Taber L.A. Nonlinear Theory of Elasticity. Applications in Biomechanics

World Scientific, 2004. — 417 p. — ISBN: 981-238-735-8.Problems involving the deformation of soft biological tissues are among the most challenging in biomechanics. Soft tissues are viscoelastic composite materials composed of cells and extracellular matrix, are frequently arranged in complex geometries, and routinely experience large strains under normal and pathological conditions. As the discipline of biomechanics matures, new problems continually appear that demand more and more sophisticated analytical and numerical solution techniques. For example, the field of tissue engineering, which deals with in vitro construction of natural replacement tissues, could benefit greatly from analyses that integrate nonlinear mechanical behavior at the molecular, cellular, tissue, and whole organ levels.
After a brief introduction in Chapter 1, Chapter 2 establishes the mathematical background that is needed to navigate the remainder of this book. This chapter covers general tensor and dyadic analysis, introducing the basic concepts of changes in coordinates and reference frames. Next, Chapters 3 and 4 develop and compare the basic measures of deformation and stress, and present the field equations of solid mechanics. Chapter 5 then discusses constitutive theory and develops stress-strain relations for nonlinear materials with various material symmetries. Finally, Chapter 6 solves several specific problems in soft tissue mechanics using the theory and techniques presented in the previous chapters.