ABSTRACT
This chapter discusses both stresses and strains, and their many permutations that are central to the field of continuum mechanics. It describes a series of characteristics common to soft tissues undergoing large deformations with only time-invariant characteristics. In mechanics, constitutive relations are the basis for identifying material mechanical properties and insomuch describe the relationships between stresses and strains. The specific class of constitutive model will dictate the interpretation of parameter meaning and determine the extent to which parameter values can be related to the compositional and/or structural features of the material. The chapter focuses on the behavior of soft biological materials that are characterized by finite deformations. To introduce and elucidate the relationships that define the nonlinear mechanics of soft biological materials in a concise manner, the equations shown throughout the chapter are defined in the Cartesian coordinate system and in three-dimensional space wherever posssible. The chapter uses the properties of tensors to describe the strain.
