This paper presents a finite element calculation of frictionless, non-adhesive, contact between a rigid plane and an clasto-plastic solid with a self-affine fractal surface. The calculations are conducted within an ex...
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This paper presents a finite element calculation of frictionless, non-adhesive, contact between a rigid plane and an clasto-plastic solid with a self-affine fractal surface. The calculations are conducted within an explicit dynamic Lagrangian framework. The elastoplastic response of the material is described by a J(2) isotropic plasticity law. Parametric studies are used to establish general relations between contact properties and key material parameters. In all cases, the contact area A rises linearly with the applied load. The rate of increase grows as the yield stress sigma(y) decreases, scaling as a power of sigma(y) over the range typical of real materials. Results for A from different plasticity laws and surface morphologies can all be described by a simple scaling formula. Plasticity produces qualitative changes in the distributions of local pressures in the contact and of the size of connected contact regions. The probability of large local pressures is decreased, while large clusters become more likely. Loading-unloading cycles are considered and the total plastic work is found to be nearly constant over a wide range of yield stresses. (c) 2005 Elsevier Ltd. All rights reserved.
We consider a random aggregate of identical frictionless elastic spheres that has first been subjected to an isotropic compression and then sheared. We assume that the average strain provides a good description of how...
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We consider a random aggregate of identical frictionless elastic spheres that has first been subjected to an isotropic compression and then sheared. We assume that the average strain provides a good description of how stress is built up in the initial isotropic compression. However, when calculating the increment in the displacement between a typical pair of contaction particles due to the shearing, we employ force equilibrium for the particles of the pair, assuming that the average strain provides a good approximation for their interactions with their neighbors. The incorporation of these additional degrees of freedom in the displacement of a typical pair relaxes the system, leading to a decrease in the effective moduli of the aggregate. The introduction of simple models for the statistics of the ordinary and conditional averages contributes an additional decrease in moduli. The resulting value of the shear modulus is in far better agreement with that measured in numerical simulations. (C) 2004 Elsevier Ltd. All rights reserved.
This new edition of the successful multi-disciplinary text Statistical Modelling in GLIM takes into account new developments in both statistical software and statistical modelling. Including three new chapters on mixt...
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ISBN:
(数字)9781383024036
ISBN:
(纸本)9780198524137
This new edition of the successful multi-disciplinary text Statistical Modelling in GLIM takes into account new developments in both statistical software and statistical modelling. Including three new chapters on mixture and random effects models, it provides a comprehensive treatment of the theory of statistical modelling with generalised linear models with an emphasis on applications to practical problems and an expanded discussion of statistical theory. A wide range of case studies is also provided, using the normal, binomial, Poisson, multinomial, gamma, exponential and Weibull distributions. This book is ideal for graduates and research students in applied statistics and a wide range of quantitative disciplines, including biology, medicine and the social sciences. Professional statisticians at all levels will also find it an invaluable desktop companion.
In this book, limit theorems are made accessibly by stating everything in terms of a game of tossing a coin: heads or tails. This book is suitable for anyone who would like to learn more about mathematical probabili...
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ISBN:
(数字)9781470421397
ISBN:
(纸本)9780821837146
In this book, limit theorems are made accessibly by stating everything in terms of a game of tossing a coin: heads or tails. This book is suitable for anyone who would like to learn more about mathematical probability and has a one-year undergraduate course in analysis.
An extensive experimental programme and detailed mechanical analysis were performed to test and model the statistical response of metallic foams under complex loading conditions. Tensile tests were performed on more t...
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An extensive experimental programme and detailed mechanical analysis were performed to test and model the statistical response of metallic foams under complex loading conditions. Tensile tests were performed on more than 80 specimens of closed-cell aluminium. foams with four different specimen sizes. These test results show a large scatter and a significant size effect especially on standard deviation. The average fracture stress and, more significantly, the corresponding scatter decrease for increasing volume sizes. An attempt is made to use the Weibull statistical analysis to interpret these variations. A Weibull modulus close to 8 is found. Compression tests were also carried out. Both mean fracture stress in tension and mean peak stress in compression and the corresponding dispersions are correctly described by a single set of Weibull parameters. The statistical model is extended to multi-axial loading conditions by introducing an effective stress measure involving both the deviatoric part of the stress tensor and its trace. One additional parameter is identified using the average shear yield stress obtained from pure shear tests and torsion tests on solid bars. It is shown that the model is able to predict the dispersion found for the shear strength. Two types of combined tension/compression-torsion loading conditions were then tested experimentally. The non-proportional loading path consists of a tension test followed by torsion, keeping the axial stress constant. In the proportional loading path, shear and axial stress follow a straight line in the stress space. The corresponding surface of average yield/fracture stress is found to be symmetric. The experimental results are in good agreement with the predictions of the statistical model. The model predicts a bell-shaped surface for the first loading path and a quasi-elliptic one for the proportional one. The scatter found in the description of this surface is also accounted for accurately by the model. A brie
The propagation of (planar) cracks in a heterogeneous brittle material characterized by a random field of toughness is considered, taking into account explicitly the effect of the crack front roughness on the local st...
