A systematic discussion of the fundamental principles, written by a leading contributor to the field.

Multiscale Modelling in Biomedical Engineering Discover how multiscale modeling can enhance patient treatment and outcomes In Multiscale Modelling in Biomedical Engineering, an accomplished team of biomedical professionals delivers a robust treatment of the foundation and background of a general computational methodology for multi-scale modeling. The authors demonstrate how this methodology can be applied to various fields of biomedicine, with a particular focus on orthopedics and cardiovascular medicine. The book begins with a description of the relationship between multiscale modeling and systems biology before moving on to proceed systematically upwards in hierarchical levels from the molecular to the cellular, tissue, and organ level. It then examines multiscale modeling applications in specific functional areas, like mechanotransduction, musculoskeletal, and cardiovascular systems. Multiscale Modelling in Biomedical Engineering offers readers experiments and exercises to illustrate and implement the concepts contained within. Readers will also benefit from the inclusion of: A thorough introduction to systems biology and multi-scale modeling, including a survey of various multi-scale methods and approaches and analyses of their application in systems biology Comprehensive explorations of biomedical imaging and nanoscale modeling at the molecular, cell, tissue, and organ levels Practical discussions of the mechanotransduction perspective, including recent progress and likely future challenges In-depth examinations of risk prediction in patients using big data analytics and data mining Perfect for undergraduate and graduate students of bioengineering, biomechanics, biomedical engineering, and medicine, Multiscale Modelling in Biomedical Engineering will also earn a place in the libraries of industry professional and researchers seeking a one-stop reference to the basic engineering principles of biological systems.

While the relevant features and properties of nanosystems necessarily depend on nanoscopic details, their performance resides in the macroscopic world. To rationally develop and accurately predict performance of these systems we must tackle problems where multiple length and time scales are coupled. Rather than forcing a single modeling approach to

Introduces readers to the fundamentals and applications of variational formulations in mechanics Nearly 40 years in the making, this book provides students with the foundation material of mechanics using a variational tapestry. It is centered around the variational structure underlying the Method of Virtual Power (MVP). The variational approach to the modeling of physical systems is the preferred approach to address complex mathematical modeling of both continuum and discrete media. This book provides a unified theoretical framework for the construction of a wide range of multiscale models. Introduction to the Variational Formulation in Mechanics: Fundamentals and Applications enables readers to develop, on top of solid mathematical (variational) bases, and following clear and precise systematic steps, several models of physical systems, including problems involving multiple scales. It covers: Vector and Tensor Algebra; Vector and Tensor Analysis; Mechanics of Continua; Hyperelastic Materials; Materials Exhibiting Creep; Materials Exhibiting Plasticity; Bending of Beams; Torsion of Bars; Plates and Shells; Heat Transfer; Incompressible Fluid Flow; Multiscale Modeling; and more. A self-contained reader-friendly approach to the variational formulation in the mechanics Examines development of advanced variational formulations in different areas within the field of mechanics using rather simple arguments and explanations Illustrates application of the variational modeling to address hot topics such as the multiscale modeling of complex material behavior Presentation of the Method of Virtual Power as a systematic tool to construct mathematical models of physical systems gives readers a fundamental asset towards the architecture of even more complex (or open) problems Introduction to the Variational Formulation in Mechanics: Fundamentals and Applications is a ideal book for advanced courses in engineering and mathematics, and an excellent resource for researchers in engineering, computational modeling, and scientific computing.

The aim of this book is to review innovative physical multiscale modeling methods which numerically simulate the structure and properties of electrochemical devices for energy storage and conversion. Written by world-class experts in the field, it revisits concepts, methodologies and approaches connecting ab initio with micro-, meso- and macro-scale modeling of components and cells. It also discusses the major scientific challenges of this field, such as that of lithium-ion batteries. This book demonstrates how fuel cells and batteries can be brought together to take advantage of well-established multi-scale physical modeling methodologies to advance research in this area. This book also highlights promising capabilities of such approaches for inexpensive virtual experimentation. In recent years, electrochemical systems such as polymer electrolyte membrane fuel cells, solid oxide fuel cells, water electrolyzers, lithium-ion batteries and supercapacitors have attracted much attention due to their potential for clean energy conversion and as storage devices. This has resulted in tremendous technological progress, such as the development of new electrolytes and new engineering designs of electrode structures. However, these technologies do not yet possess all the necessary characteristics, especially in terms of cost and durability, to compete within the most attractive markets. Physical multiscale modeling approaches bridge the gap between materials’ atomistic and structural properties and the macroscopic behavior of a device. They play a crucial role in optimizing the materials and operation in real-life conditions, thereby enabling enhanced cell performance and durability at a reduced cost. This book provides a valuable resource for researchers, engineers and students interested in physical modelling, numerical simulation, electrochemistry and theoretical chemistry.

