This monograph describes various methods for solving deformation problems of particulate solids, taking the reader from analytical to computational methods. The book is the first to present the topic of linear elasticity in mathematical terms that will be familiar to anyone with a grounding in fluid mechanics. It incorporates the latest advances in computational algorithms for elliptic partial differential equations, and provides the groundwork for simulations on high performance parallel computers. Numerous exercises complement the theoretical discussions, and a related set of self-documented programs is available to readers with Internet access. The work will be of interest to advanced students and practicing researchers in mechanical engineering, chemical engineering, applied physics, computational methods, and developers of numerical modeling software.

This accessible text presents a unified approach of treating the microstructure and effective properties of heterogeneous media. Part I deals with the quantitative characterization of the microstructure of heterogeneous via theoretical methods; Part II treats a wide variety of effective properties of heterogeneous materials and how they are linked to the microstructure, accomplished by using rigorous methods.

This book is for a general scientific and engineering audience as a guide to current ideas, methods, and models for stochastic modeling of microstructures. It is a reference for professionals in material modeling, mechanical engineering, materials science, chemical, civil, environmental engineering and applied mathematics.

An area at the intersection of solid mechanics, materials science, and stochastic mathematics, mechanics of materials often necessitates a stochastic approach to grasp the effects of spatial randomness. Using this approach, Microstructural Randomness and Scaling in Mechanics of Materials explores numerous stochastic models and methods used in the m

This contributed volume provides an up-to-date overview of the mechanics of granular materials, ranging from sparse media to soils. With chapters exploring state-of-the-art theoretical, experimental, and applied trends in the study of granular matter in various states, readers will be motivated to learn about the current challenges and potential avenues of exploration in this active area of research. Including a variety of perspectives, this volume will be a valuable reference for audiences in a number of fields. Specific topics covered include: X-ray tomography techniques for analyzing sand Evaluation of effective stress in unsaturated soils Hyper-plasticity Wave propagation in granular systems Partly saturated porous media Multi-scale approaches to the dynamics of sparse media Views on Microstructures in Granular Materials is an ideal resource for PhD students and researchers in applied mathematics, solid-state physics, civil engineering, and mechanical engineering.

Examines the advances made in the field in recent years and looks at the various methods now used; ideal for graduate students and researchers.