Stress Propagation in a Viscoelastic Composite Structure Subject to Large Deformations

Large deformations occur in practice for aircraft wings of high aspect ratio that are very flexible. The deformations and associated stress increase concerns of an in-flight, catastrophic failure. For composite aircraft wings composed of polymer resins, viscoelastic effects occur. These time-dependent effects include energy dissipation and stress memory. The time dependency must be considered when designing high aspect ratio wings for a given operation life. A novel theory is proposed to assess the stress propagation through, and over the life, of a viscoelastic structure. The theory combines the time component with the conventional three-dimensional spatial components via a Riemann manifold. The manifold includes multiple time-like dimensions to account for the initial and long term behaviour of the viscoelastic material. Following the work of Green and Adkins, a metric tensor is introduced to find the strain of the structure and the corresponding stress, in response to the applied distributed loads. The stress is modelled as a wave that propagates across the manifold. The wave at any point on the Riemann manifold represents the state of a viscoelastic structure at a given time and position. The theory is demonstrated for a viscoelastic cantilever wing subject to distributed loads.