By partitioning the total stresses in a damaged composite into either mechanical and residual stresses or into initial and pertubation stresses, it was possible to derive several exact results for the energy release rate due to crack growth. These general results automatically include the effects of residual stresses, traction-loaded cracks, and imperfect interfaces. By considering approximate solutions based on admissible stress states and admissible strain states, it was possible to derive rigorous upper and lower bounds to the energy release rate for crack growth. Two examples of using these equations are mode I fracture in adhesive double cantilever beam specimens and analysis of microcracking in composite laminates.

Multigrid methods for solving the steady-state incompressible Navier-Stokes equations require an appropriate smoother and coarse grid solution strategy to be effective. Classical pressure-correction methods, such as SIMPLE and SIMPLER, are widely used as solvers in engineering analysis codes, but can also be used as effective multigrid smoothers. An inexact Newton method preconditioned by a linear multigrid method with a pressurecorrection smoother can serve as a coarse grid solver. A hybrid nonlinear multigrid scheme based on combinations of these components is described. A standard benchmark problem is used to demonstrate the effectiveness of SIMPLER smoothing and the impact an inexact Newton coarse grid solver has on the resulting nonlinear multigrid scheme.

Neutron scattering and computer simulations are powerful tools for studying structural and dynamical properties of condensed matter systems in general and of polymer melts in particular. When neutron scattering studies and quantitative atomistic molecular dynamics simulations of the same material are combined, synergy between the methods can result in exciting new insights into polymer melts not obtainable from either method separately. We present here an overview of our recent efforts to combine neutron scattering and atomistic simulations in the study of melt dynamics of polyethylene and polybutadiene. Looking at polymer segmental motion on a picosecond time scale, we show how atomistic simulations can be used to identify molecular motions giving rise to relaxation processes observed in experimental dynamic susceptibility spectra. Examining larger length and longer time scale polymer dynamics involving chain self-diffusion and overall conformational relaxation, we show how simulation results can motivate experiment and how combined results of scattering and simulation can be used to critically test theories that attempt to describe melt dynamics of short polymer chains.

We present a new method called Reaction Class Transition State Theory (RC-TST) for estimating thermal rate constants of a large number of reactions in a class. This method is based on the transition state theory framework within the reaction class approach. Thermal rate constants of a given reaction in a class relative to those of its principal reaction can be efficiently predicted from only its differential barrier height and reaction energy. Such requirements are much less than what is needed by the conventional TST method. Furthermore, we have shown that the differential energetic information can be calculated at a relatively low level of theory. No frequency calculation beyond those of the principal reaction is required for this theory. The new theory was applied to a number of hydrogen abstraction reactions. Excellent agreement with experimental data shows that the RC-TST method can be very useful in design of fundamental kinetic models of complex reactions.

We present a new practical computational methodology for predicting thermal rate constants of reactions involving large molecules or a large number of elementary reactions in the same class. This methodology combines the integrated molecular orbital+molecular orbital (IMOMO) approach with our recently proposed reaction class models for tunneling. With the new methodology, we show that it is possible to significantly reduce the computational cost by several orders of magnitude while compromising the accuracy in the predicted rate constants by less than 40% over a wide range of temperatures. Another important result is that the computational cost increases only slightly as the system size increases.

A statistical procedure is proposed for estimating realistic confidence intervals for the activation energy determined by using an advanced isoconversional method. Nine sets of five thermogravimetric measurements have been produced for the process of gassification of ammonium nitrate at five different heating rates. Independent estimates of the confidence intervals for the activation energy have been obtained from these data sets. Agreement with these independent estimates demonstrates that the proposed statistical procedure is capable of adequately estimating the actual uncertainty in the activation energy determined from a small number of measurements. The resulting averaged relative errors in the activation energy were found to be 26, 21, and 17% for three, four, and five heating rate estimates, respectively.

Kinetics of the N+H₂↔NH+Hreaction have been studied using a direct ab initio dynamics method. Potential energy surface for low electronic states have been explored at the QCISD/cc-pVDZ level of theory. We found the ground-statereaction is N(⁴S)+H₂→NH(³Σ⁻)+H. Thermal rate constants for this reaction were calculated using the microcanonical variational transition state theory.Reaction path information was calculated at the QCISD/cc-pVDZ level of theory. Energies along the minimum energy path (MEP) were then refined at the QCISD(TQ)/cc-pVTZ level of theory. The forward and reverse barriers of the ground-statereaction are predicted to be 29.60 and 0.53 kcal/mol, respectively. The calculated rate constants for both forward and reverse reactions are in good agreement with available experimental data. They can be expressed as k(T)=2.33×10¹⁴ exp(-30.83 (kcal/mol)/RT) cm³mol⁻¹ s⁻¹ for the forward reaction and k(T)=5.55×10⁸T^1.44 exp(−0.78(kcal/mol)/RT) cm³ mol⁻¹ s⁻¹ for the reverse reaction in the temperature range 400–2500 K.

