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.

中文翻译：

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基于微观结构的多层软组织瞬态力学模型及其在椎间盘环中的应用

在最近的实验研究中，揭示了主要由力学和电化学活动之间的耦合引起的椎间盘纤维环的不寻常的时间依赖性横向行为。在这一贡献中，提出了一种基于微观结构的模型，以将多层软组织的结构特征、内在力学和电化学特性与特别关注椎间盘环联系起来。由于全场应变数据，提出了一种混合实验/建模解耦策略，以获得圆盘环每一层的本构表示。考虑到层间离子扩散以及沿界面的应力/应变连续性，这些层然后相互重新连接以获得整体时间相关响应。最终的本构模型显示了实验观察到的牛组织在自由膨胀下的行为，紧接着是准静态拉伸，偏离化学平衡并引起膨胀，然后松弛，允许平衡恢复。模型/实验比较表明，对整体时间依赖性响应的评估涉及在胶原取向/含量、层间基质间距纤维方面与扩散力学和结构特征相关的应力、体积变化和拉胀特征同时考虑。加强层和层的逐渐厚度。结合模型讨论了纤维增强和未增强的层间层对耦合的有效贡献。使用模型，