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This distinctive textbook aims to introduce readers to the basic structures of the mechanics of deformable bodies, with a special emphasis on the description of the elastic behavior of simple materials and structures composed by elastic beams.  The authors take a deductive rather than inductive approach and start from a few first, foundational principles.  A wide selection of exercises, many with hints and solutions, are provided throughout and organized in a way that will allow readers to form a link between abstract mathematical concepts and real-world applications. The text begins with the definition of bodies and deformations, keeping the kinematics of rigid bodies as a special case; the authors also distinguish between material and spatial metrics, defining each one in the pertinent space.  Subsequent chapters cover observers and classes of possible changes; forces, torques, and related balances, which are derived from the invariance under classical changes in observers of the power of the external actions over a body, rather than postulated a priori; constitutive structures; variational principles in linear elasticity; the de Saint-Venant problem; yield criteria and a discussion of their role in the representation of material behavior; and an overview of some bifurcation phenomena, focusing on the Euler rod.  An appendix on tensor algebra and tensor calculus is included for readers who need a brief refresher on these topics. Fundamentals of the Mechanics of Solids is primarily intended for graduate and advanced undergraduate students in various fields of engineering and applied mathematics.  Prerequisites include basic courses in calculus, mathematical analysis, and classical mechanics.

Applied Physics --- Engineering & Applied Sciences --- Mathematics. --- Mathematical physics. --- Mechanics. --- Continuum mechanics. --- Mathematical Applications in the Physical Sciences. --- Continuum Mechanics and Mechanics of Materials. --- Mathematical Physics. --- Mechanics, Applied. --- Solid Mechanics. --- Classical Mechanics. --- Applied mechanics --- Engineering, Mechanical --- Engineering mathematics --- Classical mechanics --- Newtonian mechanics --- Physics --- Dynamics --- Quantum theory --- Physical mathematics --- Mathematics

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Granular matter displays a variety of peculiarities that distinguish it from other appearances studied in condensed matter physics and renders its overall mathematical modelling somewhat arduous. Prominent directions in the modelling granular flows are analyzed from various points of view. Foundational issues, numerical schemes and experimental results are discussed. The volume furnishes a rather complete overview of the current research trends in the mechanics of granular matter. Various chapters introduce the reader to different points of view and related techniques. New models describing granular bodies as complex bodies are presented. Results on the analysis of the inelastic Boltzmann equations are collected in different chapters. Gallavotti-Cohen symmetry is also discussed.

Granular materials --- Matériaux granulaires --- Mathematical models. --- Modèles mathématiques --- Mathematical Theory --- Materials Science --- Mathematics --- Chemical & Materials Engineering --- Physical Sciences & Mathematics --- Engineering & Applied Sciences --- Mathematical models --- Engineering. --- Mathematics. --- Physics. --- Amorphous substances. --- Complex fluids. --- Industrial engineering. --- Production engineering. --- Industrial and Production Engineering. --- Mathematics, general. --- Mathematical Methods in Physics. --- Soft and Granular Matter, Complex Fluids and Microfluidics. --- Manufacturing engineering --- Process engineering --- Industrial engineering --- Mechanical engineering --- Management engineering --- Simplification in industry --- Engineering --- Value analysis (Cost control) --- Complex liquids --- Fluids, Complex --- Amorphous substances --- Liquids --- Natural philosophy --- Philosophy, Natural --- Physical sciences --- Dynamics --- Math --- Science --- Construction --- Industrial arts --- Technology --- Bulk solids --- Materials --- Mathematical physics. --- Physical mathematics --- Physics --- Soft condensed matter

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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.

Mathematical models. --- Engineering geology. --- Engineering—Geology. --- Foundations. --- Hydraulics. --- Applied mathematics. --- Engineering mathematics. --- Mechanics. --- Mathematical Modeling and Industrial Mathematics. --- Geoengineering, Foundations, Hydraulics. --- Applications of Mathematics. --- Classical Mechanics. --- Classical mechanics --- Newtonian mechanics --- Physics --- Dynamics --- Quantum theory --- Engineering --- Engineering analysis --- Mathematical analysis --- Flow of water --- Water --- Fluid mechanics --- Hydraulic engineering --- Jets --- Architecture --- Building --- Structural engineering --- Underground construction --- Caissons --- Earthwork --- Masonry --- Soil consolidation --- Soil mechanics --- Walls --- Civil engineering --- Geology, Economic --- Models, Mathematical --- Simulation methods --- Mathematics --- Flow --- Distribution --- Details --- Geology --- Granular materials. --- Bulk solids --- Materials