Herbert F. Wang

Bio: Herbert F. Wang is an academic researcher from University of Wisconsin-Madison. The author has contributed to research in topics: Poromechanics & Bulk modulus. The author has an hindex of 36, co-authored 90 publications receiving 7674 citations. Previous affiliations of Herbert F. Wang include University of Tokyo.

Single Crystal Elastic Constants and Calculated Aggregate Properties. A Handbook

Abstract: Data on the elastic properties of single crystals has increased dramatically since Professor Simmons completed his first book in 1965. While this book is a consolidation of his earlier work, it has been extensively updated and revised to include new material and references, is far more complete, and is presented in a more useful form.This is actually a handbook consisting of computer printout in tabular format. It presents data on the elastic properties of single crystals collected from the literature through mid-1970 and the elastic properties of isotropic aggregates which are calculated according to the schemes of Voigt and Reuss for all materials, and Hashin and Shtrikman for materials with cubic symmetry. The tables include about 3000 determinations.At present it is impossible to calculate the elastic properties of a random, macroscopically isotropic aggregate of crystals from the single crystal elastic constants, but bounds may be obtained for the aggregate properties from the single crystal constants. Accordingly the book tabulates the Voigt and Reuss averages for all materials for which single crystal data has been reported. Hashin and Shtrikman have shown that the Voigt and Reuss bounds could be improved, and they have developed expressions for the corresponding bounds of aggregates of cubic crystals.In this book all four bounds (Voigt, Hashin, Shtrikman, and Reuss) are tabulated for cubic materials while Voigt and Reuss bounds only are tabulated for non-cubic materials. The elastic properties of aggregates are those in common use and include Young's modulus, shear modulus, Poisson's ration, bulk modulus, compressibility, velocity of compressional waves, and the velocity of shear waves. Although any two of these properties suffice to uniquely characterize a given material, all are tabulated because different sets are best suited for different uses.

Introduction to Groundwater Modeling: Finite Difference and Finite Element Methods

Abstract: Introduction to Groundwater Modeling presents an overview of the fundamental concepts and applications of computerized groundwater modeling.

Ultrasonic velocities in Cretaceous shales from the Williston basin

Abstract: Compressional and shear‐wave velocities were measured in the laboratory from 1 bar to 4 kbar confining pressure for wet, undrained samples of Cretaceous shales from depths of 3200 and 5000 ft in the Williston basin, North Dakota. These shales behave as transversely isotropic elastic media, the plane of circular symmetry coinciding with the bedding plane. For compressional waves, the velocity is higher for propagation in the bedding plane than at right angles to it, and the anisotropy is greater for the 5000-ft shale. For shear waves, the SH‐wave perpendicular to bedding and the SV‐wave parallel to bedding propagate with the same speed, which is about 25 percent lower than that for the SH‐wave parallel to bedding. In general, compressional and shear velocities are higher for the indurated 5000-ft shale than for the friable 3200-ft shale. All velocities increase with in‐increasing confining pressure to 4 kbar. The 3200-ft shale exhibits velocity hysteresis as a function of pressure, whereas this effect is a...

The elastic coefficients of double‐porosity models for fluid transport in jointed rock

Abstract: Phenomenological equations (with coefficients to be determined by specified experiments) for the poroelastic behavior of a dual porosity medium are formulated, and the coefficients in these linear equations are identified. The generalization from the single-porosity case increases the number of independent coefficients for volume deformation from three to six for an isotropic applied stress. The physical interpretations are based upon considerations of different temporal and spatial scales. For very short times, both matrix and fractures behave in an undrained fashion. For very long times, the double-porosity medium behaves like an equivalent single-porosity medium. At the macroscopic spatial level, the pertinent parameters (such as the total compressibility) may be determined by appropriate field tests. At an intermediate or mesoscopic scale, pertinent parameters of the rock matrix can be determined directly through laboratory measurements on core, and the compressibility can be measured for a single fracture. All six coefficients are determined from the three poroelastic matrix coefficients and the fracture compressibility from the single assumption that the solid grain modulus of the composite is approximately the same as that of the matrix for a small fracture porosity. Under this assumption, the total compressibility and three-dimensional storage coefficient of the composite are the volume averages of the matrix and fracture contributions.

An improved technique for determining hardness and elastic modulus using load and displacement sensing indentation experiments

Abstract: The indentation load-displacement behavior of six materials tested with a Berkovich indenter has been carefully documented to establish an improved method for determining hardness and elastic modulus from indentation load-displacement data. The materials included fused silica, soda–lime glass, and single crystals of aluminum, tungsten, quartz, and sapphire. It is shown that the load–displacement curves during unloading in these materials are not linear, even in the initial stages, thereby suggesting that the flat punch approximation used so often in the analysis of unloading data is not entirely adequate. An analysis technique is presented that accounts for the curvature in the unloading data and provides a physically justifiable procedure for determining the depth which should be used in conjunction with the indenter shape function to establish the contact area at peak load. The hardnesses and elastic moduli of the six materials are computed using the analysis procedure and compared with values determined by independent means to assess the accuracy of the method. The results show that with good technique, moduli can be measured to within 5%.

Weak elastic anisotropy

Abstract: Most bulk elastic media are weakly anisotropic. -The equations governing weak anisotropy are much simpler than those governing strong anisotropy, and they are much easier to grasp intuitively. These equations indicate that a certain anisotropic parameter (denoted 6) controls most anisotropic phenomena of importance in exploration geophysics. some of which are nonnegligible even when the anisotropy is weak. The critical parameter 6 is an awkward combination of elastic parameters, a combination which is totally independent of horizontal velocity and which may be either positive or negative in natural contexts.

Verification, Validation, and Confirmation of Numerical Models in the Earth Sciences

Abstract: Verification and validation of numerical models of natural systems is impossible. This is because natural systems are never closed and because model results are always nonunique. Models can be confirmed by the demonstration of agreement between observation and prediction, but confirmation is inherently partial. Complete confirmation is logically precluded by the fallacy of affirming the consequent and by incomplete access to natural phenomena. Models can only be evaluated in relative terms, and their predictive value is always open to question. The primary value of models is heuristic.

Structural stability and lattice defects in copper: Ab initio , tight-binding, and embedded-atom calculations

Abstract: We evaluate the ability of the embedded-atom method ~EAM! potentials and the tight-binding ~TB! method to predict reliably energies and stability of nonequilibrium structures by taking Cu as a model material. Two EAM potentials are used here. One is constructed in this work by using more fitting parameters than usual and including ab initio energies in the fitting database. The other potential was constructed previously using a traditional scheme. Excellent agreement is observed between ab initio, TB, and EAM results for the energies and stability of several nonequilibrium structures of Cu, as well as for energies along deformation paths between different structures. We conclude that not only TB calculations but also EAM potentials can be suitable for simulations in which correct energies and stability of different atomic configurations are essential, at least for Cu. The bcc, simple cubic, and diamond structures of Cu were identified as elastically unstable, while some other structures ~e.g., hcp and 9R! are metastable. As an application of this analysis, nonequilibrium structures of epitaxial Cu films on~001!-oriented fcc or bcc substrates are evaluated using a simple model and atomistic simulations with an EAM potential. In agreement with experimental data, the structure of the film can be either deformed fcc or deformed hcp. The bcc structure cannot be stabilized by epitaxial constraints.