## Uintah and Related C-SAFE Publications

2004

B. Banerjee, D.O. Adams.
**“On Predicting the Effective Elastic Properties of Polymer Bonded Explosives Using the Recursive Cell Method,”** In *International Journal of Solids and Structures*, Vol. 41, No. 2, pp. 481--509. January, 2004.

DOI: 10.1016/j.ijsolstr.2003.09.016

Polymer bonded explosives are particulate composites containing elastic particles in a viscoelastic binder. The particles occupy an extremely high fraction of the volume, often greater than 90%. Under low strain rate loading (∼0.001–1 s^{−1}) and at room temperature and higher, the elastic modulus of the particles can be four orders of magnitude higher than that of the binder. Rigorous bounds and analytical estimates for the effective elastic properties of these materials have been found to be inaccurate. The computational expense of detailed numerical simulations for the determination of effective properties of these composites has led to the search for a faster technique. In this work, one such technique based on a real-space renormalization group approach is explored as an alternative to direct numerical simulations in determining the effective elastic properties of PBX 9501. The method is named the recursive cell method (RCM). The differential effective medium approximation, the finite element method, and the generalized method of cells (GMC) are investigated with regard to their suitability as homogenizers in the RCM. Results show that the RCM overestimates the effective properties of particulate composites and PBX 9501 unless large blocks of subcells are renormalized and the particles in a representative volume element are randomly distributed. The GMC homogenizer is found to provide better estimates of effective elastic properties than the finite element based homogenizer for composites with particle volume fractions less than 0.80.

S.G. Bardenhagen, E.M. Kober.
**“The Generalized Interpolation Material Point Method,”** In *Computer Modeling in Engineering and Sciences*, Vol. 5, No. 6, pp. 477--495. 2004.

The Material Point Method (MPM) discrete solution procedure for computational solid mechanics is generalized using a variational form and a Petrov-Galerkin discretization scheme, resulting in a family of methods named the Generalized Interpolation Material Point (GIMP) methods. The generalization permits iden- tification with aspects of other point or node based discrete solution techniques which do not use a body–fixed grid, i.e. the "meshless methods". Similarities are noted and some practical advantages relative to some of these methods are identified. Examples are used to demon- strate and explain numerical artifact noise which can be expected in MPM calculations. This noise results in non-physical local variations at the material points, where constitutive response is evaluated. It is shown to destroy the explicit solution in one case, and seriously degrade it in another. History dependent, inelastic constitutive laws can be expected to evolve erroneously and report inac- curate stress states because of noisy input. The noise is due to the lack of smoothness of the interpolation func- tions, and occurs due to material points crossing compu- tational grid boundaries. The next degree of smoothness available in the GIMP methods is shown to be capable of eliminating cell crossing noise.

D. Bedrov, G.D. Smith, J.F. Douglas.
**“Structural and Dynamic Heterogeneity in a Telechelic Polymer Solution,”** In *Polymer*, Vol. 45, No. 11, pp. 3961--3966. May, 2004.

DOI: 10.1016/j.polymer.2004.01.082

We utilize molecular dynamics simulations to investigate the implications of micelle formation on structural relaxation and polymer bead displacement dynamics in a model telechelic polymer solution. The transient structural heterogeneity associated with incipient micelle formation is found to lead to a ‘caging’ of the telechelic chain end-groups within dynamic clusters on times shorter than the structural relaxation time governing the cluster (micelle) lifetime. This dynamical regime is followed by ordinary diffusion on spatial scales larger than the inter-micelle separation at long times. As with associating polymers, glass-forming liquids and other complex heterogeneous fluids, the structural *τ*_{s} relaxation time increases sharply upon a lowering temperature *T*, but the usual measures of dynamic heterogeneity in glass-forming liquids (non-Gaussian parameter *α*_{2}(*t*), product of diffusion coefficient *D* and shear viscosity *η*, non-Arrhenius *T*-dependence of *τ*_{s}) all indicate a *return to homogeneity* at low *T* that is not normally observed in simulations of these other complex fluids. The greatest increase in dynamic heterogeneity is found on a length scale that lies intermediate to the micellar radius of gyration and intermicellar spacing. We suggest that the limited size of the clusters that form in our (low concentration) system limit the relaxation time growth and thus allows the fluid to remain in equilibrium at low *T*.

D. Bedrov, G.D. Smith, W. Paul.
**“Anomalous Pressure Dependence of the Structure Factor in 1,4-Polybutadiene Melts. A Molecular Dynamics Simulation Study,”** In *Physical Review, E*, Vol. 70, No. 1, pp. 011804. July, 2004.

