Murthy N. Guddati

Improved calculation method of damage parameter in viscoelastic continuum damage model

Modelling the performance of asphalt concrete using continuum damage theories is an approach that has gained international attention in recent years. These types of models are advantageous because they ignore many of the complicated physical interactions at the microscale level and instead characterise a material using macroscale observations. One such model, the viscoelastic continuum damage model, is used in this study to examine the fatigue performance of asphalt concrete mixtures. A mathematically rigorous exploration is undertaken to specialise the model for easy prediction and characterisation using cyclic fatigue tests on cylindrical specimens. This process reveals that certain theoretical shortcomings are evident in other similar models and corrects them with a newly developed model. The resulting model is capable of capturing the underlying material property, i.e. the damage characteristic curve, which is responsible for the performance of controlled stress, controlled crosshead strain and constant crosshead rate monotonic tension until failure tests.

CONTINUED-FRACTION ABSORBING BOUNDARY CONDITIONS FOR THE WAVE EQUATION

Absorbing boundary conditions are generally required for numerical modeling of wave phenomena in unbounded domains. Local absorbing boundary conditions are generally preferred for transient analysis because of their computational efficiency. However, their accuracy is severely limited because the more accurate high-order boundary conditions cannot be implemented easily. In this paper, a new arbitrarily high-order absorbing boundary condition based on continued fraction approximation is presented. Unlike the existing boundary conditions, this one does not contain high-order derivatives, thus making it amenable to implementation in conventional C0 finite element and finite difference methods. The superior numerical properties and implementation aspects of this boundary condition are discussed. Numerical examples are presented to illustrate the performance of these new high-order boundary condition.

Toward a micromechanics-based procedure to characterize fatigue performance of asphalt concrete

A lattice-based micromechanics approach is proposed to characterize the cracking performance of asphalt concrete. A random truss lattice model was introduced and investigated for simulating the following: (a) linear elastic and viscoelastic deformation of homogeneous materials in axial compression and shear loading experiments, (b) linear elastic deformation and the stress field in heterogeneous materials in an axial compression loading experiment, and (c) damage evolution in elastic solids under an indirect tensile test. The simulation results match well with the theoretical solutions and show excellent promise in predicting cracking patterns in the indirect tensile test. A brief discussion about ongoing work is also presented.

Dispersion-reducing finite elements for transient acoustics

This paper focuses on increasing the accuracy of low-order (four-node quadrilateral) finite elements for the transient analysis of wave propagation. Modified integration rules, originally proposed for time-harmonic problems, provide the basis for the proposed technique. The modified integration rules shift the integration points to locations away from the conventional Gauss or Gauss-Lobatto integration points with the goal of reducing the discretization errors, specifically the dispersion error. Presented here is an extension of the idea to time-dependent analysis using implicit as well as explicit time-stepping schemes. The locations of the stiffness integration points remain unchanged from those in time-harmonic case. On the other hand, the locations of the integration points for the mass matrix depend on the time-stepping scheme and the step size. Furthermore, the central difference method needs to be modified from its conventional form to facilitate fully explicit computation. The superior performance...

On Optimal Finite-Difference Approximation of PML

A technique derived from two related methods suggested earlier by some of the authors for optimization of finite-difference grids and absorbing boundary conditions is applied to discretization of perfectly matched layer (PML) absorbing boundary conditions for wave equations in Cartesian coordinates. We formulate simple sufficient conditions for optimality and implement them. It is found that the minimal error can be achieved using pure imaginary coordinate stretching. As such, the PML discretization is algebraically equivalent to the rational approximation of the square root on [0,1] conventionally used for approximate absorbing boundary conditions. We present optimal solutions for two cost functions, with exponential (and exponential of the square root) rates of convergence with respect to the number of the discrete PML layers using a second order finite-difference scheme with optimal grids. Results of numerical calculations are presented.

Development of a failure criterion for asphalt mixtures under fatigue loading

The failure criterion defines the applicable region associated with the continuum damage model and is important in characterising the service life of asphalt mixtures. A proper failure criterion should consistently predict the failure of the material that reaches macro-fracture. A previously developed criterion that uses the viscoelastic continuum damage (VECD) model exhibits high variability and is considered to be inefficient because it requires calibration tests at different temperatures. In this paper, a new concept that involves released pseudo strain energy is introduced. This released pseudo strain energy concept focuses on the dissipated energy that is related to stiffness reduction only and is fully compatible and predictable using the VECD model. A characteristic relationship is found between the stable rate of pseudo energy release during testing and the final fatigue life of the same mixture, independent of strain amplitude and temperature. Based on these observations, a new failure criterion is proposed. The proposed failure criterion combines the advantages of the VECD model and this characteristic relationship, which both originate from fundamental mixture properties, and is able to predict the fatigue life of asphalt concrete mixtures across different temperatures and strain amplitudes.

