This volume covers aspects of multiscale modeling of the mechanics and mechanobiology of soft biological tissues. The individual contributions focus on the constitutive modeling from the micro to the macro level in addition to computational modeling and simulation. It consists of peer-reviewed papers written by leading international authorities and will serve as a major state-of-the-art source of reference for the next few years. It includes both review articles and original articles. Previously published in the Journal of Elasticity, Volume 129, Issue 1-2, December 2017.

The structures of living tissues are continually changing due to growth and response to the tissue environment, including the mechanical environment. Tissue Mechanics is an in-depth look at the mechanics of tissues. Tissue Mechanics describes the nature of the composite components of a tissue, the cellular processes that produce these constituents, the assembly of the constituents into a hierarchical structure, and the behavior of the tissue’s composite structure in the adaptation to its mechanical environment. Organized as a textbook for the student needing to acquire the core competencies, Tissue Mechanics will meet the demands of advanced undergraduate or graduate coursework in Biomedical Engineering, as well as, Chemical, Civil, and Mechanical Engineering. Key features: Detailed Illustrations Example problems, including problems at the end of sections A separate solutions manual available for course instructors A website (http://tissue-mechanics.com/) that has been established to provide supplemental material for the book, including downloadable additional chapters on specific tissues, downloadable PowerPoint presentations of all the book's chapters, and additional exercises and examples for the existing chapters. About the Authors: Stephen C. Cowin is a City University of New York Distinguished Professor, Departments of Biomedical and Mechanical Engineering, City College of the City University of New York and also an Adjunct Professor of Orthopaedics, at the Mt. Sinai School of Medicine in New York, New York. In 1985 he received the Society of Tulane Engineers and Lee H. Johnson Award for Teaching Excellence and a recipient of the European Society of Biomechanics Research Award in 1994. In 1999 he received the H. R. Lissner medal of the ASME for contributions to biomedical engineering. In 2004 he was elected to the National Academy of Engineering (NAE) and he also received the Maurice A. Biot medal of the American Society of Civil Engineers (ASCE). Stephen B. Doty is a Senior Scientist at Hospital for Special Surgery, New York, New York and Adjunct Professor, School of Dental and Oral Surgery, Columbia University, New York, NY. He has over 100 publications in the field of anatomy, developmental biology, and the physiology of skeletal and connective tissues. His honors include several commendations for participation in the Russian/NASA spaceflights, the Spacelab Life Science NASA spaceflights, and numerous Shuttle missions that studied the influence of spaceflight on skeletal physiology. He presently is on the scientific advisory board of the National Space Biomedical Research Institute, Houston, Texas.

This book describes the current state of knowledge in the field of multi-scale ECM mechanics and mechanobiology with a focus on experimental and modelling studies in biomechanical characterization, advanced optical microscopy and imaging, as well as computational modeling. This book also discusses the scale dependency of ECM mechanics, translation of mechanical forces from tissue to cellular level, and advances and challenges in improving our understanding of cellular mechanotransduction in the context of living tissues and organisms.

Multiscale Biomechanics provides new insights on multiscale static and dynamic behavior of both soft and hard biological tissues, including bone, the intervertebral disk, biological membranes and tendons. The physiological aspects of bones and biological membranes are introduced, along with micromechanical models used to compute mechanical response. A modern account of continuum mechanics of growth and remodeling, generalized continuum models to capture internal lengths scales, and dedicated homogenization methods are provided to help the reader with the necessary theoretical foundations. Topics discussed include multiscale methods for fibrous media based on discrete homogenization, generalized continua constitutive models for bone, and a presentation of recent theoretical and numerical advances. In addition, a refresher on continuum mechanics and more advanced background related to differential geometry, configurational mechanics, mechanics of growth, thermodynamics of open systems and homogenization methods is given in separate chapters. Numerical aspects are treated in detail, and simulations are presented to illustrate models. This book is intended for graduate students and researchers in biomechanics interested in the latest research developments, as well as those who wish to gain insight into the field of biomechanics. Provides a clear exposition of multiscale methods for fibrous media based on discrete homogenization and the consideration of generalized continua constitutive models for bone Presents recent theoretical and numerical advances for bone remodeling and growth Includes the necessary theoretical background that is exposed in a clear and self-contained manner Covers continuum mechanics and more advanced background related to differential geometry, configurational mechanics, mechanics of growth, thermodynamics of open systems and homogenization methods

This book describes the current state of knowledge in the field of multi-scale ECM mechanics and mechanobiology with a focus on experimental and modelling studies in biomechanical characterization, advanced optical microscopy and imaging, as well as computational modeling. This book also discusses the scale dependency of ECM mechanics, translation of mechanical forces from tissue to cellular level, and advances and challenges in improving our understanding of cellular mechanotransduction in the context of living tissues and organisms.

MULTISCALE BIOMECHANICS Model biomechanical problems at multiple scales with this cutting-edge technology Multiscale modelling is the set of techniques used to solve physical problems which exist at multiple scales either in space or time. It has been shown to have significant applications in biomechanics, the study of biological systems and their structures, which exist at scales from the macroscopic to the microscopic and beyond, and which produce a myriad of overlapping problems. The next generation of biomechanical researchers therefore has need of the latest multiscale modelling techniques. Multiscale Biomechanics offers a comprehensive introduction to these techniques and their biomechanical applications. It includes both the theory of multiscale biomechanical modelling and its practice, incorporating some of the latest research and surveying a wide range of multiscale methods. The result is a thorough yet accessible resource for researchers looking to gain an edge in their biomechanical modelling. Multiscale Biomechanics readers will find: Practical biomechanical applications for a variety of multiscale methods Detailed discussion of soft and hard tissues, and more An introduction to analysis of advanced topics ranging from stenting, drug delivery systems, and artificial intelligence in biomechanics Multiscale Biomechanics is a useful reference for researchers and scientists in any of the life sciences with an interest in biomechanics, as well as for graduate students in mechanical, biomechanical, biomedical, civil, material, and aerospace engineering.

This special volume of the Journal of Elasticity represents the first in a new p- gram dedicated to the occasional publication of collections of invited, reviewed papers of topical interest. The purpose of this program is to spotlight the dev- opments and applications in the mechanics of materials within specific areas that can enhance growth and provide insight for the advancement of the field as well as promote fundamental understanding and basic discovery. Soft Tissue Mechanics is an area of biomechanics that draws heavily upon f- damental ideas and material models from nonlinear elasticity and viscoelasticity. A major goal of this research is to understand those mechanics properties of heart, artery, collagen and skeletal muscle tissue that can be used for the diagnosis of health problems and the improvement of human life. This volume illustrates how experiment, modeling and computation is currently employed in this emerging field. May 2001 ROGER FOSDICK Editor-in-Chief Journal of Elasticity 61: ix–xii, 2000. ix Preface There are two primary areas for the application of elasticity in the biomechanics of tissues: hard tissue mechanics (e.g., bone, teeth, horns, etc.) and soft tissue - chanics (e.g., skin, tendons, arteries, etc.). The distinguishing feature between these tissue types is the amount of physiological “normal” deformation they experience. While “hard” tissues only experience small deformations, soft tissues typically experience large deformations. From a biomechanics viewpoint soft tissues fall within the realm of finite elasticity.