PLANE DEFORMATIONS OF MEMBRANES FORMED WITH ELASTIC CORDS

Exact solutions are obtained for the plane deformation of membranes formed of two families of elastic cords. The cords are assumed to be continuously distributed and every cord of one family is joined to each cord of the other family at their point of intersection. The cords have no bending stiffness and are incapable of withstanding compression but they exhibit a general nonlinear tension-stretch relation. It is further assumed that there is no resistance to shear in the membrane. The solutions include deformations which exhibit half-slack and fully-slack regions in which the cords of one family (half-slack), or of both families (fully-slack), are unstretched and the deformation corresponds to a wrinkling or crumpling of the material. It is shown that the solutions include all the fully-stretched universal deformations and all the fully-stretched universal states of tension. The study is motivated as an attempt to examine wrinkling deformations of skin and collagenous tissues. © 1990 Oxford University Press.