A probabilistic computational framework for bridge network optimal maintenance scheduling

This paper presents a probabilistic computational framework for the Pareto optimization of the preventive maintenance applications to bridges of a highway transportation network. The bridge characteristics are represented by their uncertain reliability index profiles. The in/out of service states of the bridges are simulated taking into account their correlation structure. Multi-objective Genetic Algorithms have been chosen as numerical tool for the solution of the optimization problem. The design variables of the optimization are the preventive maintenance schedules of all the bridges of the network. The two conflicting objectives are the minimization of the total present maintenance cost and the maximization of the network performance indicator. The final result is the Pareto front of optimal solutions among which the managers should chose, depending on engineering and economical factors. A numerical example illustrates the application of the proposed approach.     

A theoretical and computational setting for a geometrically nonlinear gradient damage modelling framework

 The present work deals with the extension to the geometrically nonlinear case of recently proposed ideas on elastic- and elastoplastic-damage modelling frameworks within the infinitesimal theory. The particularity of these models is that the damage part of the modelling involves the gradient of damage quantity which, together with the equations of motion, are ensuing from a new formulation of the principle of virtual power. It is shown how the thermodynamics of irreversible processes is crucial in the characterization of the dissipative phenomena and in setting the convenient forms for the constitutive relations. On the numerical side, we discuss the problem of numerically integrating these equations and the implementation within the context of the finite element method is described in detail. And finally, we present a set of representative numerical simulations to illustrate the effectiveness of the proposed framework. Received: 13 May 2002 / Accepted: 16 September 2002     

A damage computational approach for composites: Basic aspects and micromechanical relations

The basic aspects of a damage mechanics approach for composites, capable of simulating complete fracture phenomena, are presented. First, for two material examples, ceramic composites and laminate composites, modelling difficulties and state-of-art modelling are outlined. Damage models with delay effects combined with a dynamic analysis are then introduced. Their possibilities are illustrated on one-dimensional bar problems. More complex examples, computed with a F. E. code specific to laminate damage analysis, are also highligted.Dedicated to J. C. Simo     

A computational multi-scale approach for the stochastic mechanical response of foam-filled honeycomb cores

This paper investigates the uncertainty in the mechanical response of foam-filled honeycomb cores by means of a computational multi-scale approach. A finite element procedure is adopted within a purely kinematical multi-scale constitutive modelling framework to determine the response of a periodic arrangement of aluminium honeycomb core filled with PVC foam. By considering uncertainty in the geometric properties of the microstructure, a significant computational cost is added to the solution of a large set of microscopic equilibrium problems. In order to tackle this high cost, we combine two strategies. Firstly, we make use of symmetry conditions present in a representative volume element of material. Secondly, we build a statistical approximation to the output of the computer model, known as a Gaussian process emulator. Following this double approach, we are able to reduce the cost of performing uncertainty analysis of the mechanical response. In particular, we are able to estimate the 5th, 50th, and 95th percentile of the mechanical response without resorting to more computationally expensive methods such as Monte Carlo simulation. We validate our results by applying a statistical adequacy test to the emulator.     

A description of micro- and macroscale damage of concrete structures

Some particularities of the microstructure of concrete are first presented: they lead us to conclude that damage by microcracking is the main phenomenon in the mechanical behavior of the material. An isotropic elastic damage model is then proposed by using the coupling of two damage variables, D_t (tensile effects) and D_c (compressive effects). The model is built according to the framework of thermodynamics, and then we show that it is possible to describe the birth and growth of cracks, using a combination linear elastic damage mechanics and linear elastic fracture mechanics. Some results attest the interest in that kind of approach.     

