A discrete network model for bond failure and frictional sliding in fibrous materials

Discrete network models and lattice models using trusses or beams can be used to mechanically model fibrous materials, since the discrete elements represent the individual fibers or yarns at the mesoscale of these materials. Consequently, local mesoscale phenomena, such as individual fiber failure and interfiber bond failure, can be incorporated. Only a few discrete network models in which bond failure is incorporated include frictional fiber sliding that occurs after bond failure has taken place, although this occurs in the mechanical behaviour of several fibrous materials. In this paper, a spring network model for interfiber bond failure and subsequent frictional fiber sliding is developed, which is formulated in a thermodynamical setting. The thermodynamical basis ensures that performed mechanical work is either stored in the network or dissipated due to bond failure and subsequent sliding. A numerical implementation of the framework is proposed in which the kinematic and internal variables are simultaneously solved, because the internal variables are directly coupled in the framework. Variations in network connectivity, bond strength, fiber length and anisotropy are implemented in the framework. The results show amongst others that the macroscopic yield point scales with the bond strength and that the macroscopic stiffness and the macroscopic yield point scale with the fiber length. The presented results also show that the macroscopic yield point becomes significantly less pronounced for an increase of the fiber length.