Bending and Twisting Effects in the Three-dimensional Finite Deformations of an Inextensible Network

A theory is presented for bending and twisting effects in three-dimensional deformations of an inextensible network. The networks are modeled as material surfaces endowed with kinematical variables representing bending and non-standard fiber twisting effects. By using the minimum-energy principle, the Euler-Lagrange equations and boundary conditions are derived. Also, the compatibility conditions are obtained. Finally, the Euler-Lagrange equations are simplified and then specialized to obtain the equilibrium equations of Wang and Pipkin (1986a) and those for an inextensible rod.