A microstructure-based model for time-dependent mechanics of multi-layered soft tissues and its application to intervertebral disc annulus

Abstract

In recent experimental studies an unusual time-dependent transversal behavior of the annulus fibrosus of the intervertebral disc mainly caused by the coupling between mechanics and electro-chemical activity was disclosed. In this contribution, a microstructure-based model is proposed to connect structural features, intrinsic mechanics and electro-chemical properties of multi-layered soft tissues with a special attention to disc annulus. A hybrid experimental/modeling decoupling strategy is proposed to obtain the constitutive representation of each layer of the disc annulus thanks to full-field strain data. The layers are then reconnected to each other to get the overall time-dependent response considering inter-layer ionic diffusion as well as stress/strain continuity along the interfaces. The final constitutive model is shown to describe the experimentally observed behavior of bovine tissues under free swelling immediately followed by quasi-static stretching, deviating from chemical equilibrium and provoking auxeticity, and then relaxation, allowing equilibrium return. The model/experiments comparison demonstrates that the evaluation of the overall time-dependent response involves considering stress, volumetric change and auxetic feature simultaneously in relation to diffusion-mechanics and structural features in terms of collagen orientation/content, interlamellar matrix inter-spacing fiber-reinforced layers and gradual thickness of layers. The effective contribution of fiber-reinforced and unreinforced interlamellar layers on the coupling is discussed with respect to the model. Using the model, microstructure and coupling effects are independently investigated in order to highlight their role on the damage-related annulus shearing.