Continuum theory for elastic sheets formed by inextensible crossed elasticae

An equilibrium theory for elastic surfaces formed by two families of intextensible fibers is developed. This extends the work of Wang and Pipkin, which accounts for the intrinsic flexural stiffness of the fibers, to include intrinsic twisting resistance. The constituent fibers behave mechanically like spatial Kirchhoff rods. These are regarded as being continuously distributed on the surface and convected by the underlying surface deformation as inextensible material curves.