A proper constitutive model for numerical analysis of lightweight membrane structures

True membrane structures cannot sustain any compressive stresses. Under uniaxial in-plane tension, membranes respond to in-plane in-excess Poisson's contraction, and offer an alternating out-of-plane displacement, which is called wrinkles. Therefore, membrane structures remove all compressive stresses completely by the formation of wrinkles and the minor principal stress is non-negative everywhere. A membrane structure could be in one or more of taut, slack or wrinkled states based on the loading configuration. Although most commercial numerical analysis codes offer an extensive collection of solid mechanics models in their finite element libraries, the proper constitutive model to analyze the membrane structures is generally not included. In the taut state, a membrane behaves elastically. In the slack and wrinkle states, the linear elastic model no longer works for membranes. In this research, a robust constitutive model has been developed to correctly analyze the membrane structures under the taut, slack and wrinkle states. The constitutive model uses a penalty parameter (PP) to assign a near zero stiffness ("penalize" the stiffness) in the direction of minimum "in-plane" principal stress. Maintaining a small, non-zero stiffness normal to the wrinkled direction avoided the singularity problem in the stiffness matrix and offered a converged solution of the membrane model when slack and wrinkles exist. This material model is incorporated within the non-linear finite element code ABAQUS as a user subroutine UMAT (User Material). Static analysis of membrane structures under the taut, slack and wrinkle states were performed. The numerical results were compared against the close form solution to validate the accuracy.