ABSTRACT
Classical thin-shell theory provides us with a natural framework for describing the stresses developing over the membranes enclosing capsules and cells. Under the auspices of this theory, the interfaces are regarded as distinct two-dimensional curved media embedded in three-dimensional space over which tangential and transverse shear tensions and in-plane bending moments develop as the result of deformation from a reference configuration. A variety of results may then be obtained regarding equilibrium shapes, stability, deformation, and dynamics subject to an external to internal pressure difference and under the action of an ambient viscous flow. In this chapter, the theory of thin elastic shells is reviewed with emphasis on its application to the hydrostatics and hydrodynamics of capsules and cells. Extensions of the classical approach to account for the mechanical behavior exhibited by biological membranes including area incompressibility and viscous dissipation are emphasized, and numerical methods for solving the governing equations are reviewed and further developed.
