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