Finite element analysis of partly wrinkled reinforced prestressed membranes

Abstract

Wrinkling is a well known phenomenon experimented by tension membranes in Civil Engineering applications. This paper will present an efficient numerical technique for the computational simulation of such wrinkles in a prestressed membrane. In particular, the relaxed energy approach (Pipkin in IMA J Appl Math 36:85–99, 1986) is particularized for prestressed membranes (Gil in Textile composites and inflatable structures, CIMNE, 2003) undergoing moderate strains. Wrinkling conditions in terms of the Euler-Lagrange finite deformation tensor along principal directions will be obtained. This will provide a framework to describe properly the initial instant when wrinkles start to be encountered in a prestressed Saint Venant–Kirchhoff hyperelastic membrane. Subsequently, a modified Helmholtz’s free energy functional will be introduced with the purpose of describing the modified constitutive behaviour of the continuum after the onset of wrinkling. Consistent derivations of the stress tensor as well as the constitutive tensor will de depicted. The results will be particularized for membranes and cables in a Finite Element discretization basis. Some numerical examples will prove the accuracy and robustness of the described algorithm.