The NO₂ fission reaction of gas phase α-HMX has been studied using a direct ab initio method within the framework of microcanonical variational transition state theory (μVT). The potential energy calculations were calculated using the hybrid nonlocal B3LYP density functional theory with the cc-pVDZ basis set. The calculated results show that the potential energy of breaking the axial NO₂ groups is lower than that of breaking the equatorial NO₂ groups. No traditional transition state was found along the reaction path. Microcanonical rate constants calculation shows the variational transition state varies from 2.0 to 3.5 Å of the breaking N−N bond length as a function of the excess energy. The μVT method was used for thermal rate constants calculation over a temperature range from 250 to 2000 K. The fitted Arrhenius expression from the calculated data is k(T) = 1.66 × 10¹⁵ exp(−18748K/T) s^-1, which is in good agreement with the experimental data at low temperatures.

The molecular geometries and conformational energies of model molecules of poly(vinylidene fluoride) (PVDF) have been determined from high-level quantum chemistry calculations and have been used in parametrization of a six-state rotational isomeric state (RIS) model for PVDF. The model molecules investigated were 1,1,1,3,3-pentafluorobutane, 1,1,1,3,3,5,5,5-octofluoropentane, 2,2,4,4-tetrafluoropentane, and 2,2,4,4,6,6-hexafluoroheptane (HFH). Analysis of the conformations of these molecules revealed split trans minima (t₊ = 195°, t- = 165°), as was seen in previous studies of perfluoroalkanes. In contrast, the gauche minima, which split in perfluoroalkanes, did not do so in the PVDF model compounds. The lowest energy conformer of HFH, g⁺g⁺g⁺g⁺, was found to be at least 0.4 kcal/mol lower in energy per backbone dihedral than any of the conformers of HFH resembling crystalline polymorphs of PVDF, indicating that intermolecular interactions are important in stabilizing conformations of PVDF in the crystalline phases. A six-state RIS model was able to accurately reproduce the conformer energies of the PVDF model compounds. The RIS analysis revealed that, as in n-alkanes and perfluoroalkanes, the trans conformation of the backbone dihedral is intrinsically lower in energy than the gauche conformation in the PVDF model compounds. However, very large unfavorable second-order interactions between fluorine atoms occur in −CH₂− centered t₊t₊ sequences and, to a lesser extent, t₊g⁺ and t₊g^- sequences. The quantum chemistry based RIS model yielded a characteristic ratio for PVDF in good agreement with experiment, but with significantly different conformer populations than predicted by earlier RIS models, including a much higher gauche probability. The high gauche probability of 65% for unperturbed PVDF chains (at 463 K), greater than that for poly(ethylene) and much greater than that for poly(tetrafluoroethylene), is a consequence of the unfavorable second-order interactions occurring in −CH₂− centered sequences containing trans conformations.

Dimethylnitramine (DMNA) is used as a model system for investigating accurate and efficient electronic structure methods for nitramines. Critical points on the potential energy surfaces of DMNA, CH₃NCH₃, CH₃NCH₂, NO₂, HONO, and the transition state to HONO elimination were located through geometry optimizations using the B1LYP, B3LYP, MPW1PW91, and BH&HLYP density functional methods, in addition to MP2, G2(MP2), and QCISD ab initio theories using the cc-pVDZ basis set. For cost-effective determination of nitramine reaction energetics, highly correlated single-point calculations at DFT geometries are recommended. Our best estimated reaction enthalpies for N-N bond scission and HONO elimination are 41.6 and −0.9 kcal/mol, respectively, determined at the QCISD(T)//QCISD level of theory. These numbers can be reproduced to within 1.3 kcal/mol for the N-N bond and to within 0.5 kcal/mol for the HONO reaction by calculating QCISD(T) energies at B1LYP geometries, thus saving considerable computational cost without sacrificing accuracy. Using the same strategy, the transition state energy for HONO elimination can be modeled to within 0.1 kcal/mol of the QCISD(T)//QCISD result.

An embedded cluster model is used to estimate the molecular dipole moment of crystalline dimethylnitramine (DMNA). The electrostatic potential due to the crystal is included in the calculation via the SCREEP (surface charge representation of the electrostatic embedding potential) approach. The resulting dipole moment for DMNA in the crystalline environment is 6.69 D. This number is more than 40% greater than the gas-phase value and 15% greater than the estimated dipole moment in the liquid phase, thus providing evidence of a strong polarization effect in condensed phases of DMNA.

A direct ab initio dynamics study on the gas-phase reactions of atomic hydrogen with different fluoromethanes has been carried out. The thermal rate constants were calculated using canonical variational transition state (CVT) theory augmented by multidimensional semiclassical zero and small curvature tunneling approximations. The potential energy surfaces for the reactions were calculated using hybrid density functional theory, namely, Becke's half-and-half (BH) nonlocal exchange and the Lee−Yang−Parr (LYP) nonlocal correlation functionals using the cc-pVDZ basis set. The reaction energies and barrier heights were improved by single-point energy calculations along the minimum energy path (MEP) at the spin-projected fourth order Moller−Plesset perturbation theory (PMP4) using the cc-pVTZ basis set. The calculated forward and reverse thermal rate constants are in the good agreement with the experimental data. The electronic effects of fluorine substitution on the rate of this class of reactions are examined.

