Responding to the latest developments in rock physics research, this popular reference book has been thoroughly updated while retaining its comprehensive coverage of the fundamental theory, concepts, and laboratory results. It brings together the vast literature from the field to address the relationships between geophysical observations and the underlying physical properties of Earth materials - including water, hydrocarbons, gases, minerals, rocks, ice, magma and methane hydrates. This third edition includes expanded coverage of topics such as effective medium models, viscoelasticity, attenuation, anisotropy, electrical-elastic cross relations, and highlights applications in unconventional reservoirs. Appendices have been enhanced with new materials and properties, while worked examples (supplemented by online datasets and MATLAB® codes) enable readers to implement the workflows and models in practice. This significantly revised edition will continue to be the go-to reference for students and researchers interested in rock physics, near-surface geophysics, seismology, and professionals in the oil and gas industries.

The Rock Physics Handbook

We present a semi-implicit cloth simulation technique that is very stable yet also responsive. The stability of the technique allows the use of a large fixed time step when simulating all types of fabrics and character motions. The animations generated using this technique are strikingly realistic. Wrinkles form and disappear in a quite natural way, which is the feature that most distinguishes textile fabrics from other sheet materials. Significant improvements in both the stability and realism were made possible by overcoming the post-buckling instability as well as the numerical instability. The instability caused by buckling arises from a structural instability and therefore cannot be avoided by simply employing a semi-implicit method. Addition of a damping force may help to avoid instabilities; however, it can significantly degrade the realism of the cloth motion. The method presented here uses a particle-based physical model to handle the instability in the post-buckling response without introducing any fictitious damping.

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Stable but responsive cloth

Discontinuous enrichment in finite elements with a partition of unity method

Graded finite elements are presented within the framework of a generalized isoparametric formulation. Such elements possess a spatially varying material property field, e.g. Young's modulus (E) and Poisson's ratio () for isotropic materials; and principal Young's moduli (E11,E22), in-plane shear modulus (G12), and Poisson's ratio (12) for orthotropic materials. To investigate the influence of material property variation, both exponentially and linearly graded materials are considered and compared. Several boundary value problems involving continuously nonhomogeneous isotropic and orthotropic materials are solved, and the performance of graded elements is compared to that of conventional homogeneous elements with reference to analytical solutions. Such solutions are obtained for an orthotropic plate of infinite length and finite width subjected to various loading conditions. The corresponding solutions for an isotropic plate are obtained from those for the orthotropic plate. In general, graded finite elements provide more accurate local stress than conventional homogeneous elements, however, such may not be the case for four-node quadrilateral (Q4) elements. The framework described here can serve as the basis for further investigations such as thermal and dynamic problems in functionally graded materials. ©2002 ASME

Isoparametric graded finite elements for nonhomogeneous isotropic and orthotropic materials

The effects of non-periodic microstructure on the elastic properties of two-dimensional cellular solids

The nonhomogeneous materials considered in this work are of a class whose elastic moduli are specified by continuous and generally differentiable functions of the spatial coordinates. The elastic stress and displacement fields near a crack tip in a two-dimensional nonhomogeneous cracked body are derived utilizing an extension of the Wiliams eigenfunction expansion technique. The nature of the stress and strain singularity is ascertained to be precisely of the same form as the well-known inverse square root stress singularity near a crack tip in a homogeneous material, independent of the functional form of the elastic moduli variation. A new quasipath-independent integral has been generated which proves useful for computing the energy release rate and mixed-mode stress intensity factors in nonhomogeneous cracked bodies. The integral is used in conjunction with finite element analysis for purposes of computing stress intensity factors. Numerical results are compared with certain exact solutions which are available for nonhomogeneous cracked bodies. Cracked composite bodies have traditionally been modeled and analyzed as possessing discontinuous elastic moduli, but are treated here as having rapid, but smooth variations of the material properties.

Fracture of nonhomogeneous materials

Software based on nonlinear shell theory can simulate 3D motions related to real fabric-manufacturing processes. This simulation capability advances the technologies necessary for automating the textile and apparel industries.

Finite-element modeling and control of flexible fabric parts

The boundary element method is applied to determine the effective elastic moduli of continuum models of composite materials. In this paper, we specialize to the idealized model of hexagonal arrays of infinitely long, aligned cylinders in a matrix (a model of a fiber‐reinforced material) or a thin‐plate composite consisting of hexagonal arrays of disks in a matrix. Thus, one need only consider two‐dimensional elasticity, i.e., either plane‐strain or plane‐stress elasticity. This paper examines a variety of cases in which the inclusions are either stiffer or weaker than the matrix for a wide range of inclusion volume fractions φ2. Our comprehensive set of simulation data for the elastic moduli are tabulated. Using the boundary element method, a key microstructural parameter η2 that arises in rigorous three‐point bounds on the effective shear modulus is also computed. Our numerical simulations of the elastic moduli for the hexagonal array are compared to rigorous two‐point and three‐point bounds on the respective effective properties. In the extreme instances of either superrigid particles or voids, we compare analytical relations for the elastic moduli near dilute and close packing limits to our simulation results.

J. W. Eischen

Papers

Fracture of nonhomogeneous materials

Finite-element modeling and control of flexible fabric parts

Determining elastic behavior of composites by the boundary element method

An improved method for computing the J2 integral

Realistic Modeling of Edge Effect Stresses in Bimaterial Elements