This book examines key theoretical tools that are currently used to develop mathematical models as an aid in understanding the biological response of cells and tissues to mechanical stimuli. Problems in growth and remodeling, tissue and organ development, and functional adaptation are all covered. Chapters on tensor analysis and nonlinear elasticity provide the necessary background for understanding the engineering theories that are currently used to solve challenges in mechanobiology. This is an ideal book for biomechanical engineers who work on problems in mechanobiology and tissue engineering.
This book develops continuum modeling skills and approaches the topic from three sides: (1) derivation of global integral laws together with the associated local differential equations, (2) design of constitutive laws and (3) modeling boundary processes. The focus of this presentation lies on many practical examples covering aspects such as coupled flow, diffusion and reaction in porous media or microwave heating of a pizza, as well as traffic issues in bacterial colonies and energy harvesting from geothermal wells. The target audience comprises primarily graduate students in pure and applied mathematics as well as working practitioners in engineering who are faced by nonstandard rheological topics like those typically arising in the food industry.
Material properties emerge from phenomena on scales ranging from Angstroms to millimeters, and only a multiscale treatment can provide a complete understanding. Materials researchers must therefore understand fundamental concepts and techniques from different fields, and these are presented in a comprehensive and integrated fashion for the first time in this book. Incorporating continuum mechanics, quantum mechanics, statistical mechanics, atomistic simulations and multiscale techniques, the book explains many of the key theoretical ideas behind multiscale modeling. Classical topics are blended with new techniques to demonstrate the connections between different fields and highlight current research trends. Example applications drawn from modern research on the thermo-mechanical properties of crystalline solids are used as a unifying focus throughout the text. Together with its companion book, Continuum Mechanics and Thermodynamics (Cambridge University Press, 2011), this work presents the complete fundamentals of materials modeling for graduate students and researchers in physics, materials science, chemistry and engineering.
The book unifies classical continuum mechanics and turbulence modeling, i.e. the same fundamental concepts are used to derive model equations for material behaviour and turbulence closure and complements these with methods of dimensional analysis. The intention is to equip the reader with the ability to understand the complex nonlinear modeling in material behaviour and turbulence closure as well as to derive or invent his own models. Examples are mostly taken from environmental physics and geophysics.
Continuum Mechanics Modeling of Material Behavior offers a uniquely comprehensive introduction to topics like RVE theory, fabric tensor models, micropolar elasticity, elasticity with voids, nonlocal higher gradient elasticity and damage mechanics. Contemporary continuum mechanics research has been moving into areas of complex material microstructural behavior. Graduate students who are expected to do this type of research need a fundamental background beyond classical continuum theories. The book begins with several chapters that carefully and rigorously present mathematical preliminaries: kinematics of motion and deformation; force and stress measures; and general principles of mass, momentum and energy balance. The book then moves beyond other books by dedicating several chapters to constitutive equation development, exploring a wide collection of constitutive relations and developing the corresponding material model formulations. Such material behavior models include classical linear theories of elasticity, fluid mechanics, viscoelasticity and plasticity. Linear multiple field problems of thermoelasticity, poroelasticity and electoelasticity are also presented. Discussion of nonlinear theories of solids and fluids, including finite elasticity, nonlinear/non-Newtonian viscous fluids, and nonlinear viscoelastic materials are also given. Finally, several relatively new continuum theories based on incorporation of material microstructure are presented including: fabric tensor theories, micropolar elasticity, elasticity with voids, nonlocal higher gradient elasticity and damage mechanics. - Offers a thorough, concise and organized presentation of continuum mechanics formulation - Covers numerous applications in areas of contemporary continuum mechanics modeling, including micromechanical and multi-scale problems - Integration and use of MATLAB software gives students more tools to solve, evaluate and plot problems under study - Features extensive use of exercises, providing more material for student engagement and instructor presentation
Temam and Miranville present core topics within the general themes of fluid and solid mechanics. The brisk style allows the text to cover a wide range of topics including viscous flow, magnetohydrodynamics, atmospheric flows, shock equations, turbulence, nonlinear solid mechanics, solitons, and the nonlinear Schrödinger equation. This second edition will be a unique resource for those studying continuum mechanics at the advanced undergraduate and beginning graduate level whether in engineering, mathematics, physics or the applied sciences. Exercises and hints for solutions have been added to the majority of chapters, and the final part on solid mechanics has been substantially expanded. These additions have now made it appropriate for use as a textbook, but it also remains an ideal reference book for students and anyone interested in continuum mechanics.
This book offers a broad overview of the potential of continuum mechanics to describe a wide range of macroscopic phenomena in real-world problems. Building on the fundamentals presented in the authors’ previous book, Continuum Mechanics using Mathematica®, this new work explores interesting models of continuum mechanics, with an emphasis on exploring the flexibility of their applications in a wide variety of fields.
Understanding Faults: Detecting, Dating, and Modeling offers a single resource for analyzing faults for a variety of applications, from hazard detection and earthquake processes, to geophysical exploration. The book presents the latest research, including fault dating using new mineral growth, fault reactivation, and fault modeling, and also helps bridge the gap between geologists and geophysicists working across fault-related disciplines. Using diagrams, formulae, and worldwide case studies to illustrate concepts, the book provides geoscientists and industry experts in oil and gas with a valuable reference for detecting, modeling, analyzing and dating faults. - Presents cutting-edge information relating to fault analysis, including mechanical, geometrical and numerical models, theory and methodologies - Includes calculations of fault sealing capabilities - Describes how faults are detected, what fault models predict, and techniques for dating fault movement - Utilizes worldwide case studies throughout the book to concretely illustrate key concepts
This book fills a gap by presenting our current knowledge and understanding of continuum-based concepts behind computational methods used for microstructure and process simulation of engineering materials above the atomic scale. The volume provides an excellent overview on the different methods, comparing the different methods in terms of their respective particular weaknesses and advantages. This trains readers to identify appropriate approaches to the new challenges that emerge every day in this exciting domain. Divided into three main parts, the first is a basic overview covering fundamental key methods in the field of continuum scale materials simulation. The second one then goes on to look at applications of these methods to the prediction of microstructures, dealing with explicit simulation examples, while the third part discusses example applications in the field of process simulation. By presenting a spectrum of different computational approaches to materials, the book aims to initiate the development of corresponding virtual laboratories in the industry in which these methods are exploited. As such, it addresses graduates and undergraduates, lecturers, materials scientists and engineers, physicists, biologists, chemists, mathematicians, and mechanical engineers.
