Viscoplastic cohesive zone modelling of interfacial fibrillation in soft tissue

Abstract

In the present study we propose two phenomenological CZM formulations to represent fibrillation during dissection of soft tissue. We firstly consider elastic fibrillation. In this formulation fibrillation initiates during an initial phase of interface damage/softening. Fibrils then deform elastically until an ultimate strength is reached, followed by fibril damage/rupture. Simulations reveal that such elastic fibrillation does not accurately predict the highly non-uniform crack propagation rates measured experimentally for arterial tissue. We then propose a phenomenological visco-plastic cohesive zone model (VP-CZM) for fibrillation. This approach is motivated by the observation that fibrils undergo partial pull-out (in addition to elastic stretching) during dissection of arteries. Simulations reveal that the VP-CZM provides a reasonable prediction of non-uniform crack propagation rates in arteries. Significant plasticity (representing fibril pull-out) during fracture initiation results in an initial slow phase of crack growth. The transition to fast crack growth is facilitated by the prediction of fibril rupture prior to extensive plasticity. The current implementation of fibril visco-plastic behaviour in a cohesive zone framework is limited to a phenomenological representation of axial fibril deformation and axial fibril pull-out. However, we provide extensive parametric exploration of the model behaviour under a range of mixed-mode loading paths, representing fibril reorientation in addition to fibril extension. We demonstrate that the formulation produces consistent behaviour for all loading paths and that positive incremental instantaneous dissipation is computed in all cases. The VP-CZM represents an advance on standard elastic-damage cohesive zone formulations. While the VP-CZM effectively produces such standard CZM behaviour at high interface separation rates, it predicts plastic deformation and energy dissipation (representing fibril pull-out) at low interface separation rates. The authors are not aware of a previous implementation of fibril visco-plastic behaviour in a CZM framework.