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The propagation of (planar) cracks in a heterogeneous brittle material characterized by a random field of toughness is considered, taking into account explicitly the effect of the crack front roughness on the local stress intensity factor. In the so-called strong-pinning regime, the onset of crack propagation appears to map onto a second-order phase transition characterized by universal critical exponents which are independent of the local characteristics of the medium. Propagation over large distances can be described by using a simple one-dimensional description, with a correlation length and an effective macroscopic toughness distribution that scale in a non-trivial fashion with the crack front length. As an application of the above concepts, the arrest of indentation cracks is addressed, and the analytical expression for the statistical distribution of the crack radius at arrest is derived. The analysis of indentation crack radii on alumina is shown to obey the predicted algebraic expression for the radius distribution and its dependence on the indentation load. (C) 2003 Elsevier Ltd. All rights reserved.
In this paper we introduce stochastic methods to describe the influence of scattering test data on the identification of material parameters. We employ the viscoplastic constitutive model of Chan, Bodner, and Lindholm...
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In this paper we introduce stochastic methods to describe the influence of scattering test data on the identification of material parameters. We employ the viscoplastic constitutive model of Chan, Bodner, and Lindholm in its uniaxial form. The available test data result from three types of experiments performed at 600 degreesC on AINSI SS316 stainless steel, namely creep tests, constant strain rate tension tests with intermediate relaxation, and cyclic tension-compression tests. Each test has been performed with 12 specimens at different strain rates and stress rates respectively. However, for a serious statistical evaluation a larger number of experiments is required. In order to increase the number of tests we introduce stochastic simulations based on time series analysis which generate artificial data with the same stochastic behaviour as the experimental data. The method of stochastic simulation presents a widely accepted technique in engineering which does not add complexity to the process of parameter identification, but allows an investigation of the confidence in the fits of the material parameters. To keep the computation time for the identification of the material parameters as low as possible, very efficient numerical methods have to be implemented. The methods applied here for integration and nonlinear optimization are briefly introduced. The optimization strategy contains stochastic elements. Furthermore, we apply the method of statistical design of experiments to derive which combination of tests yields the most important information for an effective identification of material parameters. (C) 2003 Elsevier Ltd. All rights reserved.
In this paper, composites with a graded distribution of heterogeneities are considered. The heterogeneities vary in statistically non-uniform fashion since in a finite layer (or region) properties such as local volume...
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In this paper, composites with a graded distribution of heterogeneities are considered. The heterogeneities vary in statistically non-uniform fashion since in a finite layer (or region) properties such as local volume fraction vary gradually. In order to study this class of composites, a procedure of analysis which leads to the effective constitutive non-local operator of the medium is proposed. For two-phase composites, an approximation of Hashin-Shtrikman type for this operator has been obtained in real space and this has been developed explicitly in the case of laminates. (C) 2004 Elsevier Ltd. All rights reserved.
In this paper, composites with a graded distribution of heterogeneities are considered. The heterogeneities vary in statistically non-uniform fashion since in a finite layer (or region) properties such as local volume...
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In this paper, composites with a graded distribution of heterogeneities are considered. The heterogeneities vary in statistically non-uniform fashion since in a finite layer (or region) properties such as local volume fraction vary gradually. In order to study this class of composites, a procedure of analysis which leads to the effective constitutive non-local operator of the medium is proposed. For two-phase composites, an approximation of Hashin-Shtrikman type for this operator has been obtained in real space and this has been developed explicitly in the case of laminates. (C) 2004 Elsevier Ltd. All rights reserved.
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