Finite Deformations of Fibre-reinforced Elastic Solids with Fibre Bending Stiffness: A Spectral Approach

In this paper, we propose a spectral approach to model finite deformations of fibre-reinforced elastic solids with fibre bending stiffness. The constructed constitutive equations depend on spectral invariants, where each one has a clear physical meaning and hence are attractive for use in experiment and analysis. With the use of spectral invariants, we easily obtain the number of independent invariants and the number of invariants in the corresponding minimal integrity or irreducible basis. The proposed finite strain energy prototypes are consistent with their infinitesimal strain energy function counterparts. Some results for pure bending of a slab, and the extension and torsion of solid cylinder, that could be useful for experiments and numerical validations, are given. The proposed model could be used to obtain numerical results via modification of some computational methods found in the literature.