A hybrid approach to multi-scale modelling of cancer

In this paper, we review multi-scale models of solid tumour growth and discuss a middle-out framework that tracks individual cells. By focusing on the cellular dynamics of a healthy colorectal crypt and its invasion by mutant, cancerous cells, we compare a cell-centre, a cell-vertex and a continuum model of cell proliferation and movement. All models reproduce the basic features of a healthy crypt: cells proliferate near the crypt base, they migrate upwards and are sloughed off near the top. The models are used to establish conditions under which mutant cells are able to colonize the crypt either by top-down or by bottom-up invasion. While the continuum model is quicker and easier to implement, it can be difficult to relate system parameters to measurable biophysical quantities. Conversely, the greater detail inherent in the multi-scale models means that experimentally derived parameters can be incorporated and, therefore, these models offer greater scope for understanding normal and diseased crypts, for testing and identifying new therapeutic targets and for predicting their impacts.     

A Trefftz approach to computational mechanics

This paper presents a Trefftz method for solving structural elasticity problems and flow problems of incompressible viscous fluids. The problem of unilateral contact is also dealt with. For each type of problem, Trefftz polynomials and associated variational formulations are given. Complex structures are studied by a sub‐structuring technique. This method requires the resolution of a non‐symmetrical linear system. It is shown that it is possible to take advantage of this Trefftz approximation in two ways: (i) the approach presented can be considered as a simplified method which enables a solution to be evaluated quickly; (ii) this approach also makes it possible to obtain a good quality solution associated with high degree polynomial bases. This method is adapted to optimization processes because the discretization of the structure requires only very few sub‐domains to build a good approximation and offers a great flexibility in use. Copyright © 2003 John Wiley & Sons, Ltd.     

A multi-scale finite element approach for modelling damage progression in woven composite structures

A significant challenge in the numerical modelling of composite structures with a multi-axis fibre architecture is the reproducibility of the textile mechanics [1]. A numerical analysis procedure for woven composite structures using a multi-scale finite element approach has been developed, and is presented in this paper. The approach is demonstrated for a flat two-dimensional woven glass/epoxy laminate. Digital microscopy is used to estimate tow cross-section and path, and quantify the amount of variation of these parameters. This data is used to generate both a meso-scale model of a single unit cell as well as a macro-scale model of the complete structure. Numerical results from the proposed approach are compared to experimental stress-strain data, which show good agreement in the lower strain range.     

A dynamical systems approach to simulating macroscale spatial dynamics in multiple dimensions

Developments in dynamical systems theory provide new support for the macroscale modelling of pdes and other microscale systems such as lattice Boltzmann, Monte Carlo or molecular dynamics simulators. By systematically resolving subgrid microscale dynamics the dynamical systems approach constructs accurate closures of macroscale discretisations of the microscale system. Here we specifically explore reaction–diffusion problems in two spatial dimensions as a prototype of generic systems in multiple dimensions. Our approach unifies into one the discrete modelling of systems governed by known pdes and the ‘equation-free’ macroscale modelling of microscale simulators efficiently executing only on small patches of the spatial domain. Centre manifold theory ensures that a closed model exists on the macroscale grid, is emergent, and is systematically approximated. Dividing space into either overlapping finite elements or spatially separated small patches, the specially crafted inter-element/patch coupling also ensures that the constructed discretisations are consistent with the microscale system/pde to as high an order as desired. Computer algebra handles the considerable algebraic details, as seen in the specific application to the Ginzburg–Landau pde. However, higher-order models in multiple dimensions require a mixed numerical and algebraic approach that is also developed. The modelling here may be straightforwardly adapted to a wide class of reaction–diffusion pdes and lattice equations in multiple space dimensions. When applied to patches of microscopic simulations our coupling conditions promise efficient macroscale simulation.     