Addresses the very topical, crucial and original subject of parameter identification and optimization within multiscale modeling methods Multiscale Modelling and Optimization of Materials and Structures presents an important and challenging area of research that enables the design of new materials and structures with better quality, strength and performance parameters as well as the creation of reliable models that take into account structural, material and topological properties at different scales. The authors’ approach is four-fold; 1) the basic principles of micro and nano scale modeling techniques; 2) the connection of micro and/or nano scale models with macro simulation software; 3) optimization development in the framework of multiscale engineering and the solution of identification problems; 4) the computer science techniques used in this model and advice for scientists interested in developing their own models and software for multiscale analysis and optimization. The authors present several approaches such as the bridging and homogenization methods, as well as the general formulation of complex optimization and identification problems in multiscale modelling. They apply global optimization algorithms based on robust bioinspired algorithms, proposing parallel and multi-subpopulation approaches in order to speed-up computations, and discuss several numerical examples of multiscale modeling, optimization and identification of composite and functionally graded engineering materials and bone tissues. Multiscale Modelling and Optimization of Materials and Structures is thereby a valuable source of information for young scientists and students looking to develop their own models, write their own computer programs and implement them into simulation systems. Describes micro and nano scale models developed by the authors along with case studies of analysis and optimization Discusses the problems of computing costs, efficiency of information transfer, effective use of the computer memory and several other aspects of development of multiscale models Includes real physical, chemical and experimental studies with modern experimental techniques Provides a valuable source of information for young scientists and students looking to develop their own models, write their own computer programs, and implement them into simulation systems.

Mathematical and computational biology is playing an increasingly important role in the biological sciences. This science brings forward unique challenges, many of which are, at the moment, beyond the theoretical techniques available. Developmental biology, due to its complexity, has lagged somewhat behind its sister disciplines (such as molecular biology and population biology) in making use of quantitative modeling to further biological understanding. This volume comprises work that is among the best developmental modeling available and we feel it will do much to remedy this situation.This book is aimed at all those with an interest in the interdisciplinary field of computer and mathematical modeling of multi-cellular and developmental systems. It is also a goal of the Editors to attract more developmental biologists to consider integrating modeling components into their research. Most importantly, this book is intended to serve as a portal into this research area for younger scientists – especially graduate students and post-docs, from both biological and quantitative backgrounds.* Articles written by leading exponents in the field* Provides techniques to address multiscale modeling* Coverage includes a wide spectrum of modeling approaches* Includes descriptions of the most recent advances in the field

This book provides an overview of multiscale approaches and homogenization procedures as well as damage evaluation and crack initiation, and addresses recent advances in the analysis and discretization of heterogeneous materials. It also highlights the state of the art in this research area with respect to different computational methods, software development and applications to engineering structures. The first part focuses on defects in composite materials including their numerical and experimental investigations; elastic as well as elastoplastic constitutive models are considered, where the modeling has been performed at macro- and micro levels. The second part is devoted to novel computational schemes applied on different scales and discusses the validation of numerical results. The third part discusses gradient enhanced modeling, in particular quasi-brittle and ductile damage, using the gradient enhanced approach. The final part addresses thermoplasticity, solid-liquid mixtures and ferroelectric models. The contents are based on the international workshop “Multiscale Modeling of Heterogeneous Structures” (MUMO 2016), held in Dubrovnik, Croatia in September 2016.

Multiscale Modeling of Additively Manufactured Metals: Application to Laser Powder Bed Fusion Process provides comprehensive coverage on the latest methodology in additive manufacturing (AM) modeling and simulation. Although there are extensive advances within the AM field, challenges to predictive theoretical and computational approaches still hinder the widespread adoption of AM. The book reviews metal additive materials and processes and discusses multiscale/multiphysics modeling strategies. In addition, coverage of modeling and simulation of AM process in order to understand the process-structure-property relationship is reviewed, along with the modeling of morphology evolution, phase transformation, and defect formation in AM parts. Residual stress, distortion, plasticity/damage in AM parts are also considered, with scales associated with the spatial, temporal and/or material domains reviewed. This book is useful for graduate students, engineers and professionals working on AM materials, equipment, process, development and modeling. Includes the fundamental principles of additive manufacturing modeling techniques Presents various modeling tools/software for AM modeling Discusses various design methods and how to optimize the AM process using these models