A traction-displacement relationship that may be embedded into a cohesive zone model for microscale problems of intergranular fracture is extracted from atomistic molecular-dynamics

A molecular-dynamics model for crack propagation under steady-state conditions is used to study dynamic instabilities along a grain boundary in aluminum that occur when the crack speed approaches 1/3 of the material's Rayleigh wave speed. Instead of crack branching, as is characteristic for a crack propagating in a homogeneous environment, the instability of an intergranular crack results in a periodic series of dislocation bursts. These bursts limit the crack speed and produce velocity oscillations with a large increase in energy dissipation that increases the grain boundary toughness.

Multiazimuth binning of 3-D P-wave reflection data is a relatively simple but robust way of characterizing the spatial distribution of gas-producing natural fractures. In our survey, data were divided into two volumes by ray azimuth (approximately perpendicular and parallel (±45 • ) to the dominant fracture strike) and separately processed. Azimuthal differences or ratios of attributes provided a rough measure of anisotropy. Improved imaging was also attained in the more coherent fractureparallel volume. A neural network using azimuthally dependent velocity, reflectivity, and frequency attributes identified commercial gas wells with greater than 85% success. Furthermore, we were able to interpret the physical mechanisms of most of these correlations and so better generalize the approach. The apparent velocity anisotropy was compared to that derived from other Pand S-wave methods in an inset three-component survey. Prestack determination of the azimuthal moveout ellipse will best quantify velocity anisotropy, but simple two-or four-azimuth poststack analysis can adequately identify regions of high fracture density and gas yield.

The dynamics and energetics of intergranular crack growth along a flat grain boundary in aluminum is studied by a molecular-dynamics simulation model for crack propagation under steady-state conditions. Using the ability of the molecular-dynamics simulation to identify atoms involved in different atomistic mechanisms, it was possible to identify the energy contribution of different processes taking place during crack growth. The energy contributions were divided as: elastic energy -defined as the potential energy of the atoms in fcc crystallographic state; and plastically stored energy -the energy of stacking faults and twin boundaries; grain-boundary and surface energy. In addition, monitoring the amount of heat exchange with the moleculardynamics thermostat gives the energy dissipated as heat in the system. The energetic analysis indicates that the majority of energy in a fast growing crack is dissipated as heat. This dissipation increases linearly at low speed, and faster than linear at speeds approaching 1/3 the Rayleigh wave speed when the crack tip becomes dynamically unstable producing periodic dislocation bursts until the crack is blunted.

A meshless local Petrov-Galerkin (MLPG) method that uses radial basis functions rather than generalized moving least squares (GMLS) interpolations to develop the trial functions in the study of Euler-Bernoulli beam problems is presented. The use of radial basis functions (RBF) in meshless methods is demonstrated for C 1 problems for the first time. This interpolation choice yields a computationally simpler method as fewer matrix inversions and multiplications are required than when GMLS interpolations are used. Test functions are chosen as simple weight functions as in the conventional MLPG method. Patch tests, mixed boundary value problems, and problems with complex loading conditions are considered. The radial basis MLPG method yields accurate results for deflections, slopes, moments, and shear forces, and the accuracy of these results is better than that obtained using the conventional MLPG method.Keywords Meshless methods, MLPG method, Beam problems, Radial basis functions IntroductionMeshless methods are developed to overcome some of the disadvantages of the finite element method (FEM) such as discontinuous secondary variables across inter-element boundaries and the need for remeshing in large deformation problems [1][2][3][4][5][6][7][8][9][10][11][12][13][15][16][17][18][19][20]. Two recent monographs [2, 10] summarize the status on meshless methods to date. Recent literature shows extensive research on meshless methods and, in particular, the meshless local PetrovGalerkin (MLPG) method. The majority of literature published to date on the MLPG method presents variations of the method for C 0 problems. A comparatively limited amount of work [1, 6-9] is reported on C 1 problems. The additional degrees of freedom involved in C 1 problems introduce levels of complexity that are difficult to implement in meshless methods. Atluri, Cho, and Kim [1] present an analysis of thin beam problems using a Galerkin implementation of the MLPG method. In reference 1, a generalized moving least squares (GMLS) approximation is used to construct the trial functions, and the test functions are chosen from the same space. In references 13, 15, and 17, an MLPG method is presented where a GMLS approximation is used to construct the trial functions and test functions are chosen from a different space. Closer scrutiny of these formulations shows that a large number of calculations are required to compute the first and second order derivatives of the moving least squares (MLS) trial functions. Hence, a computationally simpler alternative to the MLS trial functions that provides the same accuracy as the MLS functions is preferred.In this paper, the use of radial basis interpolation functions (see references 14, 21, 22) as trial functions is explored in the MLPG formulation for beam problems. The radial basis functions and their implementation are simple, and the evaluation of the derivatives is much simpler than for the traditional MLS approximations [16]. In the present radial basis MLPG formulation (abbreviated hereafter as RPG), si...