate the deviations from Schmid's law prescribed by the interatomic potential used and we study single dislocation kinetics using both projections. We calculate dislocation velocities as a function of stress, temperature, and dislocation line length. We find that considering non-Schmid effects has a strong influence on both the magnitude of the velocities and the trajectories followed by the dislocation. We finish by condensing all the calculated data into effective stress and temperature dependent mobilities to be used in more homogenized numerical methods. (C) 2014 Elsevier Ltd. All rights reserved.

关键词： Dislocations Metallic material numerical algorithms Ductility

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A 3-D model for void evolution in viscous materials under large compressive deformation

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INTERNATIONAL JOURNAL OF PLASTICITY 2015年 74卷 192-212页

作者： Feng, Chao Cui, Zhenshan Shanghai Jiao Tong Univ Inst Forming Technol & Equipment Shanghai 200030 Peoples R China

The paper presents a study on the evolution of dilute ellipsoidal voids in power-law viscous materials under triaxial loading condition. Firstly, referring to the work of Eshelby (1957), a semi-analytical expression is deduced to evaluate the deformation of ellipsoidal void in linear viscous material. Then, for the non-linear viscous materials, the concept of mesoscopic representative volume element (RVE), is applied to study the voids deformation under different stress states, and a rigid visco-plastic finite element (FE) procedure is applied to solve the RVE model. For the condition of stress triaxiality ranging from -1 to +1, it is found that the voids deformation behaves similarly in both linear and non-linear viscous materials. Due to this fact, the framework of the expression of void deformation in linear viscous material is inferred to describe the void evolution in nonlinear viscous materials, while the parameters of the expression are re-evaluated for the specific materials. The results show that the void shapes and loading conditions take important roles in the void evolution. Therefore, for an ellipsoidal void, the void radius strain rate is expressed as a function of the void shape index, the macroscopic stress and strain-rate. Meanwhile, the void volume strain rate is obtained as a function of the void radius strain rate. This void evolution model is integrated into FE code and applied to study the void closure problem in the metal forming process. The FE simulation provides the evolution of macroscopic stress, strain and strain-rate, and then the model is used to calculate the changes of void shape and volume in each step of the deformation history. It can be found that the results predicted by this model agree well with the analytical solution, experiment measurements and numerical simulations with embedded void shapes, which demonstrates that this method can be appropriately used to predict the void evolution during the large compressive deformation

关键词： Voids and inclusions Viscoplastic material numerical algorithms Representative volume element

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Vessel transform for automatic optic disk detection in retinal images

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IET IMAGE PROCESSING 2015年第9期9卷 743-750页

作者： Muangnak, Nittaya Aimmanee, Pakinee Makhanov, Stanislav Uyyanonvara, Bunyarit Thammasat Univ Sirindhorn Int Inst Technol 131 Moo 5Tiwanont Rd Muang 12000 Pathumthani Thailand

Precise localisation of an optic disk (OD) in the retinal images is one of the most important problems in the ophthalmic image processing. Although a considerable progress has been made towards a computerised solution of the problem, the numerical algorithms often fail on retinal images characterised by poor quality. Therefore, the authors propose a new method suitable for low-quality images based on exploiting the convergence of the blood vessels to the OD. The novelty of the proposed techniques includes clustering the vessels endowed with a novel correction procedure and the vessel transform (VT) which measures the distance to the main clusters. The algorithm is integrated into the scale-space (SS) analysis to detect the boundary of the OD. The integrated method is called SS algorithm with VT (SSVT). SSVT has been tested on retinal images from two databases with fair and poor images against the fuzzy convergence (FC) method and a modification of the circular transform proposed by Lu. The absolute improvement on sensitivity of SSVT against FC and Lu's are up to 12.37% and 8.18%. Bigger improvements of SSVT in terms of positive predictive value are up to 37.46% and 30.84% against FC and Lu's, respectively.

关键词： eye medical image processing blood vessels transforms fuzzy set theory biomedical optical imaging convergence of numerical methods vessel transform automatic optic disk detection retinal images ophthalmic image processing computerised solution numerical algorithms low-quality images blood vessels vessel clustering scale-space analysis integrated method SS algorithm fuzzy convergence method FC method circular transform SSVT sensitivity

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A Low Complexity Scaling Method for the Lanczos Kernel in Fixed-Point Arithmetic

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IEEE TRANSACTIONS ON COMPUTERS 2015年第2期64卷 303-315页

作者： Jerez, Juan Luis Constantinides, George A. Kerrigan, Eric C. Univ London Imperial Coll Sci Technol & Med Dept Elect & Elect Engn London SW7 2AZ England Univ London Imperial Coll Sci Technol & Med Dept Aeronaut London SW7 2AZ England

We consider the problem of enabling fixed-point implementation of linear algebra kernels on low-cost embedded systems, as well as motivating more efficient computational architectures for scientific applications. Fixed-point arithmetic presents additional design challenges compared to floating-point arithmetic, such as having to bound peak values of variables and control their dynamic ranges. algorithms for solving linear equations or finding eigenvalues are typically nonlinear and iterative, making solving these design challenges a nontrivial task. For these types of algorithms, the bounding problem cannot be automated by current tools. We focus on the Lanczos iteration, the heart of well-known methods such as conjugate gradient and minimum residual. We show how one can modify the algorithm with a low-complexity scaling procedure to allow us to apply standard linear algebra to derive tight analytical bounds on all variables of the process, regardless of the properties of the original matrix. It is shown that the numerical behavior of fixed-point implementations of the modified problem can be chosen to be at least as good as a floating-point implementation, if necessary. The approach is evaluated on field-programmable gate array (FPGA) platforms, highlighting orders of magnitude potential performance and efficiency improvements by moving form floating-point to fixed-point computation.

关键词： Computer arithmetic computations on matrices numerical algorithms design aids

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