By partitioning the total stresses in a damaged composite into either mechanical and residual stresses or into initial and pertubation stresses, it was possible to derive several exact results for the energy release rate due to crack growth. These general results automatically include the effects of residual stresses, traction-loaded cracks, and imperfect interfaces. By considering approximate solutions based on admissible stress states and admissible strain states, it was possible to derive rigorous upper and lower bounds to the energy release rate for crack growth. Two examples of using these equations are mode I fracture in adhesive double cantilever beam specimens and analysis of microcracking in composite laminates.

Keywords: Fracture Mechanics, Energy Release Rate, Residual Stresses, Adhesive Fracture, Matrix Microcracking

The thermal degradation of poly(methyl methacrylate) (PMMA) has been studied in both pure nitrogen and oxygen-containing atmospheres. The presence of oxygen increases the initial decomposition temperature by 70 °C. The stabilizing effect of oxygen may be explained by forming thermally stable radical species that suppress unzipping of the polymer. This assumption is supported by the experimental fact that introduction of NO into gaseous atmosphere increases the initial decomposition temperature by more than 100 °C. The model-free isoconversional method has been used to determine the dependence of the effective activation energy on the extent of degradation. The initial stages of the process show a dramatic difference in the activation energies that were found to be 60 and 220 kJ mol^-1 for respective degradations in nitrogen and air.

The thermal degradation of poly(methyl methacrylate) has been studied under nitrogen and air. The presence of oxygen increases the initial decomposition temperature by 70 degrees C. The stabilizing effect of oxygen is explained by the formation of thermally stable radical species that suppress unzipping of the polymer. This assumption is supported by the experimental fact that introduction of NO into the gaseous atmosphere increases the initial decomposition temperature by more than 100 degrees C.

The molecular geometries and conformational energies of octahydro-1,3,5,7-tetranitro-1,3,5,7-tetrazocine (HMX) and 1,3-dimethyl-1,3-dinitro methyldiamine (DDMD) and have been determined from high-level quantum chemistry calculations and have been used in parametrizing a classical potential function for simulations of HMX. Geometry optimizations for HMX and DDMD and rotational energy barrier searches for DDMD were performed at the B3LYP/6-311G** level, with subsequent single-point energy calculations at the MP2/6-311G** level. Four unique low-energy conformers were found for HMX, two whose conformational geometries correspond closely to those found in HMX polymorphs from crystallographic studies and two additional, lower energy conformers that are not seen in the crystalline phases. For DDMD, three unique low-energy conformers, and the rotational energy barriers between them, were located. In parametrizing the classical potential function for HMX, nonbonded repulsion/dispersion parameters, valence parameters, and parameters describing nitro group rotation and out-of-plane distortion at the amine nitrogen were taken from our previous studies of dimethylnitramine. Polar effects in HMX and DDMD were represented by sets of partial atomic charges that reproduce the electrostatic potential and dipole moments for the low-energy conformers of these molecules as determined from the quantum chemistry wave functions. Parameters describing conformational energetics for the C−N−C−N dihedrals were determined by fitting the classical potential function to reproduce relative conformational energies in HMX as found from quantum chemistry. The resulting potential was found to give a good representation of the conformer geometries and relative conformer energies in HMX and a reasonable description of the low-energy conformers and rotational energy barriers in DDMD.

We have made detailed comparison of the local and chain dynamics of a melt of 1,4-polybutadiene (PBD) as determined from experiment and molecular dynamics simulation at 353 K. The PBD was found to have a random microstructure consisting of 40% cis, 50% trans, and 10% 1,2-vinyl units with a number-average degree of polymerization 〈X_n〉 = 25.4. Local (conformational) dynamics were studied via measurements of the ¹³C NMR spin−lattice relaxation time T₁ and the nuclear Overhauser enhancement (NOE) at a proton resonance of 300 MHz for 12 distinguishable nuclei. Chain dynamics were studied on time scales up to 22 ns via neutron spin−echo (NSE) spectroscopy with momentum transfers ranging from q = 0.05 to 0.30 Å^-1. Molecular dynamics simulations of a 100 carbon (X_n = 25) PBD random copolymer of 50% trans and 50% cis units employing a quantum chemistry-based united atom potential function were performed at 353 K. The T₁ and NOE values obtained from simulation, as well as the center of mass diffusion coefficient and dynamic structure factor, were found to be in qualitative agreement with experiment. However, comparison of T₁ and NOE values for the various distinguishable resonances revealed that the local dynamics of the simulated chains were systematically too fast, whereas comparison with the center of mass diffusion coefficient revealed a similar trend in the chain dynamics. To improve agreement with experiment, (1) the chain length was increased to match the experimental M_z, (2) vinyl units groups were included in the chain microstructure, and (3) rotational energy barriers were increased by 0.4 kcal/mol in order to reduce the rate of conformational transitions. With these changes, dynamic properties from simulation were found to differ 20-30% or less from experiment, comparable to the agreement seen in previous simulations of polyethylene using a quantum chemistry-based united atom potential.