DOI: 10.1103/PhysRevE.70.011804

Neutron scattering has shown the first diffraction peak in the structure factor of a 1,4-polybutadiene melt under compression to move to larger * q* values as expected but to decrease significantly in intensity. Simulations reveal that this behavior does not result from loss of structure in the polymer melt upon compression but rather from the generic effects of differences in the pressure dependence of the intermolecular and intramolecular contributions to the melt structure factor and differences in the pressure dependence of the partial structure factors for carbon–carbon and carbon–deuterium intermolecular correlations. This anomalous pressure dependence is not seen for protonated melts.

Y. Guo, J.A. Nairn.
**“Calculation of J-Integral and Stress Intensity Factors using the Material Point Method,”** In *Computer Modeling in Engineering and Sciences*, Vol. 6, No. 3, pp. 295--308. 2004.

The Material Point Method (MPM), which is a particle-based, meshless method that discretizes material bodies into a collection of material points (the particles), is a new method for numerical analysis of dynamic solid mechanics problems. Recently, MPM has been generalized to include dynamic stress analysis of structures with explicit cracks. This paper considers evaluation of crack-tip parameters, such as *J-*integral and stress intensity factors, from MPM calculations involving explicit cracks. Examples for both static and dynamic problems for pure modes I and II or mixed mode loading show that MPM works well for calculation of fracture parameters. The MPM results agree well with results obtained by other numerical methods and with analytical solutions.

Y. He, T.R. Lutz, M.D. Ediger, C. Ayyagari, D. Bedrov, G.D. Smith.
**“NMR Experiments and Molecular Dynamics Simulations of the Segmental Dynamics of Polystyrene,”** In *Macromolecules*, Vol. 37, No. 13, pp. 5032--5039. May, 2004.

DOI: 10.1021/ma049843r

We have performed NMR spin-lattice relaxation experiments and molecular dynamics (MD) computer simulations on atactic polystyrene (a-PS). The segmental correlation times of three different molecular weight a-PS (*M*_{n} = 1600, 2100, 10 900 g/mol) were extracted from NMR by measuring the ^{2}H spin-lattice relaxation times (*T _{1}*) over a broad temperature range (390-510 K). MD simulations of an a-PS melt of molecular weight 2200 g/mol were carried out at 475, 500, and 535 K. Comparisons between experiments and simulations show that the MD simulations reproduce both the shape of the

*P*orientation autocorrelation function and its temperature dependence, while the simulated segmental correlation times are slower than experimental results by a factor of 1.8. If the simulations are rescaled by this factor, they reproduce both the experimental

_{2}(t)*T*values and the slight difference in dynamics between the backbone and side group of PS.

_{1}

C.R. Johnson, R.S. MacLeod, S.G. Parker, D.M. Weinstein.
**“Biomedical Computing and Visualization Software Environments,”** In *Comm. ACM*, Vol. 47, No. 11, pp. 64--71. 2004.

G. Krishnamoorthy, R. Rawat, P.J. Smith.
**“Parallel Computations of Radiative Heat Transfer Using the Discrete Ordinates Method,”** In *Numerical Heat Transfer, Part B: Fundamentals*, Vol. 47, No. 1, pp. 19--38. 2004.

DOI: 10.1080/10407790490487451

The discrete ordinates method is spatially decomposed to solve the radiative transport equation on parallel computers. Mathematical libraries developed by third parties are used to solve the matrices that result during the solution procedure. The radiation component is verified by comparing computed values against a benchmark. Fixed and scaled problem size efficiencies are examined. Contrary to most previous studies, the parallel efficiencies did not depend strongly on the optical thickness of the medium for our model problem. Timing studies show that GMRES, BiCGSTAB iterative methods with block Jacobi preconditioning perform the best for solving these matrix systems.

A. Violi.
**“Modeling of Soot Particle Inception in Aromatic and Aliphatic Premixed Flames,”** In *Combustion and Flame*, Vol. 139, No. 4, pp. 279--287. December, 2004.

DOI: 10.1016/j.combustflame.2004.08.013

The growth of hydrocarbon molecules up to sizes of incipient soot is computed in premixed laminar flames using kinetic Monte Carlo and molecular dynamic methodologies (AMPI code). This approach is designed to preserve atomistic scale structure (bonds, bond angles, dihedral angles) as soot precursors evolve into three-dimensional structures. Application of this code to aliphatic (acetylene) and aromatic (benzene) flame environments is able to explain results in the literature on the differences in properties of soot precursors from these two classes of flames, particularly relating to H/C ratio, particle sphericity, and depolarization ratio.

A. Violi, T.N. Truong, A.F. Sarofim.
**“Kinetics of Hydrogen Abstraction Reactions from Polycyclic Aromatic Hydrocarbons by H Atoms,”** In *Journal of Physical Chemistry, A*, Vol. 108, No. 22, pp. 4846--4852. May, 2004.

