Complementarity problem formulation for the wrinkled membrane and numerical implementation

Abstract

A linear complementarity formulation has been developed to analyze a wrinkled membrane problem which involves the nonlinearities caused by large deformitions and unilateral behavior due to wrinkling. 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. An incremental method is adopted and numerically implemented with a finite element setting.