Nonlinear Webs, Membranes and Shells

Abstract

This chapter will discuss the nonlinear theories of webs, membranes and shells. The webs and membranes are extensively used to model bio-tissues and membranes experiencing arbitrary initial configurations. Since any webs cannot resist any compressive forces, it is very difficult to determine the corresponding deformations and stresses in the webs. Traditionally, one used the membrane theory with certain constraints to determine the final configuration of webs. However, the webs can be of non-continuum and continuum. Thus, the network non-continuum web will be presented first from the cable theory, and the continuum web will be developed. Further, the nonlinear theory of membranes will be developed in an analogy way. The nonlinear theory of shells will be developed from the general theory of the 3-dimensional deformable body, and such a theory of shells can be easily reduced to the established theories.