Mechanics is the branch of physics that is concerned with the action of forces on matter. Tissue engineers can encounter mechanics in various settings. Often, the mechanical properties of replacement biological materials must replicate the normal tissue: for example, there is limited use for a tissue-engineered bone that cannot support the load encountered by its natural counterpart. In addition, the mechanical properties of cells and cell–cell adhesions can determine the architecture of a tissue during development. This phenomenon can sometimes be exploited, since the final form of engineered tissues depends on the forces encountered during assembly and maturation. Finally, the mechanics of individual cells—and the molecular interactions that restrain cells—are important determinants of cell growth, movement, and function within an organism. This chapter introduces the basic elements of mechanics applied to biological systems. Some examples of biomechanical principles that appear to be important for tissue engineering are also provided. For further reading, comprehensive treatments of various aspects of biomechanics are also available. Consider an elongated object—for example, a segment of a biological tissue or a synthetic biomaterial—that is fixed at one end and suddenly exposed to a constant applied load. The material will change or deform in response to the load. For some materials, the deformation is instantaneous and, under conditions of low loading, deformation varies linearly with the magnitude of the applied force: . . . σ[≡F/A]= Eε (5-1) . . . where σ is the applied stress and ε is the resulting strain. This relationship is called Hooke’s law, after the British physicist Robert Hooke, and it describes the behavior of many elastic materials, such as springs, which deform linearly upon loading and recover their original shape upon removal of the load. The Young’s modulus or tensile elastic modulus, E, is a property of the material; some typical values are provided in Table 5.1. Not all elastic materials obey Hooke’s law (for example, rubber does not); some materials will recover their original shape, but strain is not linearly related to stress. Fortunately, many interesting materials do follow Equation 5-1, particularly if the deformations are small.
Large elastic deformations of isotropic materials. I. Fundamental concepts