A nested modelling approach to infrastructure performance characterisation

Reliable and accurate predictions of infrastructure condition can save significant amounts of money for infrastructure management agencies through better planned maintenance and rehabilitation activities. Infrastructure deterioration is a complicated, dynamic and stochastic process affected by various factors such as design, environmental conditions, material properties, structural capacities and some unobserved variables. Previous researchers have explored different types of modelling techniques, ranging from simple deterministic models to sophisticated probabilistic models, to characterise the deterioration process of infrastructure systems; however, these models have limitations in various aspects. Traditional deterministic models are inadequate to capture the uncertainties associated with infrastructure deterioration processes. State-based probabilistic models can only predict conditions at fixed time points. Time-based probabilistic models require frequent observations that, in practice, are not easy to perform. The goal of this research is to develop a new probabilistic model that is capable of capturing the stochastic nature of infrastructure deterioration, while at the same time avoiding the limitations of previous modelling efforts. The proposed nested model is based on discrete choice model theory. It can be used to predict the probability of an infrastructure system staying at defined condition states by relating an index representing the performance of the infrastructure to a number of explanatory variables that characterise the structural adequacy, traffic loading and environmental conditions of the infrastructure. The proposed model includes different possible implementation paths (sequential versus multinomial) depending on the considered explanatory variables and the available data. In the case study, the proposed probabilistic model is implemented with pavement performance data collected in Texas, yielding promising preliminary results.     

Control of a batch-processing machine: A computational approach

Batch processing machines, where a number of jobs are processed simultaneously as a batch, occur frequently in semiconductor manufacturing environments, particularly at diffusion in wafer fabrication and at burn-in in final test. In this paper we consider a batch-processing machine subject to uncertain (Poisson) job arrivals. Two different cases are studied: (1) the processing times of batches are independent and identically distributed (IID), corresponding to a diffusion tube; and (2) the processing time of each batch is the maximum of the processing times of its constituent jobs, where the processing times of jobs are IID, modelling a burn-in oven. We develop computational procedures to minimize the expected long-run-average number of jobs in the system under a particular family of control policies. The control policies considered are threshold policies, where processing of a batch is initiated once a certain number of jobs have accumulated in the system. We present numerical examples of our methods and verify their accuracy using simulation.     

A computational approach to the investigation of impact damage evolution in discontinuously reinforced fiber composites

 A micromechanical damage constitutive model for discontinuous fiber-reinforced composites is developed to perform impact simulation. Progressive interfacial fiber debonding and a crack-weakened model are considered in accordance with a statistical function to describe the varying probability of damage. Emanating from a constitutive damage model for aligned fiber-reinforced composites, a micromechanical damage constitutive model for randomly oriented, discontinuous fiber-reinforced composites is developed. The constitutive damage model is then implemented into a finite element program DYNA3D to simulate the dynamic behavior and the progressive damage of composites. Finally, numerical simulations for a biaxial loading test and a four-point bend impact test of composite specimens are performed to validate the computational model and investigate impact damage evolution in discontinuous fiber-reinforced composite structures. Furthermore, in order to address the influence of Weibull parameter S _o on the damage evolution in composites, parametric analysis is carried out. Received 29 April 2000     

A nested dissection approach to modeling transport in nanodevices: Algorithms and applications

Modeling nanoscale devices quantum mechanically is a computationally challenging problem where new methods to solve the underlying equations are in a dire need. In this paper, we present an approach to calculate the charge density in nanoscale devices, within the context of the nonequilibrium Green's function approach. Our approach exploits recent advances in using an established graph partitioning approach. The developed method has the capability to handle open boundary conditions that are represented by full self‐energy matrices required for realistic modeling of nanoscale devices. Our method to calculate the electron density has a reduced complexity compared with the established recursive Green's function approach. As an example, we apply our algorithm to a quantum well superlattice and a carbon nanotube, which are represented by a continuum and tight binding Hamiltonian, respectively, and demonstrate significant speedup over the recursive method. Copyright © 2013 John Wiley & Sons, Ltd.     

Investigating creep rupture and damage behaviour in notched P92 steel specimen using a microscale modelling approach

Idealized random grains separated by pseudo grain boundaries were generated by using Voronoi tessellation to simulate the polycrystalline microstructure. Combined with finite element analyses, this approach made it possible to addressing crack initiation and progressive failure due to crack growth in notched bar geometries of P92 steel at high temperature. The calculations provided good predictions for creep rupture lives of notched specimen with different notch radii and external stress. Simultaneously, irregular crack growth shape, intergranular crack mode, and wedge cracks at triple grain interaction were captured in the model. The crack initiation positions were found to be influenced by notch radius and applied stress causing high stress triaxiality at the subgrain level. Furthermore, the preferential crack growth directions were changed as the notch varied from sharp to blunt.     

