Ph.D. (Engg) : Mechanical Characterization and Non-linear Analysis of Woven Hyperelastic Composite Laminate using Variational Asymptotic Method.

The increasing demand for lightweight, multifunctional structures in aerospace and civil engineering applications has driven significant interest in hyperelastic composite laminates. These materials, capable of undergoing large deformations while maintaining structural integrity, are particularly suited for deployable space structures, high altitude airships, inflatable antennas, and tensile fabric architectures. However, accurate prediction of their mechanical behavior requires rigorous constitutive modeling coupled with mathematically consistent dimensional-reduction techniques that make no ad hoc assumptions.

This thesis presents a comprehensive investigation into the constitutive modeling and asymptotic analysis of hyperelastic composite laminates for high-altitude airship and other inflatable structure applications. Through an extensive literature survey, Kapton HN® and Nomex® were identified as promising candidate materials for multifunctional membrane structures due to their desirable properties, including UV resistance, thermal stability, helium retention capability, and mechanical strength. A composite laminate was fabricated using the vacuum bagging technique with Nomex® sandwiched between Kapton HN® layers on the top and bottom, employing the hand lay-up technique with aerospace-grade epoxy.

All three constituent materials—Kapton HN®, Nomex®, and the fabricated composite laminate—were mechanically characterized through uniaxial tensile tests conducted until failure. The anisotropic nature of Nomex® was further investigated by evaluating micro-fiber angles using image processing of Scanning Electron Microscope (SEM) images taken at 1770× resolution. Incompressible hyperelastic material models were proposed to fit the experimental data for these materials, subject to constraints from continuum mechanics and the Baker-Eriksen inequalities.

The isotropic Kapton HN® was accurately represented by the incompressible vYeoh model, while Nomex® required a modified version of the Holzapfel-Gasser-Ogden (HGO) model to capture its fiber-reinforced characteristics. Notably, the modified HGO model could estimate fiber angles using an error-optimization algorithm, and these estimates were validated against fiber angles measured directly from SEM image analysis.

For the composite laminate, a superposition-of-energies approach—referred to in the literature as the Rule of Mixtures model—was proposed and mechanically characterized in both longitudinal and transverse directions. The model demonstrated excellent agreement with experimental observations.

Building upon the constitutive characterization, the three material systems were modeled within a geometrically exact kinematic framework for plates. Using the Variational Asymptotic Method (VAM), dimensionally reduced, asymptotically correct models were derived for each material up to first order. This mathematically rigorous approach makes no ad hoc assumptions and systematically accounts for the small parameters inherent in thin structures. The warping functions, which capture the through-thickness deformation patterns, were systematically solved as intermediate results for all three materials up to zeroth and first order. The two-dimensional nonlinear constitutive laws were evaluated, and the mechanical coupling responses were clearly elucidated.

Finally, a nonlinear finite element analysis was performed to model plates fabricated from these materials under various loading conditions. The VAM-based models were successfully validated against experimental data, demonstrating the accuracy and predictive capability of the asymptotically derived constitutive laws. This work establishes a rigorous framework for analyzing hyperelastic composite laminates and provides valuable insights for the design of next-generation membrane structures for aerospace and civil engineering applications.