The theory of Cosserat points applied to the analyses of wrinkled and slack membranes

Numerical simulations of wrinkling and slacking of geometrically nonlinear membrane structures are considered using planar Cosserat points. The finite element method (FEM) solves the problem by weakly projecting the governing PDEs and thus requires numerical integration. This is contrasted with Cosserat point elements wherein governing equations are solved in an averaged sense at a point. The point is equipped with a few directors and can describe the deformation kinematics of a finite region containing itself. Numerical modeling through the Cosserat point provides freedom from numerical integration and locking. Presently a plane stress quadrilateral Cosserat point element is used to study the wrinkling and slacking of isotropic membranes. The approach by Roddeman et al. (ASME J Appl Mech 54:884–892, 1987) is exploited to detect wrinkled/slack elements in the membrane structure. Here stretching parameters are employed to modify the deformation tensor to represent a fictive non-wrinkled surface. A variation of the algorithm to detect spatial variations of the stretching parameters within a point element is also described. Several numerical examples on static deformations of wrinkled/slack membranes are presented. Limited comparisons with a reported experiment and with results via the FEM as well as a mesh-free approach are provided to assess the performance of the approach.