A multi-scale approach to the propagation of non-adiabatic premixed flames

Flame propagation involves physico-chemical processes that occur over a range of temporal and spatial scales. By use of a multi-scale analysis it is shown that diffusion processes occurring on relatively small scales can be resolved analytically when the overall activation energy of the chemical reactions is large, thus providing, by asymptotic matching, explicit conditions for the state of the gas and for the flow field across the flame zone. The mathematical formulation on the larger hydrodynamic scale reduces to a free-boundary problem, with the free surface being the flame front. The front propagates into the fresh unburned gas at a rate that depends on both the local strain that it experiences and the local curvature, with coefficients that depend on the diffusion rates of heat and mass, the equivalence ratio of the mixture and the chemical kinetic parameters. The simplified model, properly termed a hydrodynamic model, involves the solution of the Navier Stokes equations with different densities and viscosities for the burned and unburned gas. The present work extends earlier studies by including volumetric heat loss, such as radiative loss, which affects the dynamics and may lead to flame extinction.     

DEM: A new computational approach to sheet metal forming problems

Many current approaches to finite element modelling of large deformation elastic—plastic forming problems use a rate form of the virtual work (equilibrium) equations, and a finite element representation of the displacement components. Called the incremental method, this approach produces a three-field formulation in which displacements, stresses and effective strain are dependent variables. Next, the formulation is converted to a one-field displacement formulation by an algebraic time discretization which uses a low order explicit time-stepping procedure to integrate the equations. This approach does not produce approximations which satisfy the discrete equilibrium equations at all times and, moreover, the advantage of the single-field algebraic formulation is realized at the expense of very small time steps needed to produce stability and accuracy in the numerical calculations. This paper describes a variant of the mixed method in which all three field variables (displacements, stresses and effective strain) are given finite element representations. The discrete equilibrium equations then generate a nonlinear system of algebraic equations whose solutions represent a manifold, while the constitutive equations form a system of ordinary differential equations. A commercially available, variable time step/variable order code is then used to integrate this differential/algebraic system. When applied to the problem of hydrostatic bulging of a membrane, the new approach requires far less computer time than the incremental method.     

A multiscale framework for computational nanomechanics: Application to the modeling of carbon nanotubes

A multiscale computational framework is presented that provides a coupled self‐consistent system of equations involving molecular mechanics at small scales and quasi‐continuum mechanics at large scales. The proposed method permits simultaneous resolution of quasi‐continuum and atomistic length scales and the associated displacement fields in a unified manner. Interatomic interactions are incorporated into the method through a set of analytical equations that contain nanoscale‐based material moduli. These material moduli are defined via internal variables that are functions of the local atomic configuration parameters. Point defects like vacancy defects in nanomaterials perturb the atomic structure locally and generate localized force fields. Formation energy of vacancy is evaluated via interatomic potentials and minimization of this energy leads to nanoscale force fields around defects. These nanoscale force fields are then employed in the multiscale method to solve for the localized displacement fields in the vicinity of vacancies and defects. The finite element method that is developed based on the hierarchical multiscale framework furnishes a two‐level statement of the problem. It concurrently feeds information at the molecular scale, formulated in terms of the nanoscale material moduli, into the quasi‐continuum equations. Representative numerical examples are shown to validate the model and demonstrate its range of applicability. Copyright © 2008 John Wiley & Sons, Ltd.     

A continuum damage mechanics model with the strain-based approach to biaxial low cycle fatigue failure

A continuum damage mechanics model for low cycle fatigue failure of initially isotropic materials under biaxial loading conditions is presented. The expression for the equivalent strain in the fatigue damage evolution equation contains the three material parameters, and the strain intensity as well as the maximum principal strain and the volume strain for amplitudes. It is shown how these material parameters can be determined from a series of basic experiments using a cruciform specimen. Particular expressions for the equivalent strain with a smaller number of material parameters and invariants are obtained. Model predictions are found to be in satisfactory agreement with the experimental low cycle fatigue data under full ranged biaxial loadings obtained in the test using a cruciform specimen.