Experimental Investigation of Anisotropy in Asphalt Concrete

Accurate multiaxial characterization of asphalt concrete requires a thorough understanding of its anisotropic behavior. For that purpose a study has been conducted to examine the anisotropic properties of asphalt concrete in the linear viscoelastic range, with growing damage, and during volumetric deformation. Tests were conducted on specimens cored in the vertical and horizontal directions from gyratory-compacted specimens. Anisotropy was found to have no effect on the linear viscoelastic properties of the material. This finding is supported by subsequent results from monotonic constant crosshead rate uniaxial tension and uniaxial compression tests. It was also found that anisotropy contributes greatly to the behavior of asphalt concrete in compression, but shows little, if any, effect on tensile properties. In addition, the strong dependence of anisotropy on temperature and strain rate is presented. Finally, promising results from a simplified method of extracting the anisotropic behavior of asphalt concrete with the use of the hydrostatic test are also introduced.

Accelerated Pavement Performance Modeling Using Layered Viscoelastic Analysis

An efficient pavement performance analysis framework is developed by combining the ideas of time-scale separation and Fourier transform-based layered analysis. First, utilizing the vast difference in time scales associated with temperature and traffic load variations, the number of stress analysis runs are reduced from several million to a few dozen. Second, the computational cost of the pavement stress analysis is reduced significantly by using Fourier transform-based analysis. The resulting pavement performance prediction tool, named the layered viscoelastic continuum damage (LVECD) program, can capture the effects of viscoelasticity, temperature (thermal stresses and changes in viscoelastic properties) and the moving nature of the traffic load. The efficiency of the LVECD program is shown through 20-year pavement simulations.

Absorbing boundary conditions for scalar waves in anisotropic media. Part 1: Time harmonic modeling

With the ultimate goal of devising effective absorbing boundary conditions (ABCs) for general anisotropic media, we investigate the accuracy aspects of local ABCs designed for the scalar anisotropic wave equation in the frequency domain (time harmonic case). The ABC analyzed in this paper is the perfectly matched discrete layers (PMDL). PMDL is a simple variant of perfectly matched layers (PML) and is equivalent to rational approximation-based local ABCs. Specifically, we derive a sufficient condition for PMDL to accurately absorb wave modes with outgoing group velocities and this condition turns out to be a simple bound on the PMDL parameters. The reflection coefficient derived in this paper clearly reveals that the PMDL absorption is based on group velocities, and not phase velocities, and hence a PMDL can be designed to correctly identify and accurately absorb all outgoing wave modes (even those with opposing signs of phase and group velocities). The validity of the sufficient condition is demonstrated through a series of frequency domain simulations. In part 2 of this paper [S. Savadatti, M.N. Guddati, Absorbing boundary conditions for scalar waves in anisotropic media. Part 2: Time-dependent modeling, J. Comput. Phys. (2010), doi:10.1016/j.jcp.2010.05.017], the accuracy condition presented here is shown to govern both the well-posedness and accuracy aspects of PMDL designed for transient (time-dependent) modeling of scalar waves in anisotropic media.

Fatigue Cracking Mechanisms in Asphalt Pavements with Viscoelastic Continuum Damage Finite-Element Program

A study of fatigue-cracking mechanisms in asphalt pavements used the finite-element program VECD-FEP++. This program employs the viscoelastic continuum damage model for the asphalt layer and a nonlinear elastic model for unbound layers. Both bottom-up and top-down cracks are investigated by taking several important variables, such as asphalt layer thickness, layer stiffness, pressure distribution under loading, and load level applied on the pavement surface, into account. The cracking mechanisms in various pavement structures under different loading conditions are studied by monitoring a damage contour. Preferred conditions for top-down cracking were identified with the results from this parametric study. The conjoined damage contours in thicker pavements suggest that a through-the-thickness crack may develop as the bottom-up and top-down cracks propagate simultaneously and coalesce; that idea supports observations from field cores and raises the question of the validity of traditional fatigue performance models that account for the growth of the bottom-up cracking only.