DOI: 10.1021/jp026557d

An application of the Reaction Class Transition State Theory/Linear Energy Relationship (RC-TST/LER) is presented for the evaluation of the thermal rate constants of hydrogen abstraction reactions by H atoms from Polycyclic Aromatic Hydrocarbons (PAH). Two classes of reactions have been considered, namely hydrogen bonded to six- and five-membered rings, respectively, and twenty-two reactions have been used to develop the RC-TST/LER parameters. B3LYP and BH&HLYP density functional theory methods were used to calculate necessary potential energy surface information. Detailed analyses of RC-TST/LER reaction factors lead to the conclusion that rate constants for any reaction in these two classes can be approximated by those of its corresponding principal reaction corrected by the reaction symmetry factor. Specifically, for hydrogen abstraction from six-membered rings such as naphthalene and pyrene, *k*(*T*) = (σ/σ_{H+C}_{6}_{H}_{6}) *k*_{H}_{+}_{C}_{6}_{H}_{6} = (σ/6)1.42 *×* 10^{8}*T*^{1.77} exp(−6570/*T*)(cm^{3}/mol·s), and for hydrogen abstraction from five-membered rings such as acenaphthylene and acephenanthrylene, *k*(*T*) = (σ/σ_{H+C}_{12}_{H}_{8}) *k*_{H+C}_{12}_{H}_{8} = (σ/2)3.27 × 10^{8}*T*^{1.71} exp(−8170/*T*) (cm^{3}/mol·s), where σ is the reaction symmetry number.

2003

B. Banerjee, D.O. Adams.
**“Micromechanics-Based Prediction of Effective Elastic Properties of Polymer Bonded Explosives,”** In *Physica, B*, Vol. 338, No. 1-4, pp. 8--15. October, 2003.

DOI: 10.1016/S0921-4526(03)00451-4

Polymer bonded explosives are particulate composites containing a high volume fraction of stiff elastic explosive particles in a compliant viscoelastic binder. Since the volume fraction of particles can be greater than 0.9 and the modulus contrast greater than 20 000, rigorous bounds on the elastic moduli of the composite are an order of magnitude different from experimentally determined values. Analytical solutions are also observed to provide inaccurate estimates of effective elastic properties. Direct finite element approximations of effective properties require large computational resources because of the complexity of the microstructure of these composites. An alternative approach, the recursive cells method (RCM) is also explored in this work. Results show that the degree of discretization and the microstructures used in finite element models of PBXs can significantly affect the estimated Young's moduli.

B. Banerjee, C.M. Cady, D.O. Adams.
**“Micromechanics Simulations of Glass--estane Mock Polymer Bonded Explosives,”** In *Modeling and Simulation in Materials Science and Engineering*, Vol. 11, No. 4, pp. 457--475. 2003.

DOI: 10.1088/0965-0393/11/4/304

Polymer bonded explosives (PBXs) are particulate composites containing explosive particles and a continuous binder. The elastic modulus of the particles, at room temperature and higher, is often three to four orders of magnitude higher than that of the binder. Additionally, the explosive particles occupy high volume fractions, often greater than 90%. Both experimental and numerical determination of macroscopic properties of these composites is difficult. High modulus contrast mock PBXs provide a means of relatively inexpensive experimentation and validation of numerical approaches to determine properties of these materials. The goal of this investigation is to determine whether the effective elastic properties of monodisperse glass–estane mock PBXs can be predicted from two-dimensional micromechanics simulations using the finite element (FEM) method. In this study, the effect of representative volume element (RVE) size on the prediction of two-dimensional properties is explored. Two-dimensional estimates of elastic properties are compared with predictions from three-dimensional computations and with experimental data on glass–estane composites containing three different volume fractions of spherical glass beads. The effect of particle debonding on the effective elastic properties is also investigated using contact analyses. Results show that two-dimensional unit cells containing 10–20 circular particles are adequate for modelling glass–estane composites containing less than 60% glass particles by volume. No significant difference is observed between properties predicted by the two- and three-dimensional models. FEM simulations of RVEs, containing particles that are perfectly bonded to the binder, produce estimates of Young's modulus that are higher than the experimental data. Incorporation of debonding between particles and the binder causes the effective Young's modulus to decrease. However, the results suggest that cracks in the composite may play a significant role in determining the effective properties of mock polymer bonder explosives composed of glass and estane. The FEM simulations indicate that two-dimensional models that incorporate debonds and cracks can be used to obtain accurate estimates of the effective properties of glass–estane composites and possibly of PBXs.

W. Ciro, E.G. Eddings, A.F. Sarofim.
**“Fast Cookoff Tests Report,”** C-SAFE Internal Report, *C-SAFE*, October, 2003.

L.E. Fried, R. Manaa, J.P. Lewis.
**“Modeling the Reactions of Energetic Materials in the Condensed Phase,”** In *Overviews of Recent Research on Energetic Materials*, Edited by D. Thompson and T. Brill and R. Shaw, 2003.

