Implementation and Validation of Schapery-Rand Anisotropic Viscoelasticity Model for Super-Pressure Balloons

Abstract

The thin fllm used for the NASA Ultra Long Duration Balloons (ULDB) shows considerable time-dependent behaviour. Furthermore, experiments on scaled ULDB balloons have revealed that wrinkles are present over a wide range of pressures. A numerical model has been developed describing the nonlinear anisotropic viscoelastic material behaviour by means of a Schapery-type model and this model has been extended to model wrinkling by means of a user-deflned subroutine in the flnite-element package ABAQUS. After a description of the viscoelastic modelling approach, a lobe of a 48 gore ULDB ∞at facet balloon is modelled and compared to experimental results. Additionally two test cases of anisotropic wrinkling are presented, one involving a ∞at membrane and one a cylindrical balloon structure. I. Introduction Large super-pressure stratospheric balloons currently under development in the NASA Ultra Long Duration Balloon (ULDB) Program make use of thin polymeric fllms to form a sealed envelope that is constrained by a series of meridional tendons. In the balloon the polymeric fllm is subject to a biaxial state of stress whose details depend on the cutting pattern, stifiness of the fllm vs. stifiness of the tendons, etc. Viscoelastic efiects, which are usually signiflcant in the fllm, play a signiflcant role in the stress distribution and shape of these balloons. So far pseudo-elastic material properties have been generally assumed for the design of the balloon structure. However, following a number of anomalies during ∞ight tests of NASA Ultra-Long-DurationBalloons (ULDB), 1 it has been realized that the behaviour of super-pressure balloons is more complex than assumed at flrst. As the complexity of these balloons is better grasped, 11,20 detailed experimental validation of the analysis models is being initiated, and this in turn requires that details of the time-dependent material behavior be also included in the models. A flnite element model of Schapery’s nonlinear viscoelastic material model has been developed 3,4 and verifled by means of cylindrical balloon structures that provide uniform states of stress. Further investigation of more complex states of stress is needed in order to enable realistic models of ULDBs. In a flrst attempt this paper presents predictions for creep strains on a ULDB 48 gore ∞at facet balloon that are compared to experimental results obtained in reference 22. Experiments on small scale ground models with 48 gores, nominal 4 m diameter, and a constant lobe radius design showed partially wrinkled regions over wide ranges of pressures. With increasing pressures and/or after some time under pressurisation these wrinkles eventually disappeared. A ULDB 48 gore ∞at facet balloon has shown the presence of wrinkles up to a difierential pressure of 500 Pa. 2 While a wrinkled surface may cause di‐culties during experimental measurements the challenge for flnite element models is even higher. The formation of wrinkles is associated with (small) compressive stresses; these stresses cannot be carried by membrane elements and consequently numerical instabilities occur. Since in general most balloon structures develop wrinkles in some regions, at least during pressurisation it is important to take wrinkling into consideration. This paper is part of an ongoing efiort to develop more realistic models for super-pressure balloons, validated with reference to representative physical models. Here we present an approach to model both