A two‐dimensional ordinary,state‐based peridynamic model for linearly elastic solids

Peridynamics is a non‐local mechanics theory that uses integral equations to include discontinuities directly in the constitutive equations. A three‐dimensional, state‐based peridynamics model has been developed previously for linearly elastic solids with a customizable Poisson's ratio. For plane stress and plane strain conditions, however, a two‐dimensional model is more efficient computationally. Here, such a two‐dimensional state‐based peridynamics model is presented. For verification, a 2D rectangular plate with a round hole in the middle is simulated under constant tensile stress. Dynamic relaxation and energy minimization methods are used to find the steady‐state solution. The model shows m‐convergence and δ‐convergence behaviors when m increases and δ decreases. Simulation results show a close quantitative matching of the displacement and stress obtained from the 2D peridynamics and a finite element model used for comparison. Copyright © 2014 John Wiley & Sons, Ltd.     

Study on the accumulative fatigue damage rules under multiaxial two‐stage step spectra constructed by loadings with similar lives

In this paper, the influence on the multiaxial fatigue damage accumulation caused by loading path variation was studied. For 2024‐T4 aluminium alloy, the damage evolution during the entire life was first observed. On the basis of the observation, the stage I of fatigue damage evolution was further divided into two sub‐stages, and the dominant stress parameters of these two sub‐stages were proposed. Taking the dominant stress parameters into account, a phased accumulative fatigue damage model was proposed. Then, 12 multiaxial two‐stage step spectra constructed by loadings with approximately identical fatigue lives were carried out on 2024‐T4 aluminium alloy. The accumulative fatigue damage was calculated by the proposed model, and another five commonly used models and the calculated results were compared. According to the comparison, the newly proposed model had the most accurate results with the smallest scatter.     

A stochastic second‐order and two‐scale thermo‐mechanical model for strength prediction of concrete materials

A stochastic thermo‐mechanical model for strength prediction of concrete is developed, based on the two‐scale asymptotic expressions, which involves both the macroscale and the mesoscale of concrete materials. The mesoscale of concrete is characterized by a periodic layout of unit cells of matrix‐aggregate composite materials, consisting of randomly distributed aggregate grains and cement matrix. The stochastic second‐order and two‐scale computational formulae are proposed in detail, and the maximum normal stress is assumed as the strength criterion for the aggregates, and the cement paste, in view of their brittle characteristics. Numerical results for the strength of concrete obtained from the proposed model are compared with those from known experiments. The comparison shows that the proposed method is validated for strength prediction of concrete. The proposed thermo‐mechanical model is also employed to investigate the influence of different volume fraction of the aggregates on the strength of concrete. Copyright © 2016 John Wiley & Sons, Ltd.     

A new continuum damage mechanics–based two‐scale model for high‐cycle fatigue life prediction considering the two‐segment characteristic in S‐N curves

In this study, we propose a new two‐scale fatigue model based on continuum damage mechanics. A representative volume element (RVE) consisting of microinclusions and a matrix is constructed. Further, damage‐coupled constitutive equations are derived. The degradation in the mechanical properties of the RVE is determined by the damaged inclusions and matrix using the Mori‐Tanaka scheme. A numerical calculation of the fatigue lives of notched specimens is executed. This new model predicts high‐cycle fatigue (HCF) life more effectively, considering the two‐segment characteristic of S‐N curves of smooth specimens. This study provides novel insights into the evolution mechanism of HCF damage.     

Numerical solution of second‐order,two‐point boundary value problems using continuous genetic algorithms

Second‐order, two‐point boundary‐value problems are encountered in many engineering applications including the study of beam deflections, heat flow, and various dynamic systems. Two classical numerical techniques are widely used in the engineering community for the solution of such problems; the shooting method and finite difference method. These methods are suited for linear problems. However, when solving the non‐linear problems, these methods require some major modifications that include the use of some root‐finding technique. Furthermore, they require the use of other basic numerical techniques in order to obtain the solution. In this paper, the author introduces a novel method based on continuous genetic algorithms for numerically approximating a solution to this problem. The new method has the following characteristics; first, it does not require any modification while switching from the linear to the non‐linear case; as a result, it is of versatile nature. Second, this approach does not resort to more advanced mathematical tools and is thus easily accepted in the engineering application field. Third, the proposed methodology has an implicit parallel nature which points to its implementation on parallel machines. However, being a variant of the finite difference scheme with truncation error of the order O(h²), the method provides solutions with moderate accuracy. Numerical examples presented in the paper illustrate the applicability and generality of the proposed method. Copyright © 2004 John Wiley & Sons, Ltd.     

