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Softening in random networks of non-identical beams

JOURNAL OF THE MECHANICS AND PHYSICS OF SOLIDS 2016年 87卷 38-50页

作者： Ban, Ehsan Barocas, Victor H. Shephard, Mark S. Picu, R. Catalin Rensselaer Polytech Inst Dept Mech Aerosp & Nucl Engn Troy NY 12180 USA Rensselaer Polytech Inst Sci Computat Res Ctr Troy NY 12180 USA Univ Minnesota Dept Biomed Engn Minneapolis MN 55455 USA

Random fiber networks are assemblies of elastic elements connected in random configurations. They are used as models for a broad range of fibrous materials including biopolymer gels and synthetic nonwovens. Although the mechanics of networks made from the same type of fibers has been studied extensively, the behavior of composite systems of fibers with different properties has received less attention. In this work we numerically and theoretically study random networks of beams and springs of different mechanical properties. We observe that the overall network stiffness decreases on average as the variability of fiber stiffness increases, at constant mean fiber stiffness. Numerical results and analytical arguments show that for small variabilities in fiber stiffness the amount of network softening scales linearly with the variance of the fiber stiffness distribution. This result holds for any beam structure and is expected to apply to a broad range of materials including cellular solids. (C) 2015 Elsevier Ltd. All rights reserved.

关键词： Heterogeneous Materials Elastic Materials Beam Structures Microstructures probability and statistics

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Tensor-valued random fields for meso-scale stochastic model of anisotropic elastic microstructure and probabilistic analysis of representative volume element size

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PROBABILISTIC ENGINEERING MECHANICS 2008年第2-3期23卷 307-323页

作者： Soize, C. Univ Paris Est Lab Mecan F-77454 Marne La Vallee France

The main objective of this paper is to present a generic meso-scale probability model for a large class of random anisotropic elastic microstructures in order to perform a parametric analysis of the Representative Volume Element (RVE) size. This new approach can be useful for a direct experimental identification of random anisotropic elastic microstructures when the standard method cannot easily be applied to anisotropic elastic microstructures. Such a RVE is used to construct the macroscopic properties in the context of stochastic homogenization. The probability analysis is not performed as usual for a given particular random microstructure defined in terms of its constituents. Instead, it is performed for a large class of random anisotropic elastic microstructures. For this class, the probability distribution of the random effective stiffness tensor is explicitly constructed. This allows a full probability analysis of the RVE size to be carried Out and its convergence to be studied. The procedure of homogenization is based on a homogeneous Dirichlet condition on the boundary of the RVE. The probability model used for the stiffness tensor-valued random field of the random anisotropic elastic microstructure is an extension of the model recently introduced by the author for elliptic stochastic partial differential operators. The stochastic boundary value problem is numerically solved by using the stochastic finite element method. The probability analysis of the RVE size is performed by Studying the probability distribution of the random operator norm of the random effective stiffness tensor with respect to the spatial correlation length of the random microstructure. (C) 2007 Elsevier Ltd. All rights reserved.

关键词： microstructures probability and statistics anisotropic material elastic material inhomogeneous material

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Strain and hysteresis by stochastic matrix cracking in ceramic matrix composites

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JOURNAL OF THE MECHANICS AND PHYSICS OF SOLIDS 1997年第2期45卷 177-209页

作者： Ahn, BK Curtin, WA Department of Engineering Science and Mechanics Virginia Polytechnic Institute and State University Blacksburg VA 24061 U.S.A.

A theory is presented to predict the stress/strain relations and unload/reload hysteresis behavior during the evolution of multiple matrix cracking in unidirectional fiber reinforced ceramic matrix composites (CMCs). The theory is based on the similarity between multiple matrix cracking and fiber fragmentation in a single fiber composite, and determines the crack and strain evolution as a function of the statistical distribution of initial flaws in the material, the interfacial sliding resistance tau, and the thermal residual stresses in the composite. The model properly includes matrix fragments of all lengths, from lengths smaller than the current slip length delta(sigma) to larger than 2 delta(sigma), at applied stress sigma, and accounts for their respective and differing contributions to the overall strain and hysteresis behavior of the composite. The procedure by which experimental stress/strain and hysteresis data can be interpreted to derive values for the interfacial shear stress, thermal stresses, and intrinsic matrix flaw distribution is discussed. The actual physical crack spacing needs only to be determined at one load level, such as post-fracture, which greatly simplifies the data acquisition and analysis. Several detailed examples are presented, and the results compared with a widely-used approach in which the crack spacing is assumed constant and equal to the average spacing obtained directly from experiment. The discrepancy between the previous and present theories is manifest in an incorrect estimate for the interfacial sliding, but only by approximately 10%. The effect of changing temperature, and hence residual stresses, without changing either matrix flaws or interfacial sliding resistance, is studied. (C) 1997 Elsevier Science Ltd.

