Modeling of unidirectional fibre-reinforced composites under fibre damage

• Unidirectional fibre-reinforced composites under fibre breakage damage.
• Coordinate-free formulation based on the integrity-basis formalism.
• Damage evolution governed by the strain history along the direction of the fibres.
• Coupling with viscoelasticity in pure shear showing tertiary creep.

Of interest in this work is the description of unidirectional fibre-reinforced composites where special emphasis is placed on the fibre breakage damage mode. A simple, but efficient, yield concept is adopted within the continuum damage mechanics framework where damage flow is directly linked to the strain history along the direction of the fibres. The modeling is embedded into a formulation of transverse isotropy that keeps the fibre-damage modeling unchanged when coupled to other phenomena that solely affect the pure shear part of the behavior. In fact, it is mostly observed that creep in fibre-reinforced composites is essentially due to the matrix constituent whose role is to deform and support stresses primarily in shear. This specific example is detailed in the present paper for illustrative purposes where, among others, the occurrence of tertiary creep is made possible to predict. On the numerical side, the algorithmic design is developed for a straightforward implementation within the context of the finite element method.