Quasi-Static Deformations of Fibre-Reinforced Materials Based on Hyperelasticity

This work addresses the quasi-static behaviour of fibre-reinforced materials whose response is based on a hyperelastic formulation augmented by viscous and damage-like effects. A transversely isotropic constitutive model is developed within the framework of an internal scalar variable, enabling the reversible description of material damage while ensuring objectivity, thermodynamic admissibility and polyconvexity of the stored-energy function. The isotropic contribution is constructed from a generalised Ciarlet model, whereas the anisotropic part accounts for a family of elastic fibres embedded in a viscoelastic matrix, interpreted through a simple mixture theory. The resulting constitutive equations are implemented in Abaqus/Standard via a UMAT subroutine, and their rate form is derived consistently with the Zaremba–Jaumann objective stress rate. The performance of the model is examined by means of finite element simulations, including homogeneous tests in uniaxial strain and simple shear, relaxation and creep problems, and an inflation-like problem. The results demonstrate the capability of the model to capture strain-rate sensitivity, creep, stress relaxation and energy dissipation, as well as non-uniform deformation patterns, while highlighting its current limitation in representing permanent deformations.