关键词： crack propagation and arrest microcracking ceramic material fiber-reinforced composite material probability and statistics

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Finite element modeling of elasto-plastic contact between rough surfaces

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JOURNAL OF THE MECHANICS AND PHYSICS OF SOLIDS 2005年第11期53卷 2385-2409页

作者： Pei, L Hyun, S Molinari, JF Robbins, MO Johns Hopkins Univ Dept Mech Engn Baltimore MD 21218 USA Johns Hopkins Univ Dept Phys & Astron Baltimore MD 21218 USA Kyungpook Natl Univ Sch Mech Engn Taegu 702701 South Korea

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.

关键词： contact mechanics elastic-plastic material finite elements probability and statistics

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The role of elastic anisotropy on the macroscopic constitutive response and yield onset of cubic oligo- and polycrystals

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INTERNATIONAL JOURNAL OF PLASTICITY 2019年 121卷 153-200页

作者： Vieira, R. R. Tenreiro de Bortoli, D. de Carvalho, M. Vieira Pires, F. M. Andrade Univ Porto Dept Mech Engn Porto Portugal Inst Sci & Innovat Mech & Ind Engn INEGI Porto Portugal

The single crystal elastic anisotropy is one of the most important properties affecting the macroscopic response of polycrystalline materials, both in the elastic regime and the early stages of plastic deformation. In this work, the impact of monocrystalline parameters on the mechanical behaviour of cubic polycrystals is studied in detail. The analysis is conducted with an RVE-based computational homogenisation framework which includes several original strategies and criteria developed to enable the efficient statistical analysis of virtual micro-structures. In particular, these developments include a stress-driven adaptation to the usually employed strain-driven homogenisation approach, used to study the plastic polycrystalline response in stress space. The effects of number of grains and realisations considered, finite element mesh discretisation level, and algorithms used to generate both the grain morphology and orientation distribution are also assessed. Considering a number of materials with cubic symmetry, expressions for the number of grains required for an elastically isotropic response are deduced, along with bounds for the homogenised elastic stiffness components of oligocrystals, in both cases as a function of the monocrystalline elastic anisotropy. In the plastic domain, multiple microscopic and macroscopic criteria to describe the yield onset of such polycrystals are evaluated and compared. This is done for both elastically isotropic and anisotropic polycrystals, where once again the effect of different levels of monocrystalline elastic anisotropy are evaluated. The numerically derived yield surface of isotropic polycrystals is fitted to both Tresca and von Mises yield functions, and for anisotropic oligocrystals, the statistical bounds for the expected distribution of micro-yield stresses are deduced, in terms of both the number of grains and of the level of single crystal elastic anisotropy. The results obtained are thus a step towards clarifying the

关键词： Yield condition Crystal plasticity Anisotropic material probability and statistics Multi-scale modelling

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Optimal utilization of the terminal for bulk cargo unloading

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SIMULATION-TRANSACTIONS OF THE SOCIETY FOR MODELING AND SIMULATION INTERNATIONAL 2012年第12期88卷 1508-1521页

作者： Bugaric, Ugljesa S. Petrovic, Dusan B. Jeli, Zorana V. Petrovic, Dragan V. Univ Belgrade Fac Mech Engn Dept Ind Engn Belgrade 11120 35 Serbia Univ Belgrade Fac Technol & Met Belgrade 11120 35 Serbia Univ Belgrade Fac Mech Engn Dept Theory Mech & Machines Belgrade 11120 35 Serbia

This paper analyses the capacity of a bulk cargo unloading river terminal, i.e. the existing terminal configuration with two unloading devices (operation without a help strategy and under a complete help strategy between unloading devices) and the predicted future terminal configuration with three unloading devices operating under a partial help strategy. The optimization procedure to determine unloading terminal optimal utilization, for each terminal configuration and operation strategy (existing and future situation) is also shown, due to the fact that ports (terminals) operation under an optimal capacity provides prompt accommodation of vessels with the minimum port waiting time and maximum use of berth facilities. For the purpose of a comprehensive analysis, three different river terminal simulation models have been developed due to the number of unloading devices and their operation strategy. Some of the obtained results have been applied and verified on the existing system.

关键词： probability and statistics queuing systems performance optimization

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Approximating stochastic biochemical processes with Wasserstein pseudometrics

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IET SYSTEMS BIOLOGY 2010年第3期4卷 193-211页

作者： Thorsley, D. Klavins, E. Univ Washington Dept Elect Engn Seattle WA 98195 USA

Modelling stochastic processes inside the cell is difficult due to the size and complexity of the processes being investigated. As a result, new approaches are needed to address the problems of model reduction, parameter estimation, model comparison and model invalidation. Here, the authors propose addressing these problems by using Wasserstein pseudometrics to quantify the differences between processes. The method the authors propose is applicable to any bounded continuous-time stochastic process and pseudometrics between processes are defined only in terms of the available outputs. Algorithms for approximating Wasserstein pseudometrics are developed from experimental or simulation data and demonstrate how to optimise parameter values to minimise the pseudometrics. The approach is illustrated with studies of a stochastic toggle switch and of stochastic gene expression in E. coli.