Estimation of missing observations in two‐level split‐plot designs

Inserting estimates for the missing observations from split‐plot designs restores their balanced or orthogonal structure and alleviates the difficulties in the statistical analysis. In this article, we extend a method due to Draper and Stoneman to estimate the missing observations from unreplicated two‐level factorial and fractional factorial split‐plot (FSP and FFSP) designs. The missing observations, which can either be from the same whole plot, from different whole plots, or comprise entire whole plots, are estimated by equating to zero a number of specific contrast columns equal to the number of the missing observations. These estimates are inserted into the design table and the estimates for the remaining effects (or alias chains of effects as the case with FFSP designs) are plotted on two half‐normal plots: one for the whole‐plot effects and the other for the subplot effects. If the smaller effects do not point at the origin, then different contrast columns to some or all of the initial ones should be discarded and the plots re‐examined for bias. Using examples, we show how the method provides estimates for the missing observations that are very close to their actual values. Copyright © 2007 John Wiley & Sons, Ltd.     

Comparison of Methods to Estimate the Time‐to‐failure Distribution in Degradation Tests

Degradation tests are alternative approaches to lifetime tests and accelerated lifetime tests in reliability studies. Based on a degradation process of a product quality characteristic over time, degradation tests provide enough information to estimate the time‐to‐failure distribution. Some estimation methods, such as analytical, the numerical or the approximated, can be used to obtain the time‐to‐failure distribution. They are chosen according to the complexity of the degradation model used in the data analysis. An example of the application and analysis of degradation tests is presented in this paper to characterize the durability of a product and compare the various estimation methods of the time‐to‐failure distribution. The example refers to a degradation process related to an automobile's tyre, and was carried out to estimate its average distance covered and some percentiles of interest. Copyright © 2004 John Wiley & Sons, Ltd.     

A two‐level nonoverlapping Schwarz algorithm for the Stokes problem without primal pressure unknowns

A two‐level nonoverlapping Schwarz algorithm is developed for the Stokes problem. The main feature of the algorithm is that a mixed problem with both velocity and pressure unknowns is solved with a balancing domain decomposition by constraints (BDDC)‐type preconditioner, which consists of solving local Stokes problems and one global coarse problem related to only primal velocity unknowns. Our preconditioner allows to use a smaller set of primal velocity unknowns than other BDDC preconditioners without much concern on certain flux conditions on the subdomain boundaries and the inf–sup stability of the coarse problem. In the two‐dimensional case, velocity unknowns at subdomain corners are selected as the primal unknowns. In addition to them, averages of each velocity component across common faces are employed as the primal unknowns for the three‐dimensional case. By using its close connection to the Dual–primal finite element tearing and interconnecting (FETI‐DP algorithm) (SIAM J Sci Comput 2010; 32 : 3301–3322; SIAM J Numer Anal 2010; 47 : 4142–4162], it is shown that the resulting matrix of our algorithm has the same eigenvalues as the FETI‐DP algorithm except zero and one. The maximum eigenvalue is determined by H/h, the number of elements across each subdomains, and the minimum eigenvalue is bounded below by a constant, which does not depend on any mesh parameters. Convergence of the method is analyzed and numerical results are included. Copyright © 2011 John Wiley & Sons, Ltd.     

Feature selection and fault‐severity classification–based machine health assessment methodology for point machine sliding‐chair degradation

In this paper, we propose an offline and online machine health assessment (MHA) methodology composed of feature extraction and selection, segmentation‐based fault severity evaluation, and classification steps. In the offline phase, the best representative feature of degradation is selected by a new filter‐based feature selection approach. The selected feature is further segmented by utilizing the bottom‐up time series segmentation to discriminate machine health states, ie, degradation levels. Then, the health state fault severity is extracted by a proposed segment evaluation approach based on within segment rate‐of‐change (RoC) and coefficient of variation (CV) statistics. To train supervised classifiers, a priori knowledge about the availability of the labeled data set is needed. To overcome this limitation, the health state fault‐severity information is used to label (eg, healthy, minor, medium, and severe) unlabeled raw condition monitoring (CM) data. In the online phase, the fault‐severity classification is carried out by kernel‐based support vector machine (SVM) classifier. Next to SVM, the k‐nearest neighbor (KNN) is also used in comparative analysis on the fault severity classification problem. Supervised classifiers are trained in the offline phase and tested in the online phase. Unlike to traditional supervised approaches, this proposed method does not require any a priori knowledge about the availability of the labeled data set. The proposed methodology is validated on infield point machine sliding‐chair degradation data to illustrate its effectiveness and applicability. The results show that the time series segmentation‐based failure severity detection and SVM‐based classification are promising.     