J.D. de St. Germain, S.G. Parker.
**“Software Integration in an Academic Environment,”** In *Software Quality Forum (SQF)*, Arlington, Virginia, pp. (published on CD). March, 2003.

J.D. de St. Germain, A. Morris, S.G. Parker, A.D. Malony, S. Shende.
**“Performance Analysis Integration in the Uintah Software Development Cycle,”** In *International Journal of Parallel Programming*, Vol. 31, No. 1, pp. 35--53. 2003.

The increasing complexity of high-performance computing environments and programming methodologies presents challenges for empirical performance evaluation. Evolving parallel and distributed systems require performance technology that can be flexibly configured to observe different events and associated performance data of interest. It must also be possible to integrate performance evaluation techniques with the programming paradigms and software engineering methods. This is particularly important for tracking performance on parallel software projects involving many code teams over many stages of development. This paper describes the integration of the TAU and XPARE tools in the Uintah Computational Framework (UCF). Discussed is the use of performance mapping techniques to associate low-level performance data to higher levels of abstraction in UCF and the use of performance regression testing to provide a historical portfolio of the evolution of application performance. A scalability study shows the benefits of integrating performance technology in building large-scale parallel applications.

**Keywords:** uintah

J.E. Guilkey, J.A. Weiss.
**“Implicit Time Integration with the Material Point Method,”** In *International Journal for Numerical Methods in Engineering*, Vol. 57, pp. 1323--1338. 2003.

J.E. Guilkey, T. Harman, A. Xia, B. Kashiwa, P.A. McMurtry.
**“An Eulerian-Lagrangian Approach for Large Deformation Fluid Structure Interaction Problems, Part 1: Algorithm Development,”** In *Fluid Structure Interaction II*, In *Fluid Structure Interaction II: Proceedings of Fluid Structure Interaction *, WIT Press, pp. 14. 143--156, 2003.

DOI: 10.2495/FSI030141

T. Harman, J.E. Guilkey, B. Kashiwa, J. Schmidt, P. McMurtry.
**“An Eulerian-Lagrangian Approach for Large Deformation Fluid Structure Interaction Problems, Part 2: Multi-Physics Simulations within a Modern Computational Framework,”** In *Fluid Structure Interaction II*, WIT Press, pp. 157--166. 2003.

A tightly coupled fluid-structure interaction (FSI) solution technique incorporating fluid and solid mechanics, phase change and chemical reactions is presented. The continuum equations are solved with a cell-centered, multi-material ICE solution method. This formulation is integrated with a Lagrangian, particle based, solid mechanics technique, known as the Material Point Method, as described by Kashiwa et al. [1] and Guilkey et al. [2]. The combined method can handle large deformations and phase change within a single grid, without the need of separate domains for fluids and solids, or the passing of boundary conditions. This paper discusses algorithmic issues involved in accounting for chemical reactions and phase transition among material phases (e.g., solid → gas). Validation is presented as are simulations showing large deformation with phase change. These simulations were performed within a computational framework that contains tools for parallelization, performance analysis, data management, algorithm integration, and data visualization. Features of this framework are described.

G. Krishnamoorthy, J.M. Veranth.
**“Computational Modeling of CO-CO2 Ratio Inside Single Char Particles during Pulverized Coal Combustion,”** In *Energy and Fuels*, Vol. 17, No. 5, pp. 1367--1371. August, 2003.

DOI: 10.1021/ef030006k

A recently developed model was used to study the CO/CO_{2} ratio inside a burning pulverized coal particle, to better understand the effect of bulk gas composition on the equilibrium partial pressure of reduced metal species at the surface of ash inclusions. The motivation was to improve the ability to model submicrometer particle formation by ash vaporization, as a function of furnace conditions. Assumptions for the CO/CO_{2} ratio that have been made in previous studies are compared to predictions from a psuedo-steady-state model for a single porous particle that considers homogeneous and heterogeneous reaction kinetics and mass transfer both in particle pores and in the boundary layer. This is the first publication of model predictions for the CO/CO_{2} ratio as a function of radius for a coal char particle in a furnace with a bulk gas CO_{2} concentration in the range of 0%−79%. A method is proposed for summarizing the effects on the CO/CO_{2} ratio that are due to changes in the bulk furnace gas O_{2} and CO_{2} concentration, furnace temperature, and particle size, using an empirical equation that is suitable for incorporation as a submodel into comprehensive computational fluid dynamics-based codes for combustion simulation. Trends from the model simulations show general agreement with experimental data; however, the accuracy of the predictions is limited by the lack of fuel-specific input data.

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