A linear complementarity(LC) formulation and its FEM-based numerical analysis method have been developed to analyze a wrinkled membrane problem which involves the nonlinearities caused by large deformation and unilateral behavior due to wrinkling. The deformation of a membrane is described by using the convected coordinate system. The incremental formulation of a large deformation wrinkling is then transformed to a set of corresponding complementarity formulas. To this end, a kinematic quantity called wrinkle strain is introduced as a measure of the physical wrinkliness of the surface by modifying the deformation gradient tensor. The wrinkle strain tensor when substituted in the constitutive equation expresses the physical stress field of the wrinkled membrane. Recognizing the existence of complementarity in the contact phenomenon, the contact condition is also incorporated in the formulation, although no numerical test has been included.
A 2-dimensional square membrane is considered as numerical tests. Two loading conditions of a simple shear and a bending moment loading are treated. The computational results of the two cases are in good agreement with analytic ones.
For applications to such complex structures as curved membranes, however, it seems necessary to refine the numerical algorithm to further elaborate the geometric nonlineraity.
