This article presents a multiscale model to predict deformation-induced damage and failure of human annulus fibrosus under multiaxial loading. In the modeling approach, formulated within the framework of nonlinear continuum mechanics, the hierarchical structure of the soft tissue is considered from the nano-sized collagen fibrils to the micro-sized oriented collagen fibers. At the macroscale, the multi-layered lamellar/inter-lamellar organization of the soft tissue is introduced by considering the effective interactions between adjacent layers. The stochastic process of progressive damage events operating at different scales of the solid phase is introduced for the extracellular matrix and the network of nano-sized fibrils/micro-sized fibers. The damage is made anisotropic due to lamellar oriented collagen fibers and special orientation distribution of the inter-fibrillar and inter-lamellar network of fibrils. The chemical-induced volumetric strain is also considered in our modeling approach to take into account the osmolarity effects along with the anisotropic time-dependent transversal deformations. The capacity of the model is discussed using a few available stretching datasets till failure along circumferential and radial directions. Model predictions under tilted stretching, biaxial stretching and shearing are also presented to illustrate further the efficiencies of our modeling approach. This work shows for the first time the directional effects on annulus mechanics and failure in relation to external loading mode, structure features, damage events and hydration.

本文提出了一个多尺度模型来预测多轴载荷下人体纤维环的变形引起的损伤和失效。在非线性连续介质力学框架内制定的建模方法中，软组织的层次结构被考虑从纳米级胶原纤维到微米级取向的胶原纤维。在宏观尺度上，通过考虑相邻层之间的有效相互作用，引入了软组织的多层层/层间组织。为细胞外基质和纳米级原纤维/微米级纤维网络引入了在固相的不同尺度上运行的渐进性损伤事件的随机过程。由于层状取向的胶原纤维和原纤维间和纤维层间网络的特殊取向分布，损伤是各向异性的。在我们的建模方法中还考虑了化学诱导的体积应变，以考虑渗透压效应以及各向异性时间相关的横向变形。使用一些可用的拉伸数据集讨论模型的容量，直到沿圆周和径向方向失效。还提供了倾斜拉伸、双轴拉伸和剪切下的模型预测，以进一步说明我们建模方法的效率。这项工作首次显示了与外部加载模式、结构特征、损坏事件和水合作用相关的对环空力学和失效的方向影响。