A second gradient formulation for a 2D fabric sheet with inextensible fibres

We present numerical simulations of rectangular woven fabrics made of two, initially orthogonal, families of inextensible bres. We consider an energy functional which includes both rst and second gradient of the displacement. The energy density is expressed in terms of the angles between the bres directions, using trigonometric functions and their gradients. In particular we focus on an energy density depending on the squared tangent of the shear angle, which automatically satis es some natural properties of the energy. The numerical results show that final con gurations obtained by the second gradient energies are smoother than the fi rst gradient ones. Moreover, we show that if a second gradient energy is considered the shear energy is better uniformly distributed.