关键词： probability theory, stochastic processes, and statistics Biology and medical computing model reduction probability and statistics model invalidation parameter estimation stochastic gene expression stochastic processes Physical chemistry of biomolecular solutions and condensed states stochastic biochemical processes E. coli continuous-time stochastic process biology computing Physics of subcellular structures biochemistry cellular processes cellular biophysics stochastic toggle switch model comparison Wasserstein pseudometrics genetics

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Global load-sharing model for unidirectional hybrid fibre-reinforced composites

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JOURNAL OF THE MECHANICS AND PHYSICS OF SOLIDS 2015年 84卷 380-394页

作者： Swolfs, Yentl McMeeking, R. M. Rajan, V. P. Zok, F. W. Verpoest, Ignaas Gorbatikh, Larissa Katholieke Univ Leuven Dept Mat Engn Louvain Belgium Univ Calif Santa Barbara Dept Mech Engn Santa Barbara CA 93106 USA Univ Calif Santa Barbara Dept Mat Santa Barbara CA 93106 USA Univ Aberdeen Sch Engn Kings Coll Aberdeen AB24 3UE Scotland

A promising strategy to increase the tensile failure strain of carbon fibre-reinforced composites is to hybridise carbon fibres with other, higher-elongation fibres. The resulting increase in failure strain is known as the hybrid effect. In the present article, a global load-sharing model for hybrid composites is developed and used to carry out a parametric study for carbon/glass hybrids. Hybrid effects of up to 15% increase in failure strain are predicted, corresponding reasonably well to literature data. Scatter in the carbon fibre strength is shown to be crucial for the hybrid effect, while the scatter in glass fibre strength is much less important. In contrast to reports in earlier literature, the ratio of failure strains of the two fibres has only a small influence on the hybrid effect. The results provide guidelines for designing optimal hybrid composites. (C) 2015 Elsevier Ltd. All rights reserved.

关键词： Strengthening and mechanisms Fibre-reinforced composite material probability and statistics Hybrid composites

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Analytical estimation of distance-disorientation function of the material microstructure

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PHILOSOPHICAL MAGAZINE 2013年第24期93卷 3314-3331页

作者： Staraselski, Yauheni Brahme, Abhijit Inal, Kaan Mishra, Raja K. Univ Waterloo Waterloo ON N2L 3G1 Canada Gen Motors Res & Dev Ctr Warren MI USA

This work presents a new functional approach to estimate the distance-disorientation correlation function of a given microstructure. The proposed approach separates the crystallographic domain into texture defined by its Euler angles () and geometrical domain defined by distance distribution function . The crystallographic domain is treated as independent (known) variable and an analytical estimate for the Euclidian distance distribution function is obtained. The proposed analytical solution for the estimation of is based on existing statistical growth models and the logistic probability distribution function. The solution is optimized for the measured experimental data and takes into account morphological features of the microstructure such as grain volume, grain radius and grain size as well as their distribution inside the material. An analytical model is proposed for constructing the distance-disorientation function (DDF) using the estimated Euclidian distance between pixel pairs. The new functional solution is a highly effective way to calculate DDF values, making it suitable for application to the real microstructure optimization problems. The DDF obtained by using the results of probabilistic solution is validated by comparing them with the DDF obtained from experimental electron back-scatter diffraction data.

关键词： two point correlation function EBSD microstructure population theory clustering probability and statistics

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Reconstructing gene regulatory networks from knock-out data using Gaussian Noise Model and Pearson Correlation Coefficient

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COMPUTATIONAL BIOLOGY AND CHEMISTRY 2015年第PartB期59卷 3-14页

作者： Salleh, Faridah Hani Mohamed Arif, Shereena Mohd Zainudin, Suhaila Firdaus-Raih, Mohd Univ Tenaga Nas Coll IT Dept Software Engn Kajang 43000 Malaysia Univ Kebangsaan Malaysia Fac Informat Sci & Technol Ctr Artificial Intelligence Ukm Bangi 43650 Malaysia Univ Kebangsaan Malaysia Fac Sci & Technol Sch Biosci & Biotechnol Bangi 43600 Selangor Malaysia

A gene regulatory network (GRN) is a large and complex network consisting of interacting elements that, over time, affect each other's state. The dynamics of complex gene regulatory processes are difficult to understand using intuitive approaches alone. To overcome this problem, we propose an algorithm for inferring the regulatory interactions from knock-out data using a Gaussian model combines with Pearson Correlation Coefficient (PCC). There are several problems relating to GRN construction that have been outlined in this paper. We demonstrated the ability of our proposed method to (1) predict the presence of regulatory interactions between genes, (2) their directionality and (3) their states (activation or suppression). The algorithm was applied to network sizes of 10 and 50 genes from DREAM3 datasets and network sizes of 10 from DREAM4 datasets. The predicted networks were evaluated based on AUROC and AUPR. We discovered that high false positive values were generated by our GRN prediction methods because the indirect regulations have been wrongly predicted as true relationships. We achieved satisfactory results as the majority of sub-networks achieved AUROC values above 0.5. (C) 2015 Elsevier Ltd. All rights reserved.

关键词： Bioinformatics probability and statistics DREAM Gene regulatory network Gaussian model Pearson Correlation Coefficient

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