Multiscale Biomechanics

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.

Part 1. Theoretical Basis: Continuum Mechanics, Homogenization Methods, Thermodynamics of Growing Solid Bodies 1. Tensor Calculus Jean-François GANGHOFFER 2. Continuum Mechanics Jean-François GANGHOFFER 3. Constitutive Models of Soft and Hard Living Tissues Jean-François GANGHOFFER 4. Discrete Homogenization of Network Materials Jean-François GANGHOFFER and Khaled EL NADY 5. Mechanics and Thermodynamics of Volumetric and Surface Growth Jean-François GANGHOFFER

Part 2. Multiscale Bone Mechanics 6. Micropolar Models of Trabecular Bone Jean-François GANGHOFFER and Ibrahim GODA 7. Size-Dependent Dynamic Behavior of Trabecular Bone Jean-François GANGHOFFER, Ibrahim GODA, Rachid RAHOUADJ 8. Prediction of Size Effects in Bone Brittle and Plastic Collapse Jean-François GANGHOFFER and Ibrahim GODA 9. Multiscale Aspects of Bone Internal and External Remodeling Jean-François GANGHOFFER and Ibrahim GODA 10. Integrated Remodeling to Fatigue Damage Model of Bone Jean-François GANGHOFFER and Ibrahim GODA

Part 3. Mechanics of Soft Biological Tissues: The Intervertebral Disk, Biological Networks, Ligaments and Tendons 11. Micromechanics of the Intervertebral Disk Adrien BALDIT 12. Effective Mechanical Response of Biological Membranes Khaled EL NADY, Jean-François GANGHOFFER and Ibrahim GODA 13. Micromechanics of Ligaments and Tendons Cédric LAURENT

Jean-François Ganghoffer was a CNRS fellow from 1992 to 2000, before being hired as fullProfessor of mechanics in Université de Lorraine (Nancy, France), where he is currently active. He isthe head of the biomechanics team of LEM3, the Laboratoired’Etude des Microstructures et de Mécanique des Matériaux. He is the leader of a national Federationof Laboratories (IMOA, Ingénierie Mécanobiologie ostéoarticulaire, FR CNRS 2003) in the field ofosteoarticular mechanobiology. He has been the Director of a GDR research group on fibrous media.His activities cover bone biomechanics, homogenization methods, mechanics of fibrous media, themultiphysical behavior of architected materials, and topology optimization methods. He hasdeveloped different types of bone remodeling models over the past decade, and he has been morerecently considering piezoelectric and flexoelectric effects in bone. He is the author of about 300scientific papers in international journals. He has been invited to many conferences and universitiesfor both research and teaching activities (ETHZ, Georgia Tech Metz, TU Delft, TU Eindhoven, UBC,Vancouver). He is collaborating with many universities worldwide (Brazil, Germany, Italy, Bulgaria,Poland, Canada, US), and he has been invited to deliver lectures at many international conferences.He has published two books, including the monograph ‘Multiscale Biomechanics’ in Wiley in 2018. Heis the frequent reviewer for over twenty international journals. He received several distinctions,including the Beltrami Prize in 2017, the Grand Prix de la Société Industrielle de l’Es in 2005, and thescientific award of excellence by the French Ministry of Research more than 10 years.

• 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