A two‐grid method for expanded mixed finite‐element solution of semilinear reaction–diffusion equations

We present a scheme for solving two‐dimensional semilinear reaction–diffusion equations using an expanded mixed finite element method. To linearize the mixed‐method equations, we use a two‐grid algorithm based on the Newton iteration method. The solution of a non‐linear system on the fine space is reduced to the solution of two small (one linear and one non‐linear) systems on the coarse space and a linear system on the fine space. It is shown that the coarse grid can be much coarser than the fine grid and achieve asymptotically optimal approximation as long as the mesh sizes satisfy H=O(h^1/3). As a result, solving such a large class of non‐linear equation will not be much more difficult than solving one single linearized equation. Copyright © 2003 John Wiley & Sons, Ltd.     

Mode I fracture toughness of the thermally pretreated red Verona marble by means of the two‐parameter model

The paper aims to analyse the effects of pretreatment thermal cycles on both mechanical and fracture parameters of the red Verona marble, which is a natural stone of sedimentary formation. The effects of the thermal pretreatment, consisting of freeze/thaw cycles and simulating the atmospheric ageing on the material, are evaluated in terms of changes of the aforementioned parameters. Note that a wide variety of both specimen types and methods to determine mode I plain strain fracture toughness of rocks are available in the literature. The two‐parameter model originally proposed for plain concrete is herein adopted. Such a method, based on the experimental data obtained from three‐point bending tests on single edge‐notched specimens, is able to take into account the slow nonlinear crack growth occurring before the peak load, typical of quasibrittle materials, and presents the advantages of easy specimens preparation and simple test configuration.     

Estimation of time‐to‐failure distribution derived from a degradation model using fuzzy clustering

Some life tests are terminated with few or no failures. In such cases, a recent approach is to obtain degradation measurements of product performance that may contain some useful information about product reliability. Generally degradation paths of products are modeled by a nonlinear regression model with random coefficients. If we can obtain the estimates of parameters under the model, then the time‐to‐failure distribution can be estimated. In some cases, the patterns of a few degradation paths are different from those of most degradation paths in a test. Therefore, this study develops a weighted method based on fuzzy clustering procedure to robust estimation of the underlying parameters and time‐to‐failure distribution. The method will be studied on a real data set. Copyright © 2000 John Wiley & Sons, Ltd.     

A front remeshing technique for a Lagrangian description of moving interfaces in two‐fluid flows

The numerical analysis of two‐fluid flows involves the treatment of a discontinuity that appears at the separating interface. Classical Lagrangian schemes applied to update the front position between two immiscible incompressible fluids have been long recognized to provide a sharp representation of the interface. However, the main drawback of these approaches is the progressive distortion in the distribution of the markers used to identify the material front. To avoid this problem, an interface remeshing algorithm based on the diffuse approximation of the interface curvature is proposed in this work. In addition, the remeshed front is enforced to preserve the global volume. These new aspects are incorporated in an existing fluid dynamics formulation for the analysis of two‐fluid flows problems. The resulting formulation is called in this work as the moving Lagrangian interface remeshing technique (MLIRT). Copyright © 2005 John Wiley & Sons, Ltd.     

A two‐scale failure model for heterogeneous materials: numerical implementation based on the finite element method

In the first part of this contribution, a brief theoretical revision of the mechanical and variational foundations of a Failure‐Oriented Multiscale Formulation devised for modeling failure in heterogeneous materials is described. The proposed model considers two well separated physical length scales, namely: (i) the macroscale where nucleation and evolution of a cohesive surface is considered as a medium to characterize the degradation phenomenon occurring at the lower length scale, and (ii) the microscale where some mechanical processes that lead to the material failure are taking place, such as strain localization, damage, shear band formation, and so on. These processes are modeled using the concept of Representative Volume Element (RVE). On the macroscale, the traction separation response, characterizing the mechanical behavior of the cohesive interface, is a result of the failure processes simulated in the microscale. The traction separation response is obtained by a particular homogenization technique applied on specific RVE sub‐domains. Standard, as well as, Non‐Standard boundary conditions are consistently derived in order to preserve objectivity of the homogenized response with respect to the micro‐cell size. In the second part of the paper, and as an original contribution, the detailed numerical implementation of the two‐scale model based on the finite element method is presented. Special attention is devoted to the topics, which are distinctive of the Failure‐Oriented Multiscale Formulation, such as: (i) the finite element technologies adopted in each scale along with their corresponding algorithmic expressions, (ii) the generalized treatment given to the kinematical boundary conditions in the RVE, and (iii) how these kinematical restrictions affect the capturing of macroscopic material instability modes and the posterior evolution of failure at the RVE level. Finally, a set of numerical simulations is performed in order to show the potentialities of the proposed methodology, as well as, to compare and validate the numerical solutions furnished by the two‐scale model with respect to a direct numerical simulation approach. Copyright © 2013 John Wiley & Sons, Ltd.     

A two‐dimensional stochastic algorithm for the solution of the non‐linear Poisson–Boltzmann equation: validation with finite‐difference benchmarks

This paper presents a two‐dimensional floating random walk (FRW) algorithm for the solution of the non‐linear Poisson–Boltzmann (NPB) equation. In the past, the FRW method has not been applied to the solution of the NPB equation which can be attributed to the absence of analytical expressions for volumetric Green's functions. Previous studies using the FRW method have examined only the linearized Poisson–Boltzmann equation. No such linearization is needed for the present approach. Approximate volumetric Green's functions have been derived with the help of perturbation theory, and these expressions have been incorporated within the FRW framework. A unique advantage of this algorithm is that it requires no discretization of either the volume or the surface of the problem domains. Furthermore, each random walk is independent, so that the computational procedure is highly parallelizable. In our previous work, we have presented preliminary calculations for one‐dimensional and quasi‐one‐dimensional benchmark problems. In this paper, we present the detailed formulation of a two‐dimensional algorithm, along with extensive finite‐difference validation on fully two‐dimensional benchmark problems. The solution of the NPB equation has many interesting applications, including the modelling of plasma discharges, semiconductor device modelling and the modelling of biomolecular structures and dynamics. Copyright © 2005 John Wiley & Sons, Ltd.     

A Bayesian Predictive Analysis of Step‐Stress Accelerated Tests in Gamma Degradation‐Based Processes

Degradation modeling might be an alternative to the conventional life test in reliability assessment for high quality products. This paper develops a Bayesian approach to the step‐stress accelerated degradation test. Reliability inference of the population is made based on the posterior distribution of the underlying parameters with the aid of Markov chain Monte Carlo method. Further sequential reliability inference on individual product under normal condition is also proposed. Simulation study and an illustrative example are presented to show the appropriateness of the proposed method. Copyright © 2017 John Wiley & Sons, Ltd.     

A Parallel Strategy for the Logical‐probabilistic Calculus‐based Method to Calculate Two‐terminal Reliability

The theory of network reliability has been applied to many complicated network structures, such as computer and communication networks, piping systems, electricity networks, and traffic networks. The theory is used to evaluate the operational performance of networks that can be modeled by probabilistic graphs. Although evaluating network reliability is an Non‐deterministic Polynomial‐time hard problem, numerous solutions have been proposed. However, most of them are based on sequential computing, which under‐utilizes the benefits of multi‐core processor architectures. This paper addresses this limitation by proposing an efficient strategy for calculating the two‐terminal (terminal‐pair) reliability of a binary‐state network that uses parallel computing. Existing methods are analyzed. Then, an efficient method for calculating terminal‐pair reliability based on logical‐probabilistic calculus is proposed. Finally, a parallel version of the proposed algorithm is developed. This is the first study to implement an algorithm for estimating terminal‐pair reliability in parallel on multi‐core processor architectures. The experimental results show that the proposed algorithm and its parallel version outperform an existing sequential algorithm in terms of execution time. Copyright © 2015 John Wiley & Sons, Ltd.     

A multi‐axial low‐cycle fatigue life prediction model considering effects of additional hardening

It is generally accepted that the additional hardening of materials could largely shorten multi‐axis fatigue life of engineering components. To consider the effects of additional hardening under multi‐axial loading, this paper summarizes a new multi‐axial low‐cycle fatigue life prediction model based on the critical plane approach. In the new model, while critical plane is adopted to calculate principal equivalent strain, a new plane, subcritical plane, is also defined to calculate a correction parameter due to the effects of additional hardening. The proposed fatigue damage parameter of the new model combines the material properties and the angle of the loading orientation with respect to the principal axis and can be established with Coffin‐Manson equation directly. According to experimental verification and comparison with other traditional models, it is clear that the new model has satisfactory reliability and accuracy in multi‐axial fatigue life prediction.