LAUSR

Abstract 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.