Paolo Maria Mariano - Böcker

Stringent industrial requirements for sophisticated performance and circumstantial control of microdevices or nanotechnology manufacturing, and other types of machinery at multiple scales, require complex materials. The adjective 'complex' indicates that the substructure influences gross mechanical behaviour in a prominent way and interactions due to substructural changes are represented directly. Examples are liquid crystals, quasi-periodic alloys, polymeric bodies, spin glasses, magnetostrictive materials and ferroelectrics, suspensions, in particular liquids with gas bubbles, polarizable fluids, etc.

The mechanical behaviour of complex bodies described in this book gives rise to a wide variety of challenging problems from the macroscopic- to the nano-world. The chapters composing this book explore various aspects of these problems, giving rise to new areas of discussion together with specific solutions.

Contributors are Carlo Cercignani, Gianfranco Capriz, Pierre Degond, Antonio Fasano, Harley T. Johnson, Sukky Jun, Krishna Kannan, Wing Kam Liu, Alberto Mancini, Paolo Maria Mariano, Ingo M�ller, Kumbakonan R. Rajagopal, Jan Jerzy Slawianowski.

Material Substructures in Complex Bodies will be a useful tool for researchers and students working on the basic mathematical and physical problems accruing from the mechanics of materials.

Leading scientific competence of contributors Clear writing style linking solutions and open problems Suggestions for direct technological applications and new research work Mathematical models for nanotechnology devices

The current use of complex materials in nanotechnology and industrial engineering has led to a number of intricate problems in mechanics, and the macroscopic behavior of such materials often depends critically on their substructures. This work, written by leading mathematicians and engineers, features a broad range of topics that offer both experimental results and clear, detailed answers to fundamental questions about the general formulation of multifield theories within the context of modeling material substructures. Applied mathematicians, mechanical and structural engineers, material scientists, graduate students, and researchers in the above areas will benefit from the work and may find suggestions for further research in its rich collection of open problems.

Toachieve design, implementation,and servicing ofcomplex systems and struc­ tures in an efficient and cost-effective way,a deeper knowledge and understanding of the subtle cast and detailed evolution of materials is needed. The analysis in demand borders with the molecular and atomic one, spanning all the way down from classical continua. The study of the behavior of complex materials in sophisticated devices also opens intricate questions about the applicability of primary axioms ofcontinuum mechanics such as the ultimate nature of the material element itselfand the possibility ofidentifying itperfectly. So it is necessary to develop tools that allow usto formulate both theoretical models and methods of numerical approximation for the analysis of material substructures. Multifield theories in continuum mechanics, which bridge classical materials science and modern continuum mechanics, provide precisely these tools. Multifield theories not only address problems of material substructures, but also encompass well-recognized approaches to the study of soft condensed matter and allow one to model disparate conditions in various states ofmatter. However, research inmultifield theories is vast, and there is little in the way of a comprehensive distillation of the subject from an engineer's perspective. Therefore, the papers in the present volume, 1 which grew out of our experience as editors for an engineeringjournal, tackle some fundamental questions,suggest solutions of concrete problems, and strive to interpret a host of experimental evidence. In this spirit, each of the authors has contributed original results having in mind their wider applicability.

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.

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.

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 sandEvaluation of effective stress in unsaturated soilsHyper-plasticityWave propagation in granular systemsPartly saturated porous mediaMulti-scale approaches to the dynamics of sparse mediaViews 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.

This volume provides a timely survey of interactions between the calculus of variations and theoretical and applied mechanics. Chapters have been significantly expanded since preliminary versions appeared in a special issue of the Journal of Optimization Theory and Applications (184(1), 2020) on “Calculus of Variations in Mechanics and Related Fields”. The variety of topics covered offers researchers an overview of problems in mechanics that can be analyzed with variational techniques, making this a valuable reference for researchers in the field. It also presents ideas for possible future areas of research, showing how the mastery of these foundational mathematical techniques can be used for many exciting applications. Specific topics covered include:Topology optimizationIdentification of material propertiesOptimal controlPlastic flowsGradient polyconvexityObstacle problemsQuasi-monotonicityVariational Views in Mechanics will appeal to researchers in mathematics, solid-states physics, and mechanical, civil, and materials engineering.

This volume provides a timely survey of interactions between the calculus of variations and theoretical and applied mechanics. Chapters have been significantly expanded since preliminary versions appeared in a special issue of the Journal of Optimization Theory and Applications (184(1), 2020) on “Calculus of Variations in Mechanics and Related Fields”. The variety of topics covered offers researchers an overview of problems in mechanics that can be analyzed with variational techniques, making this a valuable reference for researchers in the field. It also presents ideas for possible future areas of research, showing how the mastery of these foundational mathematical techniques can be used for many exciting applications. Specific topics covered include:Topology optimizationIdentification of material propertiesOptimal controlPlastic flowsGradient polyconvexityObstacle problemsQuasi-monotonicityVariational Views in Mechanics will appeal to researchers in mathematics, solid-states physics, and mechanical, civil, and materials engineering.

This special issue collects selected contributions (excluding general lectures) of a Symposium on "Micro to MACRO Mathematical Modelling in Soil Mechanics", which took place at the University of Reggio Calabria, Italy, from May 29th to June 1st, 2018.The Symposium provided an opportunity to enhance the scientific debate on the construction of mathematical models for the description of the physical behaviour of soils, as well as on the suggestions provided by the micro-mechanical observation of the matter. The focus was on the comparison between the appropriateness of models and the need of mathematics to obtain rigorous results, which involves know-how from applied mathematical physics, geotechnical engineering and mechanics of solids.The contributions were selected by the Editors and the other Members of the Scientific Committee of the Symposium: Gianfranco Capriz (Pisa, Roma), Claudio di Prisco (Milan), Wolfgang Ehlers (Stuttgart), James T. Jenkins (Cornell), Stefan Luding (Twente), David Muir Wood (Dundee), Kenichi Soga (Berkeley).