The constitutive relation of a fabric membrane composite for a stratospheric airship envelope based on invariant theory

The study of stratospheric airships has become the focus in many countries in recent years, because of its potential applications in many fields. Lightweight and high strength envelopes are the keys to the design of stratospheric airships, as it directly determines the endurance flight performance and loading deformation characteristics of the airship. A typical envelope of any stratospheric airship is a coated-fabric material which is composed of a fiber layer and several functional membrane layers. According to composite structure, nonlinearity and viscoelasticity are the two main characteristics of such envelope. Based on the analysis on the interaction between the different components in the micro-mechanical model of the coated-fabric, several invariant values reflecting the characteristics of the envelope material are obtained according to invariant theory. Furthermore, the constitutive equation that describes the viscoelasticity of the envelope material is derived. The constitutive equation can represent both the individual roles of the warp and weft fibers, and their further coupled interactions. The theoretical computation results were verified by off-axial tension tests. The results can help gain a deeper understanding of the mechanical mechanism and provide a